Doubly-fed induction generator drive based WECS using fuzzy logic controller

Abstract

The purpose of this paper is to improve the control performance of the variable speed, constant frequency doubly-fed induction generator in the wind turbine generation system by using fuzzy logic controllers. The control of the rotor-side converter is realized by stator flux oriented control, whereas the control of the grid-side converter is performed by a control strategy based on grid voltage orientation to maintain the DC-link voltage stability. An intelligent fuzzy inference system is proposed as an alternative of the conventional proportional and integral (PI) controller to overcome any disturbance, such as fast wind speed variation, short grid voltage fault, parameter variations and so on. Five fuzzy logic controllers are used in the rotor side converter (RSC) for maximum power point tracking (MPPT) algorithm, active and reactive power control loops, and another two fuzzy logic controllers for direct and quadratic rotor currents components control loops. The performances have been tested on 1.5 MW doubly-fed induction generator (DFIG) in a Matlab/Simulink software environment.

Graphical abstract

Keywords

fuzzy logic / wind turbine / vector control / doubly-fed induction generator (DFIG)

1 Introduction

Wind energy is one of the most important and promising sources of renewable energy all over the world, mainly because it is considered to be non-polluting and economically viable. At the same time, there has been a rapid development of related wind turbine technology [1,2]. The global scheme for a grid-connected wind turbine is presented in Fig. 1.

Variable speed operation of wind turbine is usually used to provide energy with the best efficiency. The wind energy conversion system (WECS) based on doubly-fed induction generator (DFIG) has several advantages [3]. It reduces the stresses of the mechanical structure and the acoustic noise, and regulates both active and reactive power [4]. Its back-to-back PWM converters, connected between the grid and the rotor circuit are sized only for 30% of the full power of the generator [5]. The wind turbine generators (WTGs) can achieve the maximum wind power provided at various wind speeds by correctly adjusting the shaft speed [6]. As far as variable-speed generation is concerned, it is necessary to produce constant frequency electrical power from a variable speed source [2,7]. This can be achieved by means of wound-rotor induction generator fed with variable frequency rotor voltage. This allows fixed-frequency electrical power to be extracted from the generator stator. Consequently, the use of DFIGs is receiving increasing attention for wind generation purposes [8,9].

The vector control of the DFIG gives very good performances because it can achieve a decoupling control of the active and reactive power. In recent years, many researches of vector control take the following manner to track the largest wind energy under the rated wind speed. However, when wind speed becomes greater than the rated speed, the output power can remain stable only by adjusting the pitch angle. Compared with the fixed pitch, the variable pitch has many characteristics, such as the smooth output power within the point of rated power, the maintenance of rated power in high-speed section and the stronger performance of gear brake. At a low wind speed, the electromagnetic torque of DFIG is controlled to achieve speed control of wind turbine [10,11]. So far, several researches concentrate on stator active and reactive power controllers. The typical PI controller is used most which can satisfy the control requirement under normal operation conditions. However, system performance will fall down when severe disturbance happens, such as voltage dip or swell, parameters variations and so on. In recent years, fuzzy control has been widely applied to power electronics system including speed control of AC drives, feedback control of converters, online and off-line diagnosis, parameter estimation, and so on [12].

In this paper, fuzzy logic control is applied to control the DFIG, a Mamdani type fuzzy logic controller (FLC) is applied to replace the conventional PI controller in the indirect vector control for speed, power and currents control loops. To show the superiority of this method, a comparative study is conducted between the FLC and the traditional PI controller in a fault operating mode and simulation results are presented.

2 Wind turbine model

Wind energy is extracted through wind turbine blades and then transferred through a gearbox and the rotor hub to the mechanical energy in the rotational shaft. The shaft drives the generator to convert the mechanical energy to electrical. The turbine model is based on the output power characteristics, expressed as Eqs. (1) and (2) [13,14].

(1)P_m=C_p(\lambda ,\beta )\cdot {\displaystyle \frac{\mathrm{1}}{\mathrm{2}}}\rho A{v}_w^{\mathrm{3}}=C_p(\lambda ,\beta )E_w,

(2){\lambda }_{TSR}={\displaystyle \frac{R_{blade}{\omega }_t}{v_w}},

where P_m is the aerodynamic extracted power in Watt, which depends on efficiency coefficient C_p, ρ is the air density, A is the turbine swept area, and v_w is the wind speed. E_w is equal to the kinetic energy contained in the wind at a particular wind speed. And R_blade and ω_t are the blade radius and angular frequency of rotational turbine.

