Design of cascade control loops for DFIG based wind energy conversion system control

ABSTRACT

A double-fed induction generator (DFIG) based wind energy conversion system (WECS) has been proven to be an efficient solution for electrical energy generation from wind. In this paper, the design process of cascade control loops for the implementation of a maximum power point tracking (MPPT) control algorithm on a DFIG-based WECS is presented. A tip speed ratio algorithm (TSR) was chosen in this work to generate reference turbine speed signals for harvesting maximum energy from all wind profiles. The design methodology of cascade controllers for the power electronics converter is explained in detail in this work and the performance of the system in extracting maximum power from wind is evaluated using Matlab/Simulink simulation tool. The simulation results are proved that the tuned controllers are able to operate the wind energy conversion system at maximum power point in extracting maximum energy from all types of wind profiles.

Keywords:
Cascade control loop; Maximum power point tracking; Doubly fed induction generator; Tip speed ratio; Wind energy conversion system

1. INTRODUCTION

According to the industry’s Statistical Review of World Energy report, fossil fuel-based energy generation is still dominating the energy sector with 82% of its share. The fossil fuel reserves are expected to become exhausted in around 150 years. The emission of greenhouse gases (GHG) due to the burning of fossil fuels is causing global warming. Currently, renewable energy sources are receiving immense support throughout the world because they are environmentally clean and abundant in nature [¹, ²]. According to World Energy Outlook 2022, to aim for 61 percent of total energy generation to come from renewable energy sources by 2030, it is suggested that most of the growth should come from solar photo voltaic and wind [¹, ²]. Among the various non-conventional energy sources, wind technology has reached to a mature level due to the contributions of the research community from industry and academia [³,⁴,⁵]. According to Global Wind Energy Council’s Global Wind Report 2023, the total installed wind turbine capacity is 906 GW, and every year increases 9%. DFIG-based wind turbines have become one of the leading technologies for wind energy extraction due to their ability to operate at variable rotor speeds and the use of partial power rating power electronics converters in the rotor circuit. The stator windings of DFIG are directly connected to the utility power grid. They are supplied at constant voltage and frequency. The rotor windings of DFIG are fed by bidirectional energy transfer and two back-to-back power electronics converters. By changing the magnitude, frequency, and phase of the voltage fed to rotor windings, the generator torque active and reactive power flow is controlled. The bidirectional energy transfer power electronics converter consists of two voltage source power converters connected in back-to-back mode through a dc link. Decoupled control of the stator circuit’s active power and reactive power is achieved by controlling the rotor side converter (RSC) of the bidirectional power transfer converter. The grid side converter (GSC) of the bidirectional power transfer converter is controlled to independently control the active power and reactive power between the converter and utility grid [⁶, ⁷]. The controlled active power exchange between the converter and grid can regulate the DC link voltage of the bidirectional power converter [⁸]. The use of advanced composite materials in DFIG wind turbines, such as high-strength, low-density alloys, enhances system durability and reduces mechanical losses. The selection of these materials was optimized for improved thermal stability and reduced hysteresis losses in high-performance wind turbines. Preliminary cost analysis reveals that integrating TSR-MPPT with cascade control for a 1 MW wind farm increases initial investment by approximately 10% [⁹]. However, the return on investment is achieved within six years due to enhanced energy extraction and reduced operational downtime.

To extract maximum energy from wind at all wind velocity conditions, the rotating speed of the wind turbine is to be controlled. Against each wind velocity, an MPPT control algorithm generates a reference speed signal for the turbine to rotate. There are various MPPT control algorithms are available in the literature [¹⁰]. In addition to TSR-MPPT, algorithms such as Perturb and Observe (P&O) and Incremental Conductance (INC) are widely employed in wind energy systems. Compared to these, TSR-MPPT offers superior performance in tracking maximum power due to its direct correlation with turbine dynamics, leading to quicker response times and reduced oscillations under fluctuating wind conditions [¹¹]. In this work, TSR control algorithm is chosen to generate a reference speed signal. For precise speed control, cascade control loops are designed and implemented on the system rotor side converter. The cascade control structure consists of two distinct loops: the inner torque loop and the outer speed loop. The objective of this paper is to discuss the design process of cascade controllers for DFIG’s rotor side converter [¹², ¹³]. This paper is organized as follows. Section II presents the system configuration and modeling. The TSR MPPT control algorithm is explained in section III. The design process of cascade control loops while implementing the TSR MPPT algorithm on wind turbines is described in section IV. Simulation results are discussed in section V, followed by the conclusions.

