Neural network–based improved active and reactive power control of wind-driven double fed induction generator under varying operating conditions

Abstract

Artificial neural network–based power controllers are trained using back propagation algorithm for controlling the active and reactive power of a wind-driven double fed induction generator under varying wind speed conditions and fault conditions. Vector control scheme is used for control of the double fed induction generator. Here stator flux–oriented vector control scheme is implemented for the rotor side converter and grid voltage vector scheme is used for control of grid side converter using tuned proportional–integral active and reactive power controllers, which is later replaced by artificial neural network–based controllers. The artificial neural network controllers are trained using the data obtained from simulation of conventional proportional–integral controllers under varying operating conditions. The intelligent controller makes the generated stator active power to track the reference active power more precisely at specified power factor in both sub-synchronous and super-synchronous modes of operations. Simulation results reveal that the neural network–based controller significantly improves the performance of variable speed wind power generating double fed induction generator under various conditions.

Keywords

Double fed induction generator neural network vector control wind power generation

Introduction

With increasing growth of wind power generation, double fed induction generators (DFIGs) are gaining more attention. Control of DFIG is one of the challenging fields of research. Vector control scheme for DFIG is used widely now a days for variable operation wind power generation. This variable operation wind energy system with DFIG is fed with variable frequency voltage from rotor side and fixed frequency power generation from stator side of the generator. The back-to-back pulse width modulation (PWM) voltage source converter has mainly two important parts: grid side converter (GSC) that maintains the direct current (DC) link voltage at constant value and rotor side converter (RSC) which controls speed of the generator. The control scheme is tuned with stator flux–oriented reference for RSC control and grid voltage vector reference frame for GSC for the decouple control of active and reactive powers of the DFIG under variable speed operations. Also, power converter is designed for low rating, just about 30% of the total generator-rated power, which makes it attractive from economical point of view (Chowdhury and Chellapilla, 2006; Tapia et al., 2003). One of the main advantages of this scheme is that d- and q-axis rotor current can be controlled separately in stator flux–oriented reference frame for decoupled control of active and reactive powers (Vas, 1990). Also as per the grid codes, the wind firms are required to provide reactive power to the grids during fault or dynamic conditions. Various methods were adopted to improve the performance of DFIG during dynamic conditions and reducing the transients in DFIG parameters during grid faults was adopted. Out of these, using proportional resonant controller, crowbar circuits and using artificial intelligent–based controllers were few methods (Hasanien and Al-Ammar, 2012; Slootweg et al., 2001; Xu and Wang, 2007). Now a days, artificial intelligent–based controllers like fuzzy logic or neural network–based controllers are used in place of proportional–integral (PI) controllers which takes into account the system nonlinearity and provides fast and accurate control of performance of DFIG during dynamic conditions (Karimi-Davijani et al., 2009; Mishra et al., 2011). Genetic algorithm tuned fuzzy logic controller is also used for wind turbine–based DFIG for fault ride through condition to improve the dynamic performance of DFIG (Vrionis et al., 2014).

The system is tested during two conditions, which are as follows:

For varying wind conditions.

For unsymmetrical fault and voltage dip.

In this article, the scheme is implemented first with the conventional PI controllers and then with neural network–based controllers in the RSC to control active and reactive power and optimize the power generation from the DFIG.

Modeling of wind turbine

Wind turbines convert the kinetic energy present in the wind into mechanical energy by producing mechanical torque. The power coefficient Cp gives the fraction of the kinetic energy that is converted into mechanical energy by the wind turbine. It is a function of the tip speed ratio (λ) and also depends on the blade pitch angle $(θ)$ for pitch-controlled turbines (Kaloi et al., 2016)

λ = ω_{r t} * \frac{R}{v}

(1)

The mechanical power is given by

Pmech = \frac{ρ}{2} * Cp (λ, θ) {* Ar * v}^{3}

(2)

The power coefficient is

\begin{matrix} Cp (λ, θ) = 0.22 ((\frac{116}{λ_{i}}) - 0.4 * θ - 5) e^{- (12.5) / λ_{i}} \\ where {\frac{1}{λ}}_{i} = \frac{1}{λ + 0.08 * θ} - \frac{0.035}{θ^{3} + 1} \end{matrix}}

(3)

There is a value of optimum tip speed ratio at which the power coefficient is maximized. The variable speed turbines can be made to capture this maximum power by operating them at a blade speed corresponding to optimum tip speed ratio. This may be done by changing the shaft speed of the turbine in proportion to the change in wind speed.