The efficiency coefficient C_p(λ, β), which depends on tip speed ratio λ_TSR and blade pitch angle β, determines the amount of wind kinetic energy that can be captured by the wind turbine system. A nonlinear model describes C_p(λ, β) as Eq. (3) [14].

(3)C_p(\lambda ,\beta )=\mathrm{0.5}\left({\displaystyle \frac{\mathrm{116}}{{\lambda }_i}}-\mathrm{0.4}\beta -\mathrm{5}\right)e^{-\mathrm{21}/{\lambda }_i},

where

{\displaystyle \frac{\mathrm{1}}{{\lambda }_i}}={\displaystyle \frac{\mathrm{1}}{{\lambda }_{TSR}+\mathrm{0.08}\beta }}-{\displaystyle \frac{\mathrm{0.035}}{{\beta }^{\mathrm{3}}+\mathrm{1}}}.

To track the maximum output power, the optimal curve of P_m(ω_m) is the map which has to follow. In this paper, for different wind speeds and fixed β = 0° (pitch angle of blades), the P_m(ω_m) curves are displayed in Fig. 2 for wind speeds ranging from 5 m/s to 12 m/s. By connecting the maximum points of all curves, the relationship between the maximum output mechanical power and the rotor speed can be expressed in Eq. (4) [15].

(4)P_{m\_max}=\mathrm{0.5572}{({\omega }_m/G)}^{\mathrm{3}}-\mathrm{0.5081}{({\omega }_m/G)}^{\mathrm{2}}+\mathrm{0.4792}({\omega }_m/G)-\mathrm{0.1449.}

Equation (4) is the look-up table for optimal active power control. Therefore, the dynamic equation of the shaft is defined by

(5){\displaystyle \frac{T_t}{G}}-T_{em}=J_{eq}{\displaystyle \frac{d{\omega }_m}{dt}}+f_{eq}{\omega }_m,

where T_em, ω_m are the generator electromagnetic torque in N·m, and the generator rotational speed in r/min,

T_{\mathrm{t}}=P_{\mathrm{m}}/{\omega }_{\mathrm{t}}\hspace{0.17em}\mathrm{a}\mathrm{n}\mathrm{d}\hspace{0.17em}{\omega }_{\mathrm{m}}={\omega }_{\mathrm{t}}G.

For the MPPT control technique of the wind turbine, the direct speed control is used which is a version of the tip speed ratio (TSR) control technique. The wind speed is measured and the optimal TSR is chosen from the C_p curve in order to calculate the optimal rotational speed as denoted in Fig. 3.

3 Mathematical model of DFIG

The classical electrical equations of the DFIG in the Park frame are given in Eq. (6) [16].

(6)\{\begin{array}{l}{V}_{ds}=R_s{i}_{ds}+{\displaystyle \frac{d}{dt}}{\phi }_{ds}-{\omega }_s{\phi }_{qs},\\ V_{qs}=R_s{i}_{qs}+{\displaystyle \frac{d}{dt}}{\phi }_{qs}+{\omega }_s{\phi }_{ds},\\ V_{dr}=R_r{i}_{dr}+{\displaystyle \frac{d}{dt}}{\phi }_{dr}-p{\omega }_m{\phi }_{qr},\\ V_{qr}=R_r{i}_{qr}+{\displaystyle \frac{d}{dt}}{\phi }_{qr}+p{\omega }_m{\phi }_{dr}.\end{array}

The stator and rotor flux can be expressed as

(7)\{\begin{array}{l}{\phi }_{ds}=L_s{i}_{ds}+M{i}_{dr},\\ {\phi }_{qs}=L_s{i}_{qs}+M{i}_{qr},\\ {\phi }_{dr}=L_r{i}_{dr}+M{i}_{ds},\\ {\phi }_{dr}=L_r{i}_{dr}+M{i}_{ds}.\end{array}

The stator active and reactive powers are defined as

(8)\{\begin{array}{l}{P}_s=V_{ds}{i}_{ds}+V_{qs}{i}_{qs},\\ Q_s=V_{qs}{i}_{ds}-V_{ds}{i}_{qs}.\end{array}

The rotor active and reactive powers are defined as

(9)\{\begin{array}{l}{P}_r=V_{dr}{i}_{dr}+V_{qr}{i}_{qr},\\ Q_r=V_{qr}{i}_{dr}-V_{dr}{i}_{qr}.\end{array}

The electromagnetic torque is expressed by

(10)T_{em}=p({\phi }_{ds}{i}_{qs}+{\phi }_{qs}{i}_{ds}).

