Maximum Power Extraction Method for Doubly-fed Induction Generator Wind Turbine

This research presents a new scheme to extract the maximal available power from a wind turbine employing a doubly fed induction generator (DFIG). This scheme is developed from the wind turbine’s MPPT-curve. Furthermore, we propose control laws for the rotor and grid side-converters. The stability of the proposed maximum available power method and the control laws are proved mathematically upon Lyapunov’s stability criterion. Their efficiency is tested through the simulations of a DFIG wind turbine in Matlab/Simulink. Simulation results are analyzed and compared with that using a conventional scheme. Thanks to the suggested scheme, the wind turbine can track its maximum power point better and the electric energy output is higher comparing with that using the conventional scheme. Furthermore, by the suggested controllers, the rotor speed and current of the DFIG converged to their desired values. In other words, the wind turbine can achieve stable operations by the suggested control laws.


INTRODUCTION
The maximum power generation of a wind turbine has been interested in several decades and many algorithms have been suggested. According to [1], previous maximum power point tracking (MPPT) methods can be listed into three groups including indirect power controller, direct power controller, and others. The indirect power controller which aims to maximize mechanical power by using tip-speed ratio [2], [3], optimal torque [4], and power signal feedback MPPT algorithm [5] is simplicity and only allows the wind turbine to track its MPPT-curve quickly when a wind speed measurement is precise and instantaneous. In the case of an unavailable wind measurement, a wind turbine using the indirect power controller fails to track its maximum power point quickly and accurately [6], [7]. The direct power controller which maximizes electric power by using the perturbation and observation (P&O) algorithm such as: Hill climb search [8], incremental conductance [9], optimal-relation based MPPT algorithm [10], [11], and hybrid MPPT algorithm [12] does not require any wind turbine knowledge and available anemometer. Unfortunately, a wind turbine using the direct power controller cannot track its maximum power because this controller cannot recognize instantaneously the variation in wind speed. Until now, this controller has been implemented to adjust the voltage and current of DC circuit in a permanent magnetic synchronous generator wind turbine. The last group is developed based on soft computing techniques like Fuzzy [13] and Neural network [14]. A wind turbine using these methods only has a good performance when the full information of the wind turbine is available. However, these methods are complexity and large memory requirement. Hence, a new MPPT scheme for DFIG wind turbines should be researched.
To control the generator-wind turbine, proportional-integral (PI) control is normally implemented because of its simplicity [7], [15], [16]. However, by using the PI control, we cannot guarantee the wind turbine system will become stable operation [17], [18]. Recently, control laws based on sliding mode were suggested for rotor speed adjustment [19], [20]. However, these control laws require an available wind speed measurement. Hence, we need 712 ISSN: 2088-8708 In this research, we suggest a new scheme to extract the maximum available power from a wind turbine employing DFIG. This scheme is developed from the feedback power algorithm but in this research, we do not require an anemometer. New control laws which are developed upon Lyapunov function for rotor speed, current, and voltage are proposed. This scheme is validated through numerical simulations of a wind turbine employing DFIG. From simulation results, we will analyze and compare with the simulation results of a wind turbine using an old MPPT scheme.

DFIG WIND TURBINE
A DFIG-wind turbine is described in previous publications, as shown in Fig. 1. Generally, it consists of a wind turbine, shaft-gearbox, doubly-fed induction generator (DFIG), and back-to-back converter.

Wind turbine
When the wind turbine is rotating at a speed of ω r and wind speed at the wind turbine is V w , the mechanical power of the turbine is calculated through blade length R, air density ρ, and power coefficient C p (λ, β) [21] P m (t) 1 2 The wind turbine's power coefficient C p (λ, β) depends on both pitch angle β and tip speed ratio λ [16] At a constant λ, when β increases C p (β) will be decreased. In contrary, at a constant β, C P (λ) reaches to a maximum value C p (λ opt ) at λ = λ opt .

DFIG
The DFIG's main objective is to convert the mechanical power P m on the wind turbine shaft to electricity power P e . Relationship between P e and P m is described through the DFIG-wind turbine's inertia J Generally, the DFIG is an induction generator so its rotor slip is defined as where p n is the number of pole pairs; N is the gearbox ratio; ω s is the rotational speed of stator flux.
In dq frame, the stator voltage v s v sd v sq and rotor voltage v r v rd v rq are computed from the stator current i s i sd i sq , rotor current i r i rd i rq , stator flux Ψ s (t) = Ψ sd (t) Ψ sq (t) , rotor flux Ψ r (t) = Ψ rd (t) Ψ rq (t) , rotor resistance r r , rotor inductance L r , stator resistance r s , stator inductance where Θ 0 −1 1 0 .
Lemma 1. If we neglect the stator resistance, r s = 0, and choose the dq frame so that Ψ s (t) ≡ Ψ sd 0 then we can write the state-space equation of the DFIG (5) as where Proof. Obviously, if we ensure Ψ s (t) ≡ Ψ sd 0 then by using (5), we have By using (8) and where we used V s = v s (t) = |ω s Ψ sd |. From (8) and (9), we have From (10) and (5), we have where we used σ = L r − L 2 m /L s . To use (11) and (5) From (12), we can extract (6) easily.
From [22] and by using (9) and (10), we calculate the stator side active power P s in the DFIG as

