Robust Control of Doubly Fed Induction Generator Using Fractional Order Control

Received Feb 27, 2018 Revised May 2, 2018 Accepted Jul 1, 2018 In this paper, we present a robust control of a variable speed Doubly Fed Induction Generator (DFIG)-based Wind Energy Conversion System (WECS), using Fractional Order Control (FOC) to prevent system deterioration under different critical conditions (external disturbance, measurement noise and DFIG parameters variation). In order to extract the maximum power from the wind, a Maximum Power Point Tracking (MPPT) strategy based on rotor speed control is proposed. Furthermore, a vector control strategy is used for controlling active and reactive powers of DFIG. Additionally, a simple design method of Fractional Order Proportional Integral (FOPI) controller is proposed. Finally, the system’s performance is tested and compared according to reference tracking, robustness, disturbance rejection and noise minimization. Keyword:


INTRODUCTION
Nowadays, a majority of the wind energy conversion systems utilize doubly fed induction generator because of its high efficiency and low cost owing to its configuration [1], [2]. DFIG have windings on both stator and rotator parts, where both of them transfer considerable power between generator and grid. In DFIG, the converters process only about 20-30% of total generated power, and the rest is fed to the grid directly from the stator [3]- [5].
Usually, DFIG is controlled using vector control strategy, which is either stator voltage oriented, or stator flux oriented. This scheme decouples nonlinear Multiple Input Multiple Output (MIMO) system of DFIG into two linear Single Input Single Output (SISO) subsystems representing direct and quadrate rotor currents separately [6]- [8]. The active and reactive power control of DFIG is attained by controlling these two linear first order SISO subsystems with two PI controllers. The drawback of the vector control strategy is that the system performance depends on the DFIG parameters, especially the rotor resistance [6], [7]. Thus, the performance degrades when the parameters of DFIG used in the control system design are altered due to temperature variation, saturation, etc.
To solve this problem, we have replaced the conventional proportional integral controller with a fractional order proportional integral one which is a generalization of the former [9], [10]. The fractional order PI controller has a potential to increase system robustness and improve the system performance with the additional parameter λ, which is the fractional order of the integration action [11], [12]. In this work, our contribution to DFIG robust control is the use of a simple and practical fractional order PI controller, which leads to good dynamic performance and robustness of DFIG in both healthy and critical conditions.
In section 2, we introduce a brief description of the wind energy conversion system to be studied. Then, the construction of a mathematical model for each component (DFIG and wind turbine) of the wind system is presented in section 3. Next, the control strategy is developed in section 4. The design of fractional order PI controller is established in section 5 followed by the simulation results and discussion in Section 6. Finally, we complete this work with a conclusion.

SYSTEM DESCRIPTION
The WECS to be studied is presented in Figure 1. This system consists of a wind turbine driving a DFIG through a gearbox. The rotor is connected through two converters, and the stator of the DFIG is directly connected to the grid.

. Wind turbine model
In WECS, due to the different losses, the extracted power available on the rotor of the wind turbine can be expressed as [13], [14]: where is the turbine power, is the power coefficient, is the air density, S is the swept turbine area and is the wind speed. The power coefficient is influenced by the pitch angle, β, and the tip-speed ratio, TSR = , where is the turbine radius and is the turbine rotational speed. The wind turbine model is shown in Figure 2, where is the speed gain of the gearbox, is the aerodynamical torque, is the gearbox output torque, is inertial moment, is viscous friction coefficient of the rotor, and Ω is the rotor speed.

DFIG model
The stator and rotor equations of the DFIG machine are derived from Park reference frame rotating at synchronous speed [15], [16], and can be described by: The stator and rotor voltage equations: where and are the direct and quadrate components of stator flux (wb), and are the direct and quadrate components of rotor flux (wb), is the mutual inductance (H) and and are the stator and rotor inductances (H).
The electromagnetic torque equation is given by: where is the number of pole pairs.

CONTROL STRATEGY 4.1. Wind turbine control
In order to extract maximum power from the wind, we apply the Maximum Power Point Tracking based on the rotor speed control. The tip-speed ratio is tuned to over different wind speeds , by adapting the rotor speed to _ = ( _ )/ [17]. The MPPT scheme is shown in Figure 2.

DFIG control
We apply vector control strategy to the DFIG, which decouples the DFIG model into two independent subsystems of flux and torque, in order to get the performance similar to DC motor speed control [18]. Thus, the stator flux is chosen to be oriented to direct axis in the park reference frame ( = and = 0), and by neglecting stator resistance, and become: = 0 and = = . Consequently, the electromagnetic torque ( _ ) and the active and reactive stator powers ( , ) become: Also, the rotor voltages can be expressed as: where is the slip of DFIG. The proposed control plan of DFIG based on two FOPI controllers is shown in Figure 3.