DFIG model

The wound-rotor machine is widely used for wind power generation, due to its varying operating speed and unique feature that it is connected from both stator and rotor side Normally, the stator side is directly connected to the grid and the rotor side is connected through a variable frequency back-to-back PWM power converter to provide bidirectional rotor power flow

\begin{matrix} \begin{matrix} \frac{d}{dt} (I_{sD}) \\ \frac{d}{dt} (I_{sQ}) \end{matrix} \\ \frac{d}{dt} (I_{r α}) \\ \frac{d}{dt} (I_{r β}) \end{matrix} = \begin{array}{l} {\begin{matrix} R_{s} L_{r} I_{sD} - L_{m} (L_{r} ω_{r} \sin θ_{r} + R_{r} \cos θ_{r}) I_{r α} - L_{r} V_{sD} + L_{m} \cos θ_{r} V_{r α} - L_{m} \sin θ_{r} V_{r β} \\ - L_{m}^{2} ω_{r} I_{sQ} + L_{m} (R_{r} \sin θ_{r} - L_{r} ω_{r} \cos θ_{r}) I_{r β} \end{matrix}} / (L_{m}^{2} - L_{s} L_{r}) \\ {\begin{matrix} L_{m}^{2} ω_{r} I_{sD} + L_{m} (L_{r} ω_{r} \cos θ_{r} - R_{r} \sin θ_{r}) I_{r α} - L_{r} V_{sQ} + L_{m} \sin θ_{r} V_{r α} + L_{m} \cos θ_{r} V_{r β} \\ + R_{s} L_{r} I_{sQ} - L_{m} (L_{r} ω_{r} \sin θ_{r} + R_{r} \cos θ_{r}) I_{r β} \end{matrix}} / (L_{m}^{2} - L_{s} L_{r}) \\ {\begin{matrix} - L_{m} (L_{s} ω_{r} \sin θ_{r} + R_{s} \cos θ_{r}) I_{sD} + R_{r} L_{s} I_{r α} + L_{m} \cos θ_{r} V_{sD} + L_{m} \sin θ_{r} V_{sQ} - L_{s} V_{r α} \\ + L_{m}^{2} ω_{r} I_{r β} + L_{m} (L_{s} ω_{r} \cos θ_{r} - R_{s} \sin θ_{r}) I_{sQ} \end{matrix}} / (L_{m}^{2} - L_{s} L_{r}) \\ {\begin{matrix} L_{m} (R_{s} \sin θ_{r} - L_{s} ω_{r} \cos θ_{r}) I_{sD} + R_{r} L_{s} I_{r β} + L_{m} \cos θ_{r} V_{sQ} - L_{m} \sin θ_{r} V_{sD} - L_{s} V_{r β} \\ - L_{m}^{2} ω_{r} I_{r α} - L_{m} (R_{s} \cos θ_{r} + L_{s} ω_{r} \sin θ_{r}) I_{sQ} \end{matrix}} / (L_{m}^{2} - L_{s} L_{r}) \end{array}}

(4)

The operating principle of a double fed machine can be explained using the classic theory of rotating magnetic fields and the well-known d-q model, as well as Clarkes transformation equations of both three-to-two and two-to three axes transformations (Ekanayake et al., 2003). In order to deal with the machine dynamic behavior in the most realistic possible way, both stator and rotor variables are referred to their corresponding natural reference frames in the developed model (Tapia et al., 2003). In other words, the stator side parameters, for example, current and voltage components, are referred to the stationary reference frame, and the rotor side current and voltage components are referred to rotating reference frame at rotor electrical speed.