Grid side converter
For the DFIG, the electricity frequency on the rotor side always depends on the rotor speed ω r . Hence, to interface to the connected grid, a back to back converter which includes a rotor side converter(RSC), a DC-link, and a grid side converter (GSC) must be installed on the rotor side of the DFIG [23]. Normally, to reduce harmonic components generated by the GSC, a filter which consists of a resistor R f , an inductor L f in series and a power factor correction pf in parallel is used as Fig. 1.

ISSN: 2088-8708
In dq frame, the relationship of voltage v g = v gd v gq and current i g = i gd i gq of the GSC is written [24] where

MAXIMUM WIND POWER EXTRACTION SCHEME
The optimal power control region of a wind turbine is limited by [25] where ω rmin and ω rrated are the minimum and rated rotor speed, respectively; V wmin and V wrated stand for the minimum and rated wind speed; β is the blade system's pitch angle. Hence, when the wind turbine operates in D, the tip-speed ratio and the rotor speed reference are limited by From (1), to extract the maximization of the mechanical power, we must adjust ω r to obtain the maximization of C p (λ(ω r , V w )). For any wind turbine, we have [24] As the wind turbine operates at λ opt , the rotor speed becomes the optimal rotor speed and the mechanical power becomes maximal In this paper, the power coefficient in D is given as it has an unique maximum point of C pmax = 0.4 at λ opt = 6.7562, and its mechanical power at different wind speed as shown in Fig. 2.

Conventional MPPT-curve scheme
The conventional MPPT-curve method [7] makes The problem is this conventional method cannot track quickly the maximum power point. Hence, we need to propose a new method as next subsection.

Proposal of maximum available power scheme
The subsection aims to propose a new scheme to maximize P m (ω r , V w ) or minimize the error |ω ropt − ω r (t)|. To obtain this target, we propose ω ref (t) satisfying where k, α, y max are positive constants; and From (23) and (24), we can see that the proposed scheme is developed from the conventional MPPT method.

CONTROLLER DESIGN FOR DFIG 4.1. Rotor side control
The purpose of RSC controller is to reduce the errors (i rd − i rdref ) and (ω r − ω rref ) in which i rdref and ω rref are the reference of i rd and ω r , respectively. From (3), (6), (13), to make ω r converge to ω rref , we can adjust i rq to a reference value i rqref corresponding ω rref . In [7], this task is carried by traditional PI controls. In this research, to obtain the above target, we design v r of the DFIG (5) as where, k pr > 0, k ir > 0 and matrix K r > 0. whereĴ Jb .

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ISSN: 2088-8708 Proof. Let define By substituting (26) into (6), we have (27) can be rewritten as and by substituting (32) into (34), we have Then, When we define a Lyapunov function as V r e r (t)E r e r (t), its derivative is By substituting (35) into (37), and noting that Q r + Q r =Q r , we have d dt V r = −e r (t) Q r + Q r e r (t) = −e r (t)Q r e r (t) ≤ −λ min (Q r )e r (t)e r (t).

Grid-Side Control
In this section, we propose a new control law such that V dc and i gq are maintained at their references V dcref and i gqref , respectively. To maintain V dc at V dcref , we need to make i gd converge to i gdref corresponding to V dcref .

Theorem 2. For any
and if there exist k pg > 0, k ig > 0, and K g > 0 with

ISSN: 2088-8708
Proof. Let define e g (t) = e v (t) e ig (t) . By using (47) and (14), we have Furthermore, by taking time derivative of (48) and then using (51), we have Hence, where If we use a Lyapunov function as V g = e g (t) E g e g (t), its time derivative will be By substituting (53) into (55), we have Hence, if (50) holds, then d dt V g < 0 for all nonzero e g . This completes the proof of Theorem 2.

