Optimization of DFIG Performance in Wind Energy Systems Using Fuzzy Logic Control and Harmonic Mitigation

The dynamic modeling and control of DFIG-based wind turbine systems are described by the authors in the study [4]. While reducing oscillation of the turbine generator and controlling real and reactive power, THD analysis must be taken into account.

According to authors in the study [5], an enhanced direct vector command (DVC) based on three-level SVPWM was presented. However, there are power and high harmonic current ripples. A SVPWM technique based on Neural Network (NN) method is suggested as a solution to the harmonics and ripple problem. Even if the stator reactive and real power oscillations are minimized, the generator side converter is not regulated.

A combined vector and direct power regulation for the rotor side converter (RSC) of the DFIG is presented in the study [6]. In a compacted control system, the system benefited from both vector control and direct power control methodologies. Fast dynamic reaction, robustness against changes in machine parameters, less processing, and ease of implementation are some of its advantages over vector control. On the other hand, it has advantages over direct power regulation, such as lower power ripple and fewer harmonic distortions. Due to the use of conventional VSC, the harmonics is increased.

In order to manage the rotor currents, the authors in the study [7] described how to control the rotor side by employing fuzzy logic-based rotor flux oriented vector control. To overcome any disturbance, rotor current components are controlled using conventional PI controllers and fuzzy logic controller; however grid side converter (GSC) regulation is not taken into account.

A wind energy conversion system using direct torque control (DTC) and a power factor management approach are described by the author in the study [8]. However, high-current harmonics and noise present in typical DTC techniques impair control performance.

The reviewed literature provides foundational insights into the modeling and control strategies of DFIG-based wind energy systems, highlighting existing limitations such as inadequate dynamic response and poor harmonic performance. To overcome these challenges, this study proposes an integrated solution that enhances the overall efficiency and grid compatibility of DFIG systems. Both the Rotor Side Converter (RSC) and Grid Side Converter (GSC) are comprehensively modeled and controlled to fully exploit the capabilities of DFIG technology. A Neutral Point Clamped (NPC) multilevel Voltage Source Converter is employed in conjunction with an LCL filter to effectively suppress the THD, ensuring the delivery of high-quality sinusoidal voltage and current waveforms to the grid. Additionally, SVPWM technique is implemented to optimize the switching performance of the multilevel converter, further improving the voltage waveform quality and reducing harmonic content.

This holistic approach addresses the key limitations in conventional DFIG systems, presenting a robust framework for high-performance wind energy conversion that aligns with IEEE 519 standards for grid integration. The proposed configuration is tested through MATLAB/Simulink simulation under variable wind conditions, demonstrating improved rotor response and compliance with harmonic standards.

2.1 System design and modeling

The necessary DFIG parameters for dynamic modeling are shown in Table 1. The proposed system model is presented in Figure 1.

Table 1. 2MW DFIG specifications

tu_pian_1.png

Figure 1. Proposed DFIG's system model

2.2 Modelling of wind turbine  

The rotor's ability to extract power is represented by aerodynamic model, which also calculates the torque based on the airflow on the blades.

The mechanical speed Ω_m, is obtained from mechanical model equation of DFIG. The expression for mechanical model is presented in Eq. (1) and the mechanical rotor speed is presented in Eq. (2) [7].

$T_{e m}-T_{m e c h}=J \frac{d \Omega_m}{d t}+f_v \Omega_m$    (1)

$\Omega_m=\frac{T_{e m}-T_{m e c h}}{J_s+f_v}$    (2)

where, J, represents inertia, and f_v, presents coefficient of damping.

2.3 Dynamic modeling of DFIG

In order to analyze the performance of DFIG and arrive at a more accurate picture, a dynamic equation must be looked at. The general voltage equation for DFIG is shown in Eq. (3) [9].

$V=I \cdot R+\frac{d|\psi|}{d t}$   (3)

where, $\psi$ is the generator’s flux linkage.

In this study, the mathematical investigation of the generator is modeled in the d-q axis to simplify the analysis and control of the generator. The Eqs. (4) and (5) represents the voltage expression for the stator and rotor part.