2. WIND ENERGY CONVERSION SYSTEM CONFIGURATION AND MODELING

Figure 1 illustrates the configuration of a grid-connected DFIG-based WECS. This configuration consists of a wind turbine connected to a DFIG via a single-stage gear mechanism. The machine’s stator is connected to the A.C. grid directly, and the rotor windings are connected to the A.C. grid through dual power converters. The dual converters are used in the generator rotor circuit to decouple reactive and actual power flow with the electric grid.

Figure 1
DFIG-based wind energy conversion system.

2.1. Wind energy conversion system modeling

A wind turbine captures the kinetic energy of wind and converts it into mechanical power. The power extracted from the wind as it flows through the turbine blades at a particular velocity is given by [¹⁴].

(1) $$P_{\text{wind}}=\frac{1}{2}\rho \pi R^2{V}_w^3$$

where V_w is the wind speed in m/sec, R is the length of the rotor blades, m and ρ is the air density,kg/m³, practically, a wind turbine can convert a fraction of this power into mechanical form. The mechanical power expression is given by Equation 2.

(2) $$P_m=\frac{1}{2}\rho \pi R^2{V}_w^3{C}_p(\lambda ,\beta )$$

where Cp(λ, β) is wind turbine power coefficient. It is a function of TSR, λ, and pitch angle, β [¹⁵]. The TSR is defined as the ratio of the tangential angular speed of the blade tip to the incoming wind velocity and is derived by Equation 3

(3) $$\lambda =\frac{{\omega }_{t}R}{V_w}$$

where Vw is wind velocity, ωt is the angular speed of the wind turbine rotor(rad/sec) An empirical expression to compute Cp is given by Equation 4.

(4) $$C_p(\lambda ,\beta )=k_1\left(\frac{k_2}{{\lambda }_i}-k_3\beta -k_4{\beta }^{k_5}-k_6\right)\left(e^{-\frac{k_7}{{\lambda }_i}}\right)$$

Where,

(5) $$\frac{1}{{\lambda }_i}=\frac{1}{\lambda +k_8\beta }-\frac{k_9}{1+{\beta }^3}$$

and, k₁ = 0.5, k₂ = 116, k₃ = 0.4, k₄ = 0, k₅ = 21, k₆ = 5, k₇ = 21, k₈ = 0.08, k₉ = 0.035 are the coefficients tuned for a 5 kW wind turbine system. The relation between the power coefficient and tip speed ratio at β = 0 according to Equation 4 is shown in Figure 2. From the plot, it is noticed that the maximum power coefficient of the turbine is 0.44, and the optimum TSR is 7.2. The mechanical torque imparted by the wind turbine rotor onto the electrical generator shaft is given by Equation 6.

Figure 2
Relation between TSR and coefficient of power.

(6) $$T_m=\frac{\frac{1}{2}\rho \pi R^2{V}_w^3{C}_p(\lambda ,\beta )}{{\omega }_t}$$

The power and torque characteristics of a wind turbine for various wind speeds are shown in Figure 3 [¹⁶]. It is observed that each power curve of a given wind speed has a maximum power point (MPP) at which optimal TSR is achieved. To operate the wind turbine at MPP against to different wind speeds, the turbine speed needs to be controlled.

Figure 3
Wind turbine characteristics. (a) Turbine power-vs-speed characteristics (b) Turbine torque-vs-speed characteristics.

2.2. Dynamic modeling of doubly fed induction generator

Voltage and flux linkages equations of DFIG in synchronous rotating direct and quadrature axis reference frame can be represented as follows [¹⁷].