4 Vector control of DFIG through back-to-back converters

A DFIG is a standard wound rotor induction machine, with its stator windings directly connected to the grid and its rotor windings connected to the grid through back-to-back frequency converters as shown in Fig. 4. In modern DFIG designs, the frequency converter is built by two self-commutated PWM converters, a rotor-side converter (RSC) and a grid-side converter (GSC), with an intermediate DC voltage link. By controlling the converters on both sides, the DFIG characteristics can be adjusted so as to achieve maximum effective power conversion or capturing capability for a wind turbine and to control its power generation with less fluctuation [17,18].

Many different d-q control algorithms have been proposed and used for controlling the DFIG machine by using the back-to-back converters for certain dynamic and transient performance achievements. Most algorithms are based on the active and reactive power control concept, a popular DFIG converter control mechanism used in modern wind turbines [19,20]. This control configuration is usually divided into RSC and GSC control systems. The RSC controls the active and reactive power of the DFIG independently, and the GSC is controlled in such a way as to maintain the DC-link capacitor voltage in a set value and to maintain the converter operation with a desired power factor.

The RSC control system, which consists of active and reactive power control of the DFIG, is commonly a two stages controller. It operates in either stator flux or stator voltage oriented reference frame and hence the q-axis rotor current component represents the active power while the d axis component represents the reactive power. The two controllers determine the d and q reference voltages by comparing the d and q references rotor current to the actual d and q rotor currents of the induction generator [18]. The GSC, also a two-stage controller operating in a grid AC voltage reference frame, regulates the DC-voltage and the rotor reactive power. Traditionally, the d-axis current component is used for active power control while the q-axis current component is used for reactive power control. The two feed-forward paths in the grid side control determine the d and q voltages by comparing the d and q current references with the actual d and q currents supplied to the grid [18]. To achieve a stator active and reactive power vector control, a d-q reference frame synchronized with the stator flux is chosen [21]. By setting null the quadratic component of the stator flux, the d and q-axis stator flux components become

(11){\phi }_{qs}={\phi }_s\hspace{0.17em}\mathrm{a}\mathrm{n}\mathrm{d}\hspace{0.17em}{\phi }_{qs}=\mathrm{0.}

In such case, Equations (12) and (13) are obtained.

(12){\phi }_{qs}=L_s{i}_{qs}+M{i}_{qr}=\mathrm{0}\Rightarrow i_{qs}=-{\displaystyle \frac{M}{L_s}}{i}_{qr},

(13)i_{ds}={\displaystyle \frac{V_s}{{\omega }_s{L}_s}}-{\displaystyle \frac{M}{L_s}}{i}_{dr}.

By using Eqs. (12) and (8), the active power equation can be expressed as

(14)P_s=-{\displaystyle \frac{V_{s}M}{L_s}}{i}_{qr}.

By using Eqs. (13) and (8), the reactive power equation can be expressed as

(15)Q_s={\displaystyle \frac{V_s{\phi }_s}{L_s}}-{\displaystyle \frac{V_{s}M}{L_s}}{i}_{dr}.

Therefore, the d-axis component of the rotor current, i_dr, can be controlled to regulate the stator reactive power (Eq. (15)), while the q-axis component of the rotor current, i_qr, can be controlled to regulate the stator active power (Eq. (14)).