$\left\{\begin{array}{l}V_{d s}=R_s I_{d s}+\frac{d \psi_{d s}}{d t}-\omega_s \psi_{q s} \\ V_{q s}=R_s I_{q s}+\frac{d \psi_{q s}}{d t}-\omega_s \psi_{d s}\end{array}\right.$      (4)

$\left\{\begin{array}{l}V_{d r}=R_r I_{d r}+\frac{d \psi_{d r}}{d t}-\omega_r \psi_{q r} \\ V_{q r}=R_r I_{q r}+\frac{d \psi_{q r}}{d t}-\omega_r \psi_{d r}\end{array}\right.$         (5)

The stator flux is represented in Eq. (6), while the rotor flux is described in Eq. (7). The electromagnetic torque expression is shown in Eq. (8).

$\left\{\begin{array}{l}\psi_{d s}=L_s I_{d s}+L_m I_{d r} \\ \psi_{q s}=L_s I_{q s}+L_m I_{q r}\end{array}\right.$     (6)

$\left\{\begin{array}{l}\psi_{d r}=L_r I_{d r}+L_m I_{d s} \\ \psi_{q r}=L_s I_{q r}+L_m I_{q s}\end{array}\right.$      (7)

$T_{e m}=\frac{3}{2} P \frac{L_m}{L_c}\left(\psi_{q s} i_{d r}-\psi_{d s} i_{q r}\right)$     (8)

2.4 Vector control approach for DFIG's RSC

AC drive control methods are typically classified into scalar and vector control techniques. Although scalar control is relatively simple to implement, it has a slow response due to the inherent coupling effects. To address this limitation, vector control is utilized. In DFIG vector control, components of rotor current along the d and q axis are regulated independently. This allows the separate regulation of stator reactive and active power using the d-q axis [10].

The control strategy typically aligns the stator flux with d-axis for simplicity. In this scenario, it is expected that the stator fluxes in direct and quadrature axis are [11]:

$\left\{\begin{array}{c}\psi_{d s}=\psi_s \\ \psi_{q s}=0\end{array}\right.$    (9)

The stator resistance part is often neglected since the stator side of the DFIG is directly linked to the grid. It’s to examine the assumptions associated with the d-q reference frame when analyzing stator voltages [11].

$\left\{\begin{array}{l}\mathrm{v}_{\mathrm{ds}}=0 \\ \mathrm{v}_{\mathrm{qs}}=\mathrm{v}_{\mathrm{s}}=\omega_{\mathrm{s}} \psi_{\mathrm{s}}\end{array}\right.$  (10)

The stator currents are displayed in Eq. (11).

$\left\{\begin{array}{c}I_{d s}=\frac{\psi_s}{L_s}-\frac{L_m}{L_s} I_{d r} \\ I_{q s}=-\frac{L_m}{L_s} I_{q r}\end{array}\right.$       (11)

The expression for real and reactive stator power are given in Eq. (12). These equations indicate that when the stator flux is positioned along the d-axis, the real and reactive powers become decoupled. Consequently, the rotor currents independently control these power components. Additionally, the electromagnetic torque depends on the stator flux and the corresponding q-axis rotor current, which is expressed in Eq. (13).

$\left\{\begin{array}{c}\mathrm{P}_{\mathrm{s}}=\frac{3}{2} \mathrm{~V}_{\mathrm{qs}} \mathrm{I}_{\mathrm{qs}}=-\frac{3}{2} \mathrm{~V}_{\mathrm{s}} \frac{\mathrm{L}_{\mathrm{m}}}{\mathrm{L}_{\mathrm{s}}} \mathrm{I}_{\mathrm{qr}} \\ \mathrm{Q}_{\mathrm{s}}=\frac{3}{2} \mathrm{~V}_{\mathrm{q} \mathrm{s}} \mathrm{I}_{\mathrm{ds}}=\frac{3}{2} \frac{V_s^2}{L_s \omega_s}-\frac{3}{2} \frac{L_m}{L_s} I_{d r}\end{array}\right.$     (12)

$\left\{\begin{array}{c}T_{e m}=\frac{3}{2} P \frac{L_m}{L_s}\left(-\psi_{d s} i_{q r}\right) \\ T_{e m}=-\frac{3}{2} P \frac{L_m}{L_s}\left|\vec{\psi}_s\right| i_{q r}=K_T i_{q r} \\ K_T=-\frac{3}{2} P \frac{L_m}{L_s}\left|\vec{\psi}_s\right|\end{array}\right.$     (13)

To power the rotor, differential frequencies and voltage amplitudes are used. Eq. (14) explains rotor voltage expression in coordinates of d-q. Since the stator is linked to a stable grid operating at a constant AC voltage, the grid voltage remains unchanged in terms of frequency and amplitude during normal operation.