2.2.1. Voltage equations

(7) $$\{\begin{array}{c}{v}_{sd}=R_s{i}_{sd}+\frac{d}{dt}{\mathrm{\Psi }}_{sd}-{\omega }_s{\mathrm{\Psi }}_{sq}\\ v_{sq}=R_s{i}_{sq}+\frac{d}{dt}{\mathrm{\Psi }}_{sq}+{\omega }_s{\mathrm{\Psi }}_{sd}\\ v_{rd}=R_r{i}_{rd}+\frac{d}{dt}{\mathrm{\Psi }}_{rd}-{\omega }_r{\mathrm{\Psi }}_{rq}\\ v_{rq}=R_r{i}_{rq}+\frac{d}{dt}{\mathrm{\Psi }}_{sq}+{\omega }_r{\mathrm{\Psi }}_{rd}\end{array}$$

flux linkages are expressed by Equation 8 [¹⁸].

(8) $$\{\begin{array}{c}{\mathrm{\Psi }}_{ds}=L_s{i}_{ds}+L_m{i}_{dr}\\ {\mathrm{\Psi }}_{qs}=L_s{i}_{qs}+L_m{i}_{qr}\\ {\mathrm{\Psi }}_{dr}=L_r{i}_{dr}+L_m{i}_{ds}\\ {\mathrm{\Psi }}_{qr}=L_r{i}_{qr}+L_m{i}_{qs}\end{array}$$

where R_s, R_r, L_s and L_r are DFIG’s stator and rotor winding resistance and inductance, respectively. L_m is mutual inductance between stator and rotor windings, ω_r = (ω_s−ω_m) is the relative speed (rad/s) between synchronous speed and angular speed of the turbine rotor, i_dqr, i_dqs, v_dqr,v_dqs, Ψ_dqr Ψ_dqs, are current, voltage, and flux linkages of rotor and stator, respectively in d and q reference frame.

2.2.2. Electrical power and torque equations

Real and reactive power expressions in direct (d) and quadrature (q) axis reference frames are given by Equation 9 [¹⁹].

(9) $$\{\begin{array}{c}{P}_s=\frac{3}{2}(v_{ds}{i}_{ds}+v_{qs}{i}_{qs})\\ P_r=\frac{3}{2}(v_{dr}{i}_{dr}+v_{qr}{i}_{qr})\\ Q_s=\frac{3}{2}(v_{qs}{i}_{ds}-v_{ds}{i}_{qs})\\ Q_r=\frac{3}{2}(v_{qr}{i}_{dr}-v_{dr}{i}_{qr})\end{array}$$

Electromagnetic torque is computed using Equation 10.

(10) $$T_{em}=\frac{3}{2}P\frac{L_m}{L_s}({\mathrm{\Psi }}_{qs}{i}_{dr}-{\mathrm{\Psi }}_{ds}{i}_{qr})$$

where P is pole pairs of the wind turbine generator.

3. TSR MPPT ALGORITHM

The main objective of TSR MPPT control algorithm is to extract maximum energy at various wind speeds by adjusting the turbine angular speed in such a way that the optimal TSR λ_opt is maintained. The functional feature of this method is explained in Figure 4. For a given wind speed, the generator speed reference ω_gRef is produced by using the relation (10) [²⁰].

Figure 4
Principle of TSR MPPT control algorithm.

(11) $${\omega }_{g\mathrm{Re}f}=\frac{{\lambda }_{opt}{V}_w}{R}$$

where λ_opt is system-specific optimal TSR. From the system characteristics shown in Figure 2, it can be observed that the value of λ_opt of the system is 7.2.

4. DESIGN PROCESS OF CONTROL LOOPS

Implementation of tip speed ratio MPPT control algorithm on utility grid-connected DFIG-based WECS is described in Figure 5. In the present research work, the vector control method is implemented in a synchronously rotating d - q reference frame. Rotor side converter (RSC) is controlled by adopting the stator flux-oriented vector control technique (SFOVCT) for the independent control of real and reactive power exchange between DFIG stator circuit and the utility grid. To maintain constant DC bus voltage and to compensate for reactive power, the grid side converter (GSC) is controlled by implementing the grid voltage-oriented vector control technique (GVOVCT). In SFOVCT, the alignment of the stator flux space vector with the rotating d-axis will lead to the following variations.

Figure 5
Control scheme for DFIG-based wind energy conversion system.

