Active and Reactive Powers Control of DFIG Based WECS Using PI Controller and Artificial Neural Network Based Controller

Variable speed wind turbines are generally a megawatt class, especially in wind farms. Currently, doubly fed induction generator based wind turbines are the preferred choice for high capacity wind farms due of its unique features such as flexible control, low cost, high efficiency and ability to independently control active and reactive powers exchange with the grid system [1-3]. The DFIG stator winding is connected directly to the grid, while its rotor is connected indirectly to the same grid via a back-to-back power converter. The back-to-back converter has to handle only a fraction (30%) of the total power [4].

Regardless of the large advantages of DFIG, there is a challenging control problem, because of its nonlinear multi-variable system and being highly coupled. Therefore, a decoupled active and reactive powers control technique is mandatory to achieve a constant operating frequency at variable wind speeds [4, 5].

Recently, several papers have studied the control techniques of DFIG [6-14]. Some used a simple field-oriented vector control using PI controllers [6-10]. Others used nonlinear model predictive control [11]. In addition, others used intelligent control techniques, such as genetic algorithm, fuzzy logic and artificial neural network [12-14].

This paper proposes a new control of a DFIG in a WECS using an ANN based controller. This new control is compared with the conventional PI controller. A brief overview of the artificial neural network is presented in section 2, followed by a brief description of the system including its modeling in sections 3. Both of the PI based control technique and ANN based control technique are presented in sections 4. Obtained simulation results of the proposed control techniques are presented and discussed in section 5.

The studied system is shown in Figure 2. The system components are: the wind turbine, induction generator, voltage source converter and the electrical grid. The process of WECS is to transforms wind energy into mechanical energy by wind turbine blades and, eventually, into electrical energy through the generator.

Wind turbines use a doubly fed induction generator consisting of a wound rotor induction generator and an AC/DC/AC converter. The stator winding is connected directly to the grid while the rotor is fed at variable frequency, phase, and magnitude through the converter.

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Figure 2. Wind energy conversion system based on a DFIG

3.1 Modeling of wind turbine

The mathematical equation of the mechanical power extracted from the wind power can expressed as follows:

${{P}_{t}}=\frac{1}{2}\rho {{R}^{2}}{{v}^{3}}{{C}_{p}}\left( \lambda ,\beta  \right)$        (1)              

The mechanical torque T_t is:

${{T}_{t}}=\frac{{{P}_{t}}}{{{\Omega }_{t}}}=\frac{1}{2\lambda }\rho \pi {{R}^{3}}{{v}^{2}}{{C}_{p}}\left( \lambda ,\beta  \right)$                          (2)

where, v is wind speed, ρ is air density (1,225 kg/m³), R is blade radius, Ω_t is angular speed of the turbine and C_p(λ,β) is the turbine power coefficient which is function of the pitch angle of the rotor blades β and the tip speed ratio λ.

The turbine power coefficient can be described as [8]:

${{C}_{p}}\left( \lambda ,\beta  \right)=\left( 0.35\text{ }-\text{ }0.0167\cdot \left( \beta -2 \right) \right)\cdot \sin \left( \frac{\pi \cdot \left( \lambda +0.1 \right)}{14.34-0.3\left( \beta -2 \right)} \right)-\left( 0.00184\cdot \left( \lambda -3 \right)\cdot \left( \beta -2 \right) \right)$             (3)

The maximum value of power coefficient C_p (C_{p_max}=0.35) is achieved for β equal to 2 degree and for λ equal to 7.07. Tip speed ratio λ is defined as:

$\lambda =\frac{\left( {{\Omega }_{t}}\cdot R \right)}{v}$         (4)

The system is composed by three-bladed wind turbine coupled to the rotor of the DFIG though a mechanical gearbox whose gear ratio G is chosen in order to set the generator shaft speed Ω_mec within a desired speed range.

The system dynamics is given by:

$J\frac{d{{\Omega }_{mec}}}{dt}={{T}_{g}}-{{T}_{em}}-f{{\Omega }_{mec}}$  (5)

where, T_g is the mechanical torque of the generator, J and f are the moment of inertia of the system and the friction coefficient.

The turbine model in the form of diagram blocks is represents in Figure 3.