The direct and quadrature axis flux linkage components

\begin{matrix} λ_{sD} \\ λ_{sQ} \end{matrix} \begin{matrix} = L_{s} I_{sD} + L_{m} I_{rd} \\ = L_{s} I_{sQ} + L_{m} I_{rq} \end{matrix}}

(5)

The torque equations

T_{e m} = \frac{3}{2} * \frac{P}{2} * \frac{L_{m}}{L_{s}} (λ_{s Q} * Ι_{r d} - λ_{s D} * I_{r q})

(6)

The generator equation of motion in per unit

P (\frac{ω_{r}}{ω_{b}}) = \frac{1}{2 H} * (T_{m e c h} - T_{e m} - D * ω_{m})

(7)

RSC control

The variable speed wind turbines can be made to capture the maximum power by operating them at a rotational speed corresponding to the optimum tip speed ratio. Therefore, the tracking of the maximum (reference) power is essential to exploit the advantage of variable speed operation.

This control uses the principle that in the stator flux–oriented frame, the rotor current variation will reflect the stator current variations and hence by controlling the rotor current, the stator active and reactive powers can be controlled, as shown in Figure 1 (Chowdhury and Chellapilla, 2006; Tapia et al., 2003). Reference active power is obtained from maximum power point tracking (MPPT) using the wind turbine equations. This reference active power at a particular wind velocity is computed online using Simulink/S-function coded block. The reactive power set point can also be calculated from active power set point using a desired power factor. In the stator flux–oriented reference frame, reactive power can be controlled by controlling the d-axis rotor current Irx and active power can be controlled by q-axis rotor current Iry obtained from active and reactive power PI controller.

A reference current Iry_ref is derived from the error between reference and actual active power by tuning an active power PI controller. Similarly, a reference current Irx_ref is obtained from the error between reference and actual reactive power by tuning a reactive power PI controller. Both the reference currents are then transformed to a-b-c reference frame for implementing hysteresis modulation for the RSC.

In stator flux–oriented reference frame, Vsy =|Vs.| Thus, the active and reactive power equations in stator flux–oriented reference frame are

P_{S} = - (\frac{3}{2}) * | Vs | {*L}_{m} / L_{s} {*I}_{ry}

(8)

Q_{S} = (\frac{3}{2}) * | Vs | {* L}_{m} / L_{s} (I_{ms} - I_{rx})

(9)

It can be seen that for any given wind speed, there is an optimum rotational speed which generates a maximum power $P_{m a x}$ . It is also important to consider that when a wind speed changes, this optimum rotor speed also varies so as to track the maximum power at any time

P_{sref} = P_{\max}

(10)

Q_{sref} = - P_{sref} *tan φ_{sref}

(11)

The reference rotor currents in stator flux–oriented reference frame which is the output from active and reactive power controllers’ are

I_{rD}^{*} = I_{rx}^{*} \cos ρ_{s} - I_{ry}^{*} \sin ρ_{s}

(12)

I_{rQ}^{*} = I_{rx}^{*} \sin ρ_{s} + I_{ry}^{*} \cos ρ_{s}

(13)

Estimation of the stator flux linkage space phasor angular position with respect to the stationary direct axis as follows

I_{msD} = (L_{s} / L_{m}) {* I}_{sD} + I_{rD}

(14)

I_{msQ} = (L_{s} / L_{m}) {* I}_{sQ} + I_{rQ}

(15)

I_{ms} = \sqrt{I_{msD}^{2} + I_{msQ}^{2}}

(16)

ρ_{s} = \tan^{- 1} (\frac{I_{msQ}}{I_{msD}})

(17)

The rotor side current components need to be changed from their natural frame to the stationary reference frame using rotor angular position with respect to the stationary direct axis as follows

I_{rD} = I_{rα} \cos θ_{r} - I_{r β} \sin θ_{r}

(18)

I_{rQ} = I_{rα} \sin θ_{r} + I_{r β} \cos θ_{r}

(19)

The reference and actual rotor currents in stationary 2-axes are then transformed into a-b-c reference frame for the implementation of hysteresis modulation for the RSC. Each phase current error is compared with the upper and lower hysteresis band. If current error of one of the phases is crossing upper hysteresis band, the lower device of the respective converter leg is turned “ON” and the upper device of the leg is turned “OFF.” If the current error crosses lower hysteresis band, the lower device is turned “OFF” and the upper device is turned “ON.”