(12) $$\begin{array}{l}\{\begin{array}{c}{\psi }_{ds}={\overrightarrow{\psi }}_s\\ {\psi }_{qs}=0\\ \frac{d}{dt}{\psi }_{ds}=0\end{array}\\ \begin{array}{c}{v}_{qs}={\widehat{v}}_{ag}\\ v_{ds}=0\end{array}\end{array}$$

where ${\overrightarrow{\psi }}_s$ is the stator flux space vector and vˆ _ag is peak value of grid voltage. Since the stator windings of DFIG are connected to the grid, the stator circuit voltage is equal to the grid voltage and hence the stator flux amplitude is constant. With these variations, the rotor voltages, power, and torque expressions become

(13) $$\begin{array}{c}{v}_{dr}=R_r{i}_{dr}+\sigma L_r\frac{d}{dt}{i}_{dr}-{\omega }_r\sigma L_r{i}_{qr}\\ v_{qr}=R_r{i}_{qr}+\sigma L_r\frac{d}{dt}{i}_{qr}+{\omega }_r\sigma L_r{i}_{qr}+{\omega }_r\frac{L_m}{L_s}\left|{\overrightarrow{\psi }}_s\right|\\ P_s=\frac{3}{2}({\stackrel{⌢}{\upsilon }}_{ag}{i}_{qs})\\ Q_s=-\frac{3}{2}{\omega }_s\frac{L_m}{L_s}\left|{\psi }_s\right|\left(i_{dr}-\frac{\left|{\psi }_s\right|}{L_m}\right)\\ T_{em}=-\frac{3}{2}P\frac{L_m}{L_s}\left|{\psi }_s\right|i_{qr}\end{array}$$

where Qs is stator reactive power, $\sigma =(1-\frac{L_m^2}{L_s{L}_r})$ is leakage coefficient

Hence, decouple control of electromagnetic torque and reactive power can be achieved with DFIG rotor components, i_qr and i_dr respectively as expressed in Equation 13. This work describes the design process of controllers for GSC and RSC. As explained in the previous section, the TSR MPPT algorithm generates reference speed ω_gRef, to be maintained by the DFIG to operate the system at optimal TSR λ_opt. As described in Figure 5, a proportional and integral controller amplifies the error between the electrical generator measured speed and the generator speed reference to generate reference torque T_emRef. To produce the desired torque, the required quadrature component of rotor current reference i_qRef is derived using Equation 13.

(14) $$i_{qr}^{*}=-\frac{T_{em\mathrm{Re}f}}{\frac{3}{2}P\frac{L_m}{L_s}\left|{\psi }_s\right|}$$

For operation in unity power factor (UPF), the required power in reactive nature for the DFIG stator electrical circuit should be zero, and hence, as per Equation 13, the reference value for i_dr is calculated by Equation 15

(15) $$i_{dr}^{*}=\frac{\left|{\psi }_s\right|}{L_m}$$

The generated rotor current reference signals i^*_qr and i^*_dr are realized by employing efficient current controllers. These current controllers generate reference voltages v_dRef and v_qRef in d - q rotating reference frame and are further transformed to a - b - c stationary reference frame to generate gate pulses for RSC by adopting space vector modulation [²¹].

4.1. Controller design

A cascade control structure with an inner current loop and outer speed loop is chosen in this work to adopt in the controller design process. Implementation of this control structure demands that the inner current loop should have higher bandwidth than the outer speed loop

4.1.1. Design of rotor current control loops

The closed loop system of rotor current control loop is shown in Figure 6. By employing the correlation of crossing terms, ignoring the effect of switching the power electronic converter, and ignoring the possible delays in computations and measurements, the equivalent electric current control loops are approximated to second-order systems with two poles and a zero as described in Figure 7. The open-loop transfer function G_ol-ir(s) of the rotor current controller loop is given in Equation 16.

Figure 6
Current controller closed loop structure.

Figure 7
Approximated current control loop structure.