$\left\{\begin{array}{l}\mathrm{V}_{\mathrm{dr}}=\mathrm{R}_{\mathrm{r}} \mathrm{i}_{\mathrm{dr}}-\omega_{\mathrm{r}} \sigma \mathrm{L}_{\mathrm{r}} \mathrm{i}_{\mathrm{qr}}+\sigma \mathrm{L}_{\mathrm{r}} \frac{\mathrm{d}}{\mathrm{dt}} \mathrm{i}_{\mathrm{dr}}+\frac{\mathrm{L}_{\mathrm{m}}}{\mathrm{L}_{\mathrm{s}}} \frac{\mathrm{d}}{\mathrm{dt}} \psi_{\mathrm{ds}} \\ \mathrm{V}_{\mathrm{qr}}^{-}=\mathrm{R}_{\mathrm{r}} \dot{\mathrm{r}} \mathrm{i}_{\mathrm{qr}}+\omega_{\mathrm{r}} \sigma \mathrm{L}_{\mathrm{r}} \dot{\mathrm{I}} \mathrm{dr}+\sigma \mathrm{L}_{\mathrm{r}} \frac{\mathrm{d}}{\mathrm{dt}} \dot{\mathrm{i}}_{\mathrm{qr}}+\omega_{\mathrm{r}} \frac{\mathrm{L}_{\mathrm{m}}}{\mathrm{L}_{\mathrm{s}}} \psi_{\mathrm{ds}} \\ K_i=\omega_n{ }^2 \sigma L\end{array}\right.$     (14)

The d and q axis rotor currents, along with the d-component of stator flux, are referred to as coupling components. The term influenced by rotor speed and direct rotor current, as well as the direct stator flux, is identified as a perturbation. This perturbation is directly proportional to the stator flux.

2.5 Dynamic modeling and control of grid side system

In similar way to DFIG rotor side converter dynamic modeling, voltage equation in space vector notation for the grid side converter is given by Eq. (15) [9, 12].

$\left\{\begin{array}{c}V_{d f}=R_f i_{d g}+L_f \frac{d i_{d g}}{d t}+V_{d g}-\omega_{\mathrm{a}} L_f i_{q g} \\ V_{q f}=R_f i_{q g}+L_f \frac{d i_{q g}}{d t}+\omega_{\mathrm{a}} L_f i_{d g}\end{array}\right.$        (15)

The real (P_g) and reactive (Q_g) powers exchanged between the grids and the system is given by Eq. (16).

$\left\{\begin{array}{l}P_g=\frac{3}{2}\left(V_{d g} i_{d g}+V_{q g} i_{q g}\right) \\ Q_g=\frac{3}{2}\left(V_{q g} i_{d g}-V_{d g} i_{q g}\right)\end{array}\right.$   (16)

2.6 Vector control strategy of DFIG for GSC

For converters in grid side, vector control technique offers good performance attributes with essentially simple execution requirements. Such control approach is used to achieve flow of real and reactive power in decoupled manner between the GSC and network. It is assumed that the grid voltage along the q axis is zero, while the d axis voltage matches the grid voltage [13].

$\left\{\begin{array}{l}V_{q g}=0 \\ V_{d g}=V_q\end{array}\right.$     (17)

By regulating rotor current, the flow of real and reactive power is regulated independently.

$\left\{\begin{array}{c}P_g=\frac{3}{2}\left(V_{d g} i_{d g}\right) \\ Q_g=-\frac{3}{2}\left(V_{d g} i_{q g}\right)\end{array}\right.$    (18)

$\left\{\begin{array}{c}V_{d f}=R_f i_{d g}+L_f \frac{d i_{d g}}{d t}+V_{d g}-\omega_s L_f i_{q g} \\ V_{q f}=R_f i_{q g}+L_f \frac{d i_{q g}}{d t}+\omega_s L_f i_{d g}\end{array}\right.$      (19)

For this study, the NPC multilevel voltage source converter was used. Compared to flying capacitor and modular multilevel converters (MMC), the NPC inverter presents a practical balance for medium-voltage applications such as 2 MW wind turbines. Flying capacitor inverters, while capable of producing good waveform quality, suffer from complex voltage balancing and higher component count. MMCs, though scalable and highly modular, demand complex control and are typically used in very high power systems [14]. NPC inverters are favored for their lower cost, simpler control, and mature commercial availability in wind power applications [7]. Therefore, the NPC topology was chosen as the most feasible and efficient option for the targeted power rating and application [15, 16].