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Figure 3. Wind Turbine model

3.2 Modeling of double fed induction generator

Park mathematical model of the DFIG is given by the following Eqns. [2-8]:

$\left\{ \begin{align}  & {{v}_{sd}}=-{{R}_{s}}{{i}_{sd}}+\frac{d}{dt}{{\phi }_{sd}}-{{\omega }_{s}}{{\phi }_{sq}} \\  & {{v}_{sq}}=-{{R}_{s}}{{i}_{sq}}+\frac{d}{dt}{{\phi }_{sq}}+{{\omega }_{s}}{{\phi }_{sd}} \\  & {{v}_{rd}}={{R}_{r}}{{i}_{rd}}+\frac{d}{dt}{{\phi }_{rd}}-{{\omega }_{r}}{{\phi }_{rq}} \\  & {{v}_{rq}}={{R}_{r}}{{i}_{rq}}+\frac{d}{dt}{{\phi }_{rq}}+{{\omega }_{r}}{{\phi }_{rd}} \\ \end{align} \right.$             (6)

$\left\{ \begin{align}  & {{\phi }_{sd}}=-{{L}_{s}}{{i}_{sd}}+M{{i}_{rd}} \\  & {{\phi }_{sq}}=-{{L}_{s}}{{i}_{sq}}+M{{i}_{rq}} \\  & {{\phi }_{rd}}={{L}_{r}}{{i}_{rd}}-M{{i}_{sd}} \\  & {{\phi }_{rq}}={{L}_{r}}{{i}_{rq}}-M{{i}_{sq}} \\ \end{align} \right.$           (7)

The DFIG electromagnetic torque can be expressed by:

${{T}_{em}}=\frac{pM}{{{L}_{s}}}\left( {{i}_{rd}}{{\phi }_{sq}}-{{i}_{rq}}{{\phi }_{sd}} \right)$       (8)

The stator active and reactive powers equations can be written as:

$\left\{ \begin{align}  & {{P}_{s}}=-{{v}_{sd}}{{i}_{sd}}-{{v}_{sq}}{{i}_{sq}} \\  & {{Q}_{s}}=-{{v}_{sq}}{{i}_{sd}}+{{v}_{sd}}{{i}_{sq}} \\ \end{align} \right.$            (9)

here:

• v_sd,v_sq,v_rd,v_rq: stator and rotor voltage components.

• i_sd,i_sq,i_rd,i_rq: stator and rotor current components.

• Φ_sd, Φ_sq, Φ_rd, Φ_rq: stator and rotor flux components.

• ω_s,ω_r: stator and rotor pulsations.

• R_s,R_r: are stator and rotor resistances.

• L_s,L_r are stator and rotor inductances.

• M is mutual inductance.

The stator active and reactive powers vector uncoupled control can be accomplished by orienting the Park frame (d,q) so that the (d) axis is aligned with the stator flux [2-8]. Hence, the stator flux becomes:

$\left\{ \begin{align}  & {{\phi }_{sd}}={{\phi }_{s}}=-{{L}_{s}}{{i}_{sd}}+M{{i}_{rd}} \\  & {{\phi }_{sq}}=0=-{{L}_{s}}{{i}_{sq}}+M{{i}_{rq}} \\ \end{align} \right. $           (10)

By neglecting the stator windings resistances (for high power generators) the stator voltages equations become:

$\left\{ \begin{align}  & {{v}_{sd=0}} \\  & {{v}_{sq}}={{v}_{s}}={{\omega }_{s}}{{\phi }_{s}} \\ \end{align} \right.$                  (11)

The stator currents depend on rotor currents via the following equation:

$\left\{ \begin{smallmatrix}  {{i}_{sd}}=\frac{M}{{{L}_{s}}}{{i}_{rd}}-\frac{{{\phi }_{s}}}{{{L}_{s}}} \\  {{i}_{sq}}=\frac{M}{{{L}_{s}}}{{i}_{rq}} \end{smallmatrix} \right.$             (12)

The stator active and reactive powers can be written as:

$\left\{ \begin{smallmatrix}  {{P}_{s}}=-{{v}_{s}}{{i}_{sq}}=-\frac{{{v}_{s}}M}{{{L}_{s}}}{{i}_{rq}} \\  {{Q}_{s}}=-{{v}_{s}}{{i}_{sd}}=-\frac{{{v}_{s}}M}{{{L}_{s}}}{{i}_{rd}}+\frac{{{v}_{s}}^{2}}{{{L}_{s}}{{\omega }_{s}}} \end{smallmatrix} \right.$          (13)

Combining (7) and (12) yields:

$\left\{ \begin{align}  & {{\phi }_{rd}}=\left( {{L}_{r}}-\frac{{{M}^{2}}}{{{L}_{s}}} \right){{i}_{rd}}+\frac{M}{{{L}_{s}}}{{\phi }_{s}}=\sigma {{L}_{r}}{{i}_{rq}}+\frac{M}{{{L}_{s}}}\phi  \\  & {{\phi }_{rq}}=\left( {{L}_{r}}-\frac{{{M}^{2}}}{{{L}_{s}}} \right){{i}_{rq}}=\sigma {{L}_{r}}{{i}_{rq}} \\ \end{align} \right.$              (14)