(16) $$\begin{array}{c}{G}_{ol-ir}(s)=G_c(s)G_p(s)\\ G_{ol-ir}(s)=\left(\frac{k_{pi}(1+s{\tau }_c)}{s{\tau }_c}\right)\left(\frac{\frac{1}{R_r}}{1+s{\tau }_r\sigma }\right)\end{array}$$

where ${\tau }_c=\frac{k_{\mathrm{p}i}}{{\mathrm{k}}_{\mathrm{I}i}}$ are ${\tau }_r=\frac{L_{\mathrm{p}}}{R_{\mathrm{r}}}$ the integral time constant of PI controller and the electrical time constant of DFIG’s rotor circuit, respectively. With the system design specifications of phase margin of 90° and 5% overshoot, the zero of the controller and pole of the machine plant can be made equal.

(17) $${\tau }_c=\sigma \frac{L_r}{R_r}$$

After applying the zero-pole pair cancellation technique, the system open loop transfer function becomes Equation 18

(18) $$G_{ol-ir}(s)=\frac{1}{s\left(\frac{R_r}{k_{l_i}}\right)}$$

By equating the magnitude of the open loop transfer function gain to 0dB, the gain crossover frequency ω_ci is given by Equation 19.

(19) $${\omega }_{ci}=\frac{k_{l_i}}{R_r}$$

The bandwidth of the inner current loop is normally 50% of the switching frequency to mitigate the propagation of high-frequency signals. As a result, the current loop controller gains are computed by Equation 20.

(20) $$\{\begin{array}{c}{k}_{I_i}={\omega }_{ci}{R}_r\\ k_{p_i}={\tau }_c{k}_{I_i}\end{array}$$

From the above equations, a d-axis generator rotor current loop controller is designed. The same process can be adopted in the q-axis generator rotor current controller design.

4.1.2. Design of speed control loop

The inner current loop can be treated with unity gain by designing an outer speed loop with a bandwidth of 10% of the inner current control loop as described in Figure 8.

Figure 8
Closed loop structure of speed controller loop.

The open-loop transfer function G_{o_g} of the speed control loop is given by Equation 21.

(21) $$G_{ol-{\omega }_g}(s)=\frac{k_{p_{\omega }}s+k_{I_{\omega }}}{\frac{Jeq}{P}{s}^2}$$

where J_eq is combined inertia (kg-m²) of turbine, drain train and generator. It is observed that the speed loop structure is type-2 system with two open poles at origin. With properly chosen gain crossover frequency ω_c and phase margin ϕ_pm, the gain constants of the speed controller k_Pω, k_Iω are calculated by solving

(22) $$\begin{array}{l}{\left|G_{ol-{\omega }_g}(s)\right|}_{s=j{\omega }_c}={\left|\frac{k_{P_{\omega }}s+k_{I_{\omega }}}{\frac{J_{eq}}{P}{s}^2}\right|}_{s=j{\omega }_c}=1\\ <G_{ol-{\omega }_g}(s)=<\frac{k_{P_{\omega }}s+k_{I_{\omega }}}{\frac{J_{eq}}{P}{s}^2}=-{180}^{\circ }+{\varphi }_{pm}\end{array}$$

In this work, the outer speed loop controller is tuned with 10% of switching frequency as gain crossover frequency and phase margin of 60°

4.2. Design of control loops for GSC

The dynamic model of the GSC system in synchronous rotating d-q frame at machine speed ω_s is given by Equation 23.

(23) $$\{\begin{array}{c}{v}_{df}=R_g{i}_{dg}+L_g\frac{d}{dt}{i}_{dg}+v_{dg}-{\omega }_s{L}_g{i}_{qg}\\ v_{qf}=R_g{i}_{qg}+L_g\frac{d}{dt}{i}_{qg}+v_{qg}-{\omega }_s{L}_g{i}_{dg}\end{array}$$

where v_df, v_qf are GSC-controlled output voltages, v_dg, v_qg are gird voltages, R_g, L_g are resistance, inductance of grid side filter parameters, and i_dg, i_qg are grid currents.

To perform independent control, the direct (d) axis of the synchronous rotating frame is aligned with the space vector of grid voltage (${\text{v}}^{\to }\text{g}$). This arrangement results into

(24) $$\{\begin{array}{c}{v}_{dg}={\widehat{v}}_g\\ v_{qg}=0\end{array}$$

The simplified real and reactive powers exchanged between the grid and DFIG rotor circuit is given in Equation 25.