2.7 LCL filter analysis and design

The PWM output of a grid-connected inverter contains significant high-frequency harmonics, which can introduce unwanted current distortion into the grid. To mitigate these harmonics, a filter is placed between the voltage source converter (VSC) and the grid [17]. While a simple L filter offers basic attenuation, it compromises dynamic performance and limits the converter's operating range [18]. An LCL filter is a better alternative due to its superior harmonic attenuation capability. It effectively reduces current ripple and ensures that the Total Harmonic Distortion (THD) remains below 5%, complying with IEEE 519-1992 standards [19]. Designing an LCL filter involves determining base impedance (Zb), base capacitance (Cb), and base inductance (Lb) based on the converter’s rated power, grid parameters, and switching frequency. The converter-side inductor (L1) primarily attenuates high-frequency harmonics generated by switching actions. The objective of the input filter L1 is to reduce the high harmonics at the converter side [13].

According to IEEE 519-1992 the THD factor is given Eqs. (20) and (21) [20].

$T H D_{I E E E}=\sqrt{\sum_{h=2}^{50} I^2(h) * 100 \%}$     (20)

$Z_b=\frac{V_n^2}{P_n}, L_b=\frac{Z_b}{\omega_n}, C_b=\frac{1}{\omega_n Z_b}$     (21)

2.8 Controller design of DFIG for RSC

The controller for the DFIG’s rotor side VSC regulates rotor speed, torque and the exchange of real and reactive power. To improve the efficiency of maximum power transfer, a FLC is applied mainly to control the rotor speed.

2.9 PI controller tuning

The PI controller gains for the RSC and GSC are tuned using a pole placement method assuming a critically damped second-order system. This method ensures a fast and stable dynamic response by selecting the natural frequency $\omega_n$ based on control bandwidth requirements [21]. The tuning formulas used are $K_p=2 \omega_n \sigma L-R$ and $K_i=\omega_n^2 \sigma L$. Compared to conventional Ziegler-Nichols-based PI tuning, the proposed method resulted in a 40% reduction in settling time, improving from 0.25 s to 0.15 s in simulation under identical test conditions [22].

2.10 Fuzzy logic controller design

The fuzzy logic controller in this study utilizes rotor speed error and its variation as input parameters for the control strategy [23, 24]. The block diagram for the speed control system is displayed in Figure 2.

tu_pian_2.png

Figure 2. Block diagram for speed loop

Five triangular membership functions are employed for both the input and output variables of the Mamdani-type fuzzy inference system. These functions are defined as, NM: medium negative value, Z: zero, PM: medium positive value, PB: large positive value., offering a balanced linguistic representation for fuzzy logic reasoning. The input variables are the error e(t) and its change Δe(t), while the output represents the control signal to the rotor side converter (RSC).

The chosen range of [−80000,80000] for both inputs and output is not arbitrary but is based on simulations and analysis of the maximum expected rotor speed deviation and voltage fluctuation under extreme wind speed variations. This range is wide enough to capture the full dynamic envelope of system response, while ensuring resolution and sensitivity in control actions.

The rule base in Table 2 was initially structured using expert knowledge and then refined using an iterative trial-and-error tuning process during simulation.

Table 2. Fuzzy speed control rules

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Figure 3. Fuzzy membership function for input

This process involved observing the dynamic response (overshoot, settling time, and steady-state error) and adjusting rules to minimize performance deviations. Although empirical, this tuning strategy is a common and accepted method in fuzzy control design, especially when system dynamics are nonlinear and analytically complex. This approach provides a flexible, adaptive control mechanism suitable for the nonlinear behavior of DFIG systems, especially under wind fluctuations and grid disturbances.

For speed control utilizing a FLC technique, the membership functions for the input and output are illustrated in Figures 3 and 4, respectively.

tu_pian_4.png

Figure 4. Fuzzy membership function for output