FRACTIONAL ORDER PI CONTROLLER TUNING PROCEDURE
In the previous section, the general form of the transfer function of the plants was: where T and K are constants. In this section, two different controllers are proposed: the integer order PI and the Fractional Order PI (FOPI). The transfer functions of the two controllers can be described as follows: where , and are real numbers, ∈ [0,1].

Design specifications
In [19], [20], a tuning method for PI controller and FOPI controller is proposed. We choose the gain crossover frequency, , and phase margin, , to be the same for both controllers. For the system stability and robustness, the following constraints are considered: [19], [20] a) Phase margin constraint:

Fractional order PI controller Tuning
Based on the design specifications introduced in the previous section, we present the tuning procedure of the Fractional Order PI controller, for the first order plant. The open-loop transfer function with the FOPI controller is, where K and T are known and , and should be designed in the controller design process. The FOPI controller can be expressed as: Since = /2 , thus = /2 = ( /2) + ( /2), which gives, The open-loop phase at the gain cross-over frequency is, Hence, the relationship between and can be established as, And the open-loop gain using at the crossover frequency: For tuning the FOPI controller and classical PI controller for the rotor current control loop, the same cross-over frequency, , is presumed: = 500 / . Furthermore, in order to get a damping ratio of = 0.707, the phase margin should be the same for both controllers: φ = 64°. Hence, the tuned current controllers give,

RESULTS AND DISCUSSION
In order to verify and study the efficiencies of the control strategy, two sets of simulations were performed. The first set is carried out on an isolated DFIG current control loop to prove the effectiveness of the proposed controller design. Whereas, the second one is carried out on DFIG-based WECS to confirm the dynamic of the whole system. The WECS system's parameters used during simulations are listed in Table 1. Case 1: The isolated DFIG (without WECS) current control loop This simulation analyses and compares the performance of the FOPI controller with the classical PI controller of the DFIG current control loop. Under four different specifications, i.e. the set-point reference, the robustness, the disturbance rejection and the noise minimization. Figure 4 shows the unit step responses of the DFIG current control loop with the FOPI controller as shown in Figure 4(a), and classical PI controller as shown in Figure 4(b). The unit step responses are designed with three different closed-loop gain ( ): 1 , 2 1 and 0.5 1 . It is clear that the FOPI controller exhibits a good reference tracking and, on contrary to the classical PI controller, its overshoots were not affected by the different gains. Therefore, the controlled system using the fractional controller remains robust over gain changes. The unit step responses of DFIG current control loop with the FOPI controller and the classical PI controller are depicted in Figure 5. A disturbance of 0.5 is applied on the output of the plant from = 0.2 on, and a measurement noise with Gaussian distributed random signal with zero mean and 0.1 variance value is assumed in the output of the plant from = 0.4 on. By comparing the two curves we notice that a faster disturbance-rejection, and better minimization of the measurement noise effect is achieved using the FOPI controller, indicating superior disturbance-rejection and measurement noise minimization for the controlled system with the fractional controller. Step current responses using FOPI controller and classical PI controller Case 2: the DFIG-based wind energy conversion system In this case, we simulated the DFIG inside wind energy conversion system using the classical PI and the FOPI controllers. The following simulation results were obtained for reactive stator power reference − = 0 and wind speed profile modeled using the sum of harmonics [21], [22]: Furthermore, a disturbance of 500 A is applied on the output of the currents plants from = 10 on, and a Gaussian distributed random signal measurement noise with zero mean and 30 variance value is assumed in the output of the currents plants from = 20 on. Figures 6(a), (b), (c) and (d) present the evolution with time of the wind speed, the power coefficient, the wind turbine power and DFIG slip, respectively. As shown in Figure 6(b), the power coefficient achieved a maximum value 0.55 rapidly and remains constant over wind speed evolution. However, the wind turbine power and the slip vary according to the wind speed profile.
Electromagnetic torque, stator active and reactive powers of the DFIG are shown respectively in Figure 7(a), (b) and (c). From these figures it is clear that the WECS with the FOPI controller exhibits better dynamic performance in terms of the set-point reference, the disturbance rejection and the noise minimization, than the WECS with classical PI controller.

CONCLUSION
In this paper, we proposed a robust control of a variable speed DFIG-based WECS using vector control strategy based on two Fractional Order PI Controllers, to prevent system deterioration under critical conditions, namely: DFIG parameters variation, disturbance and measurement noise. The two Fractional Order PI controllers were designed with a simple analytical method. The simulation results show that the WECS with the FOPI controllers exhibit better dynamic performance even in critical conditions. This is reflected in the robustness to rotor resistance variation, superior disturbance-rejection and measurement noise minimization.