By substituting (14) in (6), we obtain:

$\left\{ \begin{smallmatrix}  {{v}_{rd}}={{R}_{r}}{{i}_{rd}}+\sigma {{L}_{r}}\frac{d{{i}_{rd}}}{dt}-\sigma {{L}_{r}}{{\omega }_{r}}{{i}_{rq}} \\  {{v}_{rq}}={{R}_{r}}{{i}_{rq}}+\sigma {{L}_{r}}\frac{d{{i}_{rq}}}{dt}+\sigma {{L}_{r}}{{\omega }_{r}}{{i}_{rd}}+\frac{M}{{{L}_{s}}}{{\omega }_{r}}{{\phi }_{s}} \end{smallmatrix} \right.$              (15)

where, $\sigma =1-\frac{{{M}^{2}}}{{{L}_{s}}{{L}_{r}}}$ is leakage factor.

In steady state, the voltage expressions are given by:

$\left\{ \begin{smallmatrix}  {{v}_{rd}}={{R}_{r}}{{i}_{rd}}+{{e}_{rd}} \\  {{v}_{rq}}={{R}_{r}}{{i}_{rq}}+{{e}_{rq}}+{{e}_{\phi }} \end{smallmatrix} \right.$                   (16)

$\left\{ \begin{matrix}   {{e}_{rd}}=-\sigma {{L}_{r}}{{\omega }_{r}}{{i}_{rq}}  \\   {{e}_{rq}}=\sigma {{L}_{r}}{{\omega }_{r}}{{i}_{rd}}  \\   {{e}_{_{\phi }}}={}^{M}/{}_{Ls}{{\omega }_{r}}{{\phi }_{s}}  \\\end{matrix} \right.$             (17)

These previous equations can represent the DFIG simplified Model scheme as shown in Figure 4.

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Figure 4. DFIG Simplified Model scheme

The system modeling was developed and simulated in MATLAB/SIMULINK environment using the Simscape Power Systems toolbox for verifying the validity of the proposed control strategy. System parameters are given in Table 1.

Table 1. Simulation parameters

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(a) active power control ANN

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(b) reactive power control ANN

Figure 8. Training performance for DFIG

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Figure 9. DFIG stator active and reactive powers

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Figure 10. WECS Simulink model block diagram

Figure 8 shows the training performance plot for DFIG active and reactive powers control ANNs. Training performance is based on mean square error between desired output and actual output of ANNs. From Figure 8a, it can be seen that best training performance for active power control ANN is equal to 0.30145e-5. Likewise, from Figure 8b, it can be seen that best training performance for reactive power control ANN is equal to 0.53278e-5.

Table 2. Comparative results between PI based control and ANN based control

Figure 9 shows the step response simulation results of DFIG active and reactive powers control using the average model (IGBT’s of the RSC are represented by equivalent voltage sources). To verify the proposed control strategy, the ANN based control is compared with the PI based control. As can be seen below (Figure 9), stator active and reactive powers, tracks there references for both ANN based control and PI based control. However, the ANN based control provide a fast response and robust control. The overall measurement results are summarized in Table 2.

Figure 10 shows the detailed WECS Simulink model in MATLAB/Simulink environment. This model includes detailed representation of power electronic IGBT converters, in order to achieve more accuracy. Pulse width modulation frequency is set to 10 kHz.

A wind speed of 13 m/s has been applied on blades of the turbine, which corresponds to the nominal operation of the DFIG. The slip equal to -30% in hyper-synchronous mode, with a rotational speed equal to 1950 rpm, as shown in Figure 11.

As can be seen from Figure 12, both of the stator active power (P_s) and stator reactive power (Q_s) are well regulated near their reference values.

The reference stator active power (P_s^*) is generated using the MPPT control strategy. The WECS operates at unity power factor before the time t = 4.6 s and after the time t = 5.4 s because the reference reactive power Q_s^* is equal to 0 VAR. In the time interval of t = [4.6 s, 5.0 s] and t = [5.0 s, 5.4 s], the reference stator reactive power is set to −1 MVAR and 1 MVAR respectively. A little variation of stator active power (P_s^*) can be observed, due to the important variation of rotor reactive power.

Figure 13 shows the temporal evolutions of different electrical powers of the WECS. It can be seen that, the stator reactive power Q_s changes correspondently to the changing in the rotor current i_rd and rotor reactive power Q_r. It is also noticed that when the stator reactive power Q_s equal to 0 VAR (before the time t = 4.6 s and after the time t = 5.4 s), the rotor reactive power Q_r is not equal to 0 VAR, because the DFIG requires a reactive power for its magnetization. It also can be observed that, the WECS operated in nominal conditions and generate a total power P_dfig equal to 3 MW, which demonstrate the performance