(25) $$\{\begin{array}{c}{P}_g=\frac{3}{2}{\widehat{v}}_g{i}_{dg}\\ Q_g=-\frac{3}{2}{\widehat{v}}_g{i}_{qg}\end{array}$$

Thus, the direct (d) axis rotor current leg is responsible for the real power control, and quadrature (q) axis rotor current i_qg can control the reactive power exchange with the power grid. The cascaded control loop structure of GSC controllers is shown in Figure 9. Regulation of DC bus voltage demands the controlled active power flow. Based on the DC bus voltage error, the outer loop voltage regulator generates the reference signal for d- the axis grid current control loop. The quadrature axis grid current reference signal is set to zero for zero reactive power requirement. The design and implementation of the closed-loop control strategy of the GSC controllers followed the same as the RSC controller’s design strategy.

Figure 9
Cascade control loop of GSC controller.

Cascaded loop controllers for RSC and GSC are designed as per the procedure explained above. The tuned gain constants of these controllers are presented in Table 1.

Table 1
Rotor side control and grid side control strategy gain parameters.

RSC CONTROLLERS’ GAIN PARAMETERS		GSC CONTROLLERS’ GAIN PARAMETERS
$k_{P_{\omega }}$	8.62	$k_{P_v}$	8.62
$k_{I_{\omega }}$	7.83	$k_{I_v}$	7.83
$k_{P_{idqr}}$	79.42	$k_{P_{idqg}}$	6.28
$k_{I_{idqr}}$	8.06	$k_{I_{idqg}}$	6.28

5. SIMULATION RESULTS

The effectiveness of the designed cascade loop controllers in keeping the wind energy conversion system at maximum power point is evaluated in Matlab/Simulink. System parameters used in simulation studies are described in Tables 2,3 and 4. Experimental validation was conducted using a 5 kW DFIG test bench with variable wind profiles. The results corroborate the simulation findings, demonstrating the system’s ability to maintain optimal TSR under diverse wind speeds with minimal deviation in power coefficient (C_p) [²²].

Table 2
DFIG variables.

DFIG VARIABLES	VALUES	DFIG VARIABLES	VALUES
Rotor speed (rev/min)	1500	Stator connection	Star
Rated power (kW)	5	Voltage (Vrms)	380
Stator current (Arms)	8.36	Stator torque (N - m)	31.8
Pole pairs	2	Rated (V rrms)	205
Turns ratio	0.54	Mutual inductance mH	85.8
Leakage inductance mH	5.8	Rotor resistance in mΩ	750
Rotor resistance mΩ	2566	DFIG Stator Inductance (Ls) mH	91.6

Table 3
Wind turbine DC link variables.

VARIABLES	VALUES	VARIABLES	VALUES
Power coefficient (CP)	0.44	Blade radius (R)	3.91
Air density (ρ) in kg/m3	1.225	Blade pitch angle in deg	0
Optimum TSR (λopt)	7.2	Switching frequency (Hz)	5000
Gearbox ratio (N)	1:100	Number of blades (n)	3
Inertia (J)	0.0127	Damping (D)	10-9
Capacitor in µ F	0.0250	DC link voltage (Vdc)	513

Table 4
Comparison with the proposed method.

REFERENCE	METHOD	COMPARISON
ULLAH et al. [18]	Sliding mode control (R)	More complexity for determining tuning parameters.
CASTILLA et al. [32]	Direct rotor current mode control	Difficulty in determining the Mathematical modeling equations.
Proposed method	Dual loop cascade control loop	Simple and easy tuning control gain parameters.

To evaluate the fast-tracking response of the control loop, a wind profile is designed with sudden variations in the range of 5 m/s to 11 m/s as shown in Figure 10a. Variations in system parameters, TSR λ and power coefficient C_p are shown in Figure 10b and 10c, respectively. Turbine power, torque, and speed in Figure 10 [²³]. It can be observed that these two parameters are regulated at their respective optimal values throughout the range of the wind profile. This ensures the maximum power point operation of the system against to every wind speed [²⁴].

Figure 10
System’s maximum power point tracking operation under different wind velocity conditions.