The rotor side voltage source PWM converter block is coded in S-function with user-definable parameter and integrated to the Simulink environment. With an isolated neutral, the rotor phase voltages are determined from the following equations (Bose, 2002)

\begin{array}{l} v_{a n} = \frac{2}{3} v_{a 0} - \frac{1}{3} v_{b 0} - \frac{1}{3} v_{c 0} \\ v_{b n} = \frac{2}{3} v_{b 0} - \frac{1}{3} v_{a 0} - \frac{1}{3} v_{c 0} \\ v_{c n} = \frac{2}{3} v_{c 0} - \frac{1}{3} v_{a 0} - \frac{1}{3} v_{b 0} \end{array}

(20)

where $v_{a o}, v_{b o}, a n d v_{c o}$ are either $+ 0.5 v_{d c}$ or $- 0.5 v_{d c}$ corresponding to a upper switch is “ON” or lower switch is “ON,” respectively.

GSC control

The objective of the GSC is to keep the DC link voltage constant irrespective of the direction of rotor power flow. Decoupled control of active and reactive powers flowing between rotor and grid is done using supply voltage vector–oriented control, as shown in Figure 2. In such a scheme, the DC link voltage can be controlled by the control of direct axis line current Ix between the converter and grid in the voltage vector–oriented reference frame. The line current Iy is used to obtain the desired value of reactive power flow between the converter and the grid. Thus, a reference current Ixref is derived from the DC link voltage error, that is, the error between the reference and actual DC link voltage of the converter bridge by tuning a voltage PI controller. The current Iyref is forced to make zero so as to make the displacement to be equal to zero. The actual line current components Ix and Iy are computed considering the line inductance drop between the converter and grid. The reference and actual line currents in the grid voltage vector–oriented frame are then transformed to a-b-c natural reference frame in order to implement hysteresis modulation for GSC using S-function block as like the RSC.

The scheme makes use of the supply voltage angle scheme. By definition, the supply voltage angle $(θ_{s})$ can be stated as

θ_{s} = \tan^{- 1} \frac{V_{s} Q}{V_{s} D}

(21)

The real axis (x) is aligned with the supply voltage phasor. Thus, $V_{y} = 0$ . Hence, the powers between the GSC and the grid are

P_{grid} = (\frac{3}{2}) * (V_{x} {* I}_{x} + V_{y} {* I}_{y}) = (\frac{3}{2}) * (V_{x} {* I}_{x})

(22)

Q_{grid} = (\frac{3}{2}) * (V_{y} {*I}_{x} + V_{x} {*I}_{y}) = (\frac{3}{2}) * (V_{x} {*I}_{y})

(23)

Then the line current components Ix and Iy between the grid and the converter can be obtained from equations (24) and (25)

V_{x} = {R*I}_{x} + L* \frac{d}{dt} (I_{x}) - ω_{S} {*L*I}_{y} + V_{conv_x}

(24)

V_{y} = {R*I}_{y} + L* \frac{d}{dt} (I_{y}) - ω_{S} {*L*I}_{x} + V_{conv_y}

(25)

Modeling of DC link voltage is as follows

P_{ac_grid_conv} = \frac{3}{2} * (I_{x} {*V}_{conv_x} + I_{y} {*V}_{conv_y})

(26)

P_{ac_rotor_conv} = \frac{3}{2} * (I_{rx} {*V}_{rx} + I_{ry} {*V}_{ry})

(27)

DC link power and voltage can be evaluated using equations (28) and (29)

P_{dc} = P_{ac_grid} - P_{ac_rotor} = {E * I}_{dc}

(28)

E = \frac{1}{C} * \int^{} I_{dc} dt

(29)

Design of neural network controller

A feed forward three layered neural network architecture with sigmoid activation function in hidden layer is taken. The layers include the input layer, the hidden layer, and the output layer. The hidden layer consists of multiple numbers of neurons connected to input layer via weights. The network is trained with Levenberg–Marquardt back propagation algorithm (trainlm) (Madhav and Obulesu, 2015; Soares et al., 2009).