SIMULATION RESULT AND DISCUSSION
To evaluate the performance of the suggested MPPT scheme, we compare the simulation results of the 1.5 MW DFIG wind turbine with that using the conventional MPPT-curve scheme with traditional PI controls [7]. In this research, the generator and turbine parameters [22] as shown in Table 1 are used. With the power coefficient (20), the region D is In this region, ζ(ω r , V w ) as Fig. 3, which gives the minimum value ζ, min ζ(ω r , V w ) = 1.271 × 10 5 . Here, we use RSC controller's parameter as k ir = 0.4J, k pr = 0.65J, K r = J diag(0.5, 1), k = 0.3J, α = 0.2, y max = 0.1ω rrated .
For a wind profile with d dt V w ≤ 0.44m/s 2 , the boundary of |ω ropt − ω r | is determined as Table 2. Table 2. Limitation of |ω ropt − ω r | as µ 1 = 1 and µ 2 = 2 0.1895 0.5915 |ω ropt − ω r | 1.2248rad/s 0.3775 rad/s When the wind profile as Fig. 4a is used, simulation results are demonstrated in Fig. 4. Fig. 4b shows that when the wind speed has an insignificant change, the turbine speed is almost kept up at its optimal value. Since the wind turbine's large inertia, the turbine speed fails to respond instantaneously to the rapid change of the wind; this makes the turbine speed impossible to keep up at its optimal value. Therefore, the error |ω ropt − ω r | increases when the wind velocity changes rapidly. However, comparing with the turbine using the old MPPT scheme, by using the suggested scheme, the turbine speed can retain its optimal value more promptly because of the decrease in inertia from J to (J − α) and the error |ω ropt − ω r | is smaller. As a result, during a rapid change in wind conditions, in the ISSN: 2088-8708 proposed method, C p restores C pmax more quickly, as shown in Fig. 4c. Obviously, by implementing the old MPPT scheme, the C p can be reduced to to 0.363 while by implementing the proposed scheme, this data is 0.393. Figure 4d shows the efficiency of the suggested method comparing with the conventional one in terms of mechanical power. When the wind velocity varies insignificantly, the error (P max − P m ) in the wind turbine using the suggested scheme is like that using the conventional one. However, this error becomes significant when the wind changes suddenly; by using the new method this error is significant smaller comparing with that using the old one thanks to the restoration of C p . Fig. 4e indicates that to increase the turbine velocity in the period of 20s-40s, the turbine using the offered scheme requires a higher mechanical power comparing with that using the old one. However, the stored mechanical power is returned in the interval of 60s-75s in which the rotor speed decreases. Hence, in the period of 20s-40s, comparing with the DFIG using the suggested scheme, the electric energy generated by the DFIG using the old MPPT method is little higher but in the 60s-75s interval, it becomes opposite. As a result, accumulating to the end of simulation, the wind turbine using the conventional method fails to generate the electrical energy in total as high as that using the proposed method, as Fig. 4e. This indicates the quality of the suggested MPPT scheme. Fig. 5 shows the control quality of the RSC and GSC. Both (ω 3 rref − ω 3 r ) and (i rdref − i rd ) in Fig. 5a are very small, it means ω r and i rd track their reference values; in other words, the control law proposing for the RSC has a good performance. Likely, from Fig. 5b, the errors of (V 2 dcref − V 2 dc ) and (i gqref − i gq ) are about zero; in other words, the controller suggesting for the GSC has a qualified performance.
When a measurement noise, 5% of rated values, is added to the measurement signals, i, ω r , with the wind profile as Fig. 4a, the simulation results are shown in Fig. 6. This figure indicates that with the above noise measurement, the turbine using the recommended MPPT scheme still tracks its maximum points more exactly comparing with the turbine using the old MPPT scheme. However, comparing with the case of pure measurement as Fig. 4, the measurement noise causes a negative impact on the turbine performance but this impact is insignificant. Fig. 7 is the simulation results for a wind profile which varies rapidly as Fig. 7a. It is easy to see from Fig. 7b and Fig. 7c that the turbine using the suggested scheme has more qualified performance in both the power coefficient C p and the electrical energy in total comparing with the case using the conventional scheme.

CONCLUSIONS
This paper suggested a new MPPT scheme for variable speed wind turbines using a DFIG. The suggested scheme allows the turbine tracking the maximum-power-point more effectively than the turbine using the MPPTcurve scheme. As can be seen from the simulation results, by using the suggested scheme, C p almost keeps up C pmax , ω r was approximate to ω ropt and the electric energy generated by the DFIG was higher comparing with that using the conventional scheme. Furthermore, by the suggested controllers, the rotor speed and current of the DFIG converged to their desired values. Thus, by the suggested control law, the wind turbine can achieve stable operations.