5 Application of fuzzy logic control in DFIG wind power system

The dynamic mathematical model of DFIG is a nonlinear, complex and multivariable time-varying system. Accurate vector and field-oriented control are nearly impossible, and there may be a wide parameter variation problem in the system. Fuzzy logic control has the capability to control nonlinear, uncertain and adaptive systems, which gives a strong robust performance for parameter variation. Fuzzy control does not strictly need any mathematical model of the plant. Its control rule can be qualitatively expressed based on logic language variation, and fuzzy model of plant is very easy to apply. In fact, fuzzy control is possibly the best adaptive control among the techniques discussed so far. In this paper, fuzzy logic control is applied to the active and reactive power control of DFIG, which ensures the precision and robustness of control [12,22].

The general structure of a fuzzy controller system is illustrated in Fig. 5. The controller observes the pattern of the error signal and its derivative of the active or reactive power control loops and correspondingly updates the output U so that the active power P_s matches its reference active power P_{\mathrm{s}}^{*}, and the reactive power Q_s matches its reference reactive power Q_{\mathrm{s}}^{*}. There are two input signals to each fuzzy controller, the error signal E and its derivative dE/dt. These two signals are normalized through their respective scaling factors (G_e and G_de). The output control signal U is derived by multiplying the du/dt by the output scale factor G_du, and then integrated it to generate the command signal. The real control signals are the rotor currents of reference i_{qr}^{*} and i_{d\mathrm{r}}^{*} obtained from the active and reactive power control loops respectively. Considering the fuzzy controller basically as an input/output static nonlinear mapping, the controller action can be written as [12]

(16)K_{\mathrm{1}}\mathrm{E}dt+K_{\mathrm{2}}d\mathrm{E}=dU,

where K₁and K₂ are nonlinear coefficients, including the summation process shown in Fig. 5, Equation (17) can be obtained.

(17){\displaystyle \int \mathrm{d}U}={\displaystyle \int K_{\mathrm{1}}E}\mathrm{d}t+{\displaystyle \int K_{\mathrm{2}}\mathrm{d}E}.

Therefore,

(18)U=K_{\mathrm{1}}{\displaystyle \int E}dt+K_{\mathrm{2}}E.

This is nothing but a fuzzy PI controller with nonlinear gain factors. The nonlinear adaptive gains in the fuzzy controller that are varied online give the power to the fuzzy controller to make the system response robust against the parameter variation and load disturbance [23]. Figure 6 shows the fuzzy sets and corresponding triangular membership functions (MFs) description of each signal. The fuzzy MFs are defined as Z= zero, PS= Positive-small, PM= Positive-medium, PB= Positive-big, NS= Negative-small, NM= Negative-medium, NB= Negative-big.

The universe of discourse of all the variables, covering the whole region, is expressed in per unit values (pu). There are seven MFs for the input and the output signals (e, de/dt and du/dt). All MFs are symmetric for positive and negative regions of the variables. The fuzzy control rule database consists of a series of “If-And-Then” fuzzy logic condition sentences. Table 1 shows the corresponding rule for the power controller. The top row and the leftist column of the matrix indicate the fuzzy sets of the variables e and de/dt, respectively. The MFs of the output variable du are shown in the body of the matrix. There may be 49 possible rules in the matrix.

6 System configuration

The system considered in this paper is a grid connected DFIG with the rotor circuit connected to the grid through back-to-back PWM voltage source converters in a configuration demonstrated in Fig. 4. The wind turbine has a power rating of 1.5 MW and its output power changes as a function of the wind speed as displayed in Fig. 2. The wind speed is measured in order to determine the reference values for both the maximum output power and the corresponding generator speed in order to track the maximum power curve as shown in the MPPT component in Fig. 3. The active power reference value is used to calculate the error signal. The values of the error signal and its derivative are used as the inputs to the fuzzy inference which depend on the membership functions and the fuzzy rules. The same fuzzy controller is used for the reactive power with zero reference set. The outputs of these two controllers are the d and q-axis components of the rotor current (i_dr, i_qr). Another two fuzzy controllers for the d- and q- axis components of the rotor current are used. The outputs of these two controllers are the d- and q- axis components of the rotor voltage (V_dr,V_qr). These two control stages takes place as the power fuzzy logic control (PFLC), and the current fuzzy logic control (CFLC) as shown in Fig. 7.