Two neural network–based controllers are designed, with input as the error of the reference and actual stator active power and error of the reference and actual stator reactive power, respectively. MATLAB neural network toolbox is used for training the data. The data are obtained by running the simulation using conventional PI controller and exporting the data into the workspace. The input and targets are fixed. Total number of input and output to each neural controller are kept one. Total number of neuron used is 50 for active power controller and 45 for reactive power controller. Total number of hidden layer is 1.

Neural network–based active power controller

Input = Psref-Ps

Target = Iry ref

Output = Iry

Neural network–based reactive power controller

Input = Qsref-Qs

Target = Irxref

Output = Irx

The conventional PI controller–based power controller is replaced by neural network–based active and reactive power controllers. The training of neural is more fast and easy.

Back propagation algorithm

Algorithm for back propagation learning method are as follows:

Initialize random weight and choose learning rate η.

Forward pass for each input patterns and target outputs. Assuming j hidden layer nodes and N input for a two-layer MLP $Y_{k} = f (\sum_{j = 0} w_{jk} O_{j})$ . Where $O_{j}$ is output from each hidden node j: $O_{j} = f (\sum_{j = 0} w_{ij} x_{i})$ .

For each output unit k, compute $δ_{K} = (y_{target} - y_{k}) y_{k} (1 - y_{k})$ .

For hidden unit j (from last to first hidden layer, for the case of more than 1 hidden layer), compute delta: $δ_{j} = O_{j} (1 - O_{j}) \sum_{k} w_{jk} δ_{k}$ .

For all weights change weight by gradient descent $Δ w_{ji} (n) = η δ_{j} (n) y_{j} (n)$ .

For weight from input layer unit i to hidden layer unit j the weight changes by $Δ w_{ji} (n) = η δ_{j} x_{j}$ .

For weight from hidden layer unit j to output layer unit k the weight changes by $Δ w_{jk} (n) = η δ_{k} O_{j}$ .

Levenberg–Marquardt algorithm

To solve second-order training patterns without computing Hessian matrix another algorithm, the Levenberg–Marquardt algorithm designed. For performance function in the form of a least squares, the Hessian matrix can be calculated as

H = J^{T} J

and the gradient can be computed as

{g = J}^{T} e

where J is the Jacobian matrix that contains first derivatives of the network errors with respect to the biases and weights, and e is the error vector. Error back propagation algorithm is used to calculate the Jacobian matrix which is easier than computing Hessian matrix

The approximation to Hessian matrix in the Levenberg–Marquardt is done by the following method

x_{k + 1} = x_{k} - {[J^{T} J + μ I]}^{- 1} J^{T} e

When the constant µ is zero, it is similar to Newton’s method. When µ is larger, then it is similar to gradient descent algorithm with smaller step size. Newton’s method is usually faster and gives better accuracy near error minimum, so it is better to shift toward Newton’s method quickly for fast convergence. Thus, constant µ is gradually decreased after each successful step and is increased only when a tentative step would increase the performance function. In this way, the performance function is always reduced at each iteration of the algorithm (Figure 3).

Simulation results and discussions

During varying wind conditions

Performance of DFIG for varying wind conditions using PI controller and neural network–based controller

The comparative analysis of responses of the DFIG scheme using PI controller and artificial neural network (ANN) controllers is shown in Figures 4 to 9 for constant wind velocity of 6 m/s, for step change in wind velocity (5–7 m/s) and ramp change in wind velocity. Simulation results show various plots such as the reference and actual stator active power, the actual reactive power, rotor speed referred to generator side, the DC link voltage for varying wind conditions.