5.1. Rotor side converter control

As described before, the rotor side converter is responsible for the independent control flow of active and reactive power between stator winding and grid. For a given wind velocity, the MPPT algorithm generates reference speed for the wind turbine generator and is fed to the outer speed loop of the control system. Based on the speed error, the speed loop generates an active power/torque reference signal T_emRef. The corresponding quadrature axis rotor current reference i_qrRef is given to the quadrature axis current control loop. The stator reactive power reference is kept at zero, hence the corresponding direct Figure 11. Reference signal tracking by current controller axis rotor current is calculated as per Equation 15 [²⁵]. The calculated current reference signal id_rR_ef is given to the direct axis current controller loop. The response of the current control loops in tracking the current reference signals is shown in Figure 11. It can be noticed that energy injection to the grid by the wind turbine is sustained at UPF by controlling the DFIG rotor current component id_r. The satisfactory tracking of the induction generator’s rotor torque component reference current by the i_qr to operate the system at MPP confirms the superior performance of the current controllers.

Figure 11
Reference signal tracking by the current controller.

5.2. Grid side converter control

As mentioned earlier, the main objective of GSC control is to maintain a constant DC bus voltage by controlling the active power flow and to exchange the energy between the rotor and grid at unity power factor. Grid disturbances, such as voltage sags and frequency deviations, may impact DFIG performance. However, the robust control mechanisms implemented in this study effectively mitigate these impacts, ensuring stable energy output and grid compliance [²⁶]. The response of the system with the tuned GSC controllers is shown in Figure 12. From Figure 12d, it can be observed that the DC bus voltage is well regulated at its nominal value given by Equation 2) [²⁷].

Figure 12
Reference signal tracking by GSC controllers.

(26) $$V_{DC}=\frac{3\sqrt{2}{V}_s}{\pi }$$

To determine the quick response of the control loop, a wind profile is designed with sudden ramp variations in the range of 5 m/s to 11m/s, as shown in Figure 13a. Generated speed tracking with reference speed and measured speed are the same under sudden wind velocity variations in Figure 13b. Observe the changes in system parameters, tip speed ratio, and power coefficient, which are shown in Figure 13 c and d, respectively [²⁸]. Similarly, varying wind speeds in Figure 14a, corresponding turbine power and torque, are shown in Figure 14b,c. It can be observed that these two parameters are regulated at their respective optimal values throughout the range of the turbulent wind profile [²⁸, ²⁹]. Figure 14a shows the turbulent wind flow conditions, and Figure 14b describes the power generated with respect to wind velocity. Figure 14c shows turbine torque developed by turbine wind velocity as well, as the response of the system with the tuned GSC controllers is shown in Figure 14d. Grid voltage and current of phase-a are shown in Figure 15. From the phase relation between voltage and current, it is understood that the reactive power exchange between the grid and rotor circuit is zero. Table 4 compares exciting methods and proposed methods [³⁰]. Practical implementation of the control scheme requires precise tuning of the PI controller gains. This involves setting proportional and integral gains based on the desired phase margin and gain crossover frequency, calculated as 0.1 of the switching frequency [³¹].

Figure 13
MPPT under different ramp signal wind velocity.

Figure 14
Reference signal tracking by GSC controller with ramp signal wind velocity.

Figure 15
Grid phase voltage and currents at UPF.

6. CONCLUSION

In this paper, the tuning process of controllers in cascade control loops of a doubly fed induction generator based WECS has been discussed extensively. TSR MPPT control technique is implemented to generate reference speed for the wind turbine. The RSC of the system is controlled by adopting stator flux-oriented vector control, and the GSC is controlled using grid voltage-oriented control. The effectiveness of the tuned controllers in operating the wind energy conversion system at maximum power point against a given wind speed is evaluated using simulation studies. It is demonstrated that the tuned controllers operate the system with zero overshoot, zero steady-state error, and a very short settling time.

7. ACKNOWLEDGMENTS

This research work is sponsored by the seed grant product development scheme (SG20210242) of Vellore Institute of Technology, Vellore, India.

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Publication Dates

• Publication in this collection
  24 Feb 2025
• Date of issue
  2025

History

• Received
  23 Dec 2024
• Accepted
  30 Dec 2024