7 System results and discussion

The experiment has been performed on a DFIG system incorporating the proposed FLCs for the vector control as presented in Fig. 7. The induction machine parameters are inspired from Refs. [13,24] and are listed in Tables 2 and 3. The performance of the vector control with the proposed fuzzy controllers is compared with a vector control employing the conventional PI controllers with fixed proportional and integral gains chosen to give the most accurate response. The wind speed is set at 6 m/s which corresponds to a set rotational speed of 78 rad/s (Fig. 8(a)). According to the MPPT system and Fig. 2, P_s-ref is equal to –0.2 × 10⁶ W and Q_s-ref is chosen to be –0.5 × 10⁶ var at t = 0.1 s. At t = 0.3 s the wind speed changed to become 10m/s, so the generator reference speed is changed to 130.5 rad/s and the P_s-ref became –0.95 × 10⁶ W to track the maximum power point curve while keeping Q_s-ref constant at –0.5 × 10⁶ var.

Figure 8 (a) shows the variation of rotational speed in the MPPT operating mode. The fuzzy controller is faster than the PI controller in the closed loop speed control of the MPPT system, but both of them achieved zero steady-state error. Figure 8 (b) shows the response of efficiency coefficient. The fuzzy controller is faster but both the fuzzy controller and the PI controller reach the same value of the efficiency coefficient of approximately 0.48. It can be seen from Fig. 8 (c) and (d) that by using the proposed FLCs, a faster dynamic response can be achieved. Moreover, there is no overshoot, and less settling time compared with the PI controller. Figure 8(e) and (f) shows the rotor d- and q-axis current components i_dr and i_qr, respectively. It can be observed that to increase the amount of active power generated, an increase in the q-axis component of the rotor current i_qr is required, and the same thing is going on between the reactive power and the rotor current i_dr. Besides, in the currents the fuzzy controller seems faster. At t = 0.1s, the generator is coupled with the grid. Figure 8 (g) and (h) presents the three-phase currents of the stator and the rotor, respectively. It is noticed from Fig. 8 (g) and (h) that they are changing proportionally to the stator active and reactive power changes. In addition, the frequency of the rotor current decreases when the rotor speed approaches to the synchronous speed, but its magnitude translates the power exchanged with the DC-link in the rotor circuit.

To insure the robustness of the proposed fuzzy controllers against the parameters variations and the grid voltage unbalance, three different faults are introduced separately to the system, and compared with the response of the conventional PI control system. The faults are introduced as follows:

1)The first one is an increase of the stator and the rotor winding resistances by 300% (in Fig. 9).

2)The second one is a decrease of the stator, rotor and mutual inductances by 90% (in Fig. 10).

3)The third one concerns a phase grid voltage failure, which present a dip by 20% at t = 1s and a swell by 20% at t = 1.3 s (in Fig. 11).

According to Figs. 9, 10 and 11, a degradation in the performance appears in the conventional PI control, for the resistances variation case and a huge static error appears. For the leakage inductances variation case, an increase of the ripple band appears, and for the grid voltage fault, a big disturbance appears. All of these electrical faults have been limited by using the intelligent FLC. Therefore, these simulations results insure the robustness of the FLC and its superiority compared with the PI controller.

Jabr and Kar [21] have made a comparative study in which the proposed fuzzy PI gain tuner is compared with a vector controller employing the conventional PI controller with three different configurations of constant proportional and integral gains. Fuzzy logic together with the well-known PI controllers provides a good control system, faster dynamic response with almost no overshoot, shorter settling time and no steady-state error. In this paper, the fuzzy system is directly used as controllers in speed, power and currents. In the robustness tests, a faster dynamic response with definitely no overshoot and a shorter settling time is achieved compared to Ref. [21] with no steady-state error. In addition, the proposed controller is verified against the parameter variations and a short grid voltage unbalance, and good responses are achieved.

8 Conclusions

In this paper, a nonlinear fuzzy inference system has been used to control the power electronic systems of the DFIG. The conventional PI controllers in the indirect vector control have been replaced by FLCs. Simulation of brusque wind speed change, parameter variations and grid voltage unbalance operating conditions of the system are conducted and compared with conventional PI controllers. The simulation results show that by using fuzzy controllers, the settling time is reduced considerably, no overshoot appears and oscillations are damped out faster compared with the conventional PI controllers. Therefore, the transient response provided by the FLCs has been found superior as compared with the conventional PI controllers.

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