From Figure 4, it can be observed that using neural network–based controllers, the active power generation increases and approaches the reference power more closely; the reactive power drawn by the DFIG is less and tracking the reference stator reactive power calculated in section “RSC control,” while maintaining the specified power factor at the supply end (from Figure 10). From Figure 5, we observe that the DC link voltage remains almost constant for the entire operating period.

Figure 6 presents the generated stator active power of DFIG for step change in wind speed. From the waveforms obtained, we observe that the actual active power is tracking the reference stator active power obtained from MPPT closely with ANN controllers. In Figure 7, we observe that, with the aid of ANN controllers, the DC link capacitor voltage is almost constant under varying wind velocity. In Figures 8 and 9, the same DFIG parameters were tested but for ramp change in wind speed variation. In this case also we obtain better performance of DFIG using ANN controller. The blue line represents performance using PI controller and black line represents performance using ANN controller

Performance of DFIG during sub-synchronous to super-synchronous mode of operation

Figure 11 shows the performance of DFIG during sub-synchronous mode to super-synchronous mode of operation for ramp change in wind velocity from 4 to 12 m/s. The rotor current changes its phase while the operation changes from sub-synchronous to super-synchronous mode of operation. This ensures that the scheme works well on both sub-synchronous and super-synchronous modes of operation.

During fault and voltage dip conditions

The simulation model of 7.5 kW DFIG was tested for unsymmetrical fault condition (Line-to-Line (LL) fault) with fault clearing time of 200 ms. When the voltage at the stator winding drops suddenly due to grid fault, there is a sudden change in the stator flux of the generator. Demagnetization occurs and electromagnetic torque decreases as compared to mechanical torque from wind turbine. Due to the increase in Mechanical torque, acceleration occurs due to which over-current appears in the stator and rotor circuit and the generator speed increases (Wu et al., 2013). As a result, the reactive power demand of induction generators increases. A reactive power backup or support should be available at the generator terminals; otherwise, it will be drawn from the grid. This over current may cause severe damage to the semiconductors devices in the RSC and large fluctuations of the DC link voltage. If the unbalance is not taken care of, there will be high transients in the stator current with a small amount of disturbance in stator voltage. The unbalanced currents in the windings can create unequal heating as well as disturbances in torque and power pulsation in the generator (Ling, 2016). According to the Indian Grid codes (Central Electricity Regulatory Commission, 2006) during a fault, if the turbine was to stay on line, the active power output has to be reduced in a controlled manner to prevent tripping of the generator. All the same, the active power output should be brought back to the prefault value after the fault is cleared. For this, an intelligent neural network–based active and reactive power controller is used (ElKholy et al., 2017).

The neural network controller improves the performance of DFIG during the grid fault conditions by controlling the reactive power of the DFIG. Figure 12 shows that with the aid of ANN controller generator speed transients is highly reduced, rotor over current is reduced thereby keeping DC link voltage almost constant and giving much smoother response. Figure 13 shows that active power is also smoothly controlled. The pulsations that were present in generated active power were reduced to great extent. During the grid fault reactive power requirement is smoothly achieved and thereby giving reactive power support to the grid.

Conclusion

A neural network–based active and reactive power control method is used to maximize the power generation at a specified power factor from a wind turbine–driven DFIG has been presented in this article. Also the system is tested under unsymmetrical grid fault. The first stage of simulation work yields that with the constant wind velocity, the generator speed also tries to track the maximum power output from the wind turbine using active power PI controller while trying to maintain the supply side power factor at specified value using reactive power PI controller. The DC link voltage also tries to be stable at a constant value using DC link voltage PI controller under varying wind velocities. Hysteresis current controller–based PWM switching for both rotor side and grid side converter (GSCs) ensures fast control of active and reactive power. Furthermore, in order to improve the performance of DFIG, the active and reactive power neural network a based controller are also trained and replaces the existing conventional PI controllers. The neural network–based controller improves the performance of DFIG as compared to that of PI controllers, such as generated active power tracks the reference maximum power at specified power factor more closely; the reactive power supplied to grid is less for maintaining the same power factor at the supply end; fluctuation in reactive power is less and the constancy of DC link voltage is better for any change in wind speed; the rotor over current is also reduced. The scheme also works well in both sub-synchronous and super-synchronous modes of operations. During voltage dip and fault conditions, it is observed that the over currents in rotor circuit have reduced to great extent. The active power fluctuations have decreased. The DC link voltage is almost constant even during the fault. The generator speed fluctuations also decreases to great extent during fault, thus ensuring fast, precise and accurate operation of as the ANN controllers.

Footnotes

Appendix 1

Appendix 2

Rating of the wind turbine:

Wound rotor induction machine:

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

References

Bose

(2002) Modern Power Electronics and AC Drives. Upper Saddle River, NJ: Prentice Hall.

Chowdhury

Chellapilla

(2006) Double-fed induction generator control for variable speed wind power generation. Electric Power Systems Research 76: 786–800.

Central Electricity Regulatory Commission (2006) Indian electricity grid code, 1 April. Available at: http://cercind.gov.in/Regulations/Indian-Electricity-Grid-Code-2006.pdf

Ekanayake

Holdsworth

Jenkins

(2003) Comparison of 5th order and 3rd order machine models for doubly fed induction generator (DFIG) wind turbines. Electric Power Systems Research 67: 207–215.

ElKholy

Metwally

Regal

et al . (2017) Optimal active and reactive power control of wind turbine driven DFIG using TLBO algorithm and artificial neural networks. International Journal of Renewable Energy Technology 8: 132–153.

Hasanien

Al-Ammar

(2012) Dynamic response improvement of doubly fed induction generator-based wind farm using fuzzy logic controller. Journal of Electrical Engineering 63: 281–288.

Kaloi

Wang

Baloch

(2016) Active and reactive power control of the doubly fed induction generator based on wind energy conversion system. Energy Reports 2: 194–200.

Karimi-Davijani

Sheikholeslami

Livani

et al . (2009) Fuzzy logic control of doubly fed induction generator wind turbine. World Applied Sciences Journal 6: 499–508.

Ling

(2016) The fault ride through technologies for doubly fed induction generator wind turbines. Wind Engineering 40: 31–49.

10.

Madhav

Obulesu

(2015) A new hybrid artificial neural network based control of doubly fed induction generator. International Journal of Electrical & Computer Engineering 5: 379–390.

11.

Mishra

Hore

Rahman

(2011) Fuzzy logic based improved active and reactive power control operation of DFIG for wind power generation. In: 2011 IEEE 8th international conference on power electronics and ECCE Asia (ICPE & ECCE), Jeju, 30 May–3 June, pp. 654–661. New York: IEEE.

12.

Pena

. (1996) Doubly fed induction generator using back-to-back PWM converters and its application to variable-speed wind-energy generation. IEE Proceedings-Electric Power Applications 143: 231–241.

13.

Slootweg

Polinder

Kling

(2001) Dynamic modelling of a wind turbine with doubly fed induction generator. In: Power engineering society summer meeting, Vancouver, BC, Canada, 15–19 July, pp. 644–649. New York: IEEE.

14.

Soares

Gonçalves

Martins

et al . (2009) Analysis and NN-based control of doubly fed induction generator in wind power generation. Available at: http://www.icrepq.com/ICREPQ’09/260-soares.pdf

15.

Tapia

Ostolaza

et al . (2003) Modeling and control of a wind turbine driven doubly fed induction generator. IEEE Transactions on Energy Conversion 18: 194–204.

16.

Vas

(1990) Vector Control of AC Machines. Oxford: Oxford University Press.

17.

Vrionis

Koutiva

Vovos

(2014) A genetic algorithm-based low voltage ride-through control strategy for grid connected doubly fed induction wind generators. IEEE Transactions on Power Systems 29: 1325–1334.

18.

Zhu

(2013) Improved control strategy for DFIG wind turbines for low voltage ride through. Energies 6: 1181–1197.

19.

Wang

(2007) Dynamic modeling and control of DFIG-based wind turbines under unbalanced network conditions. IEEE Transactions on Power Systems 22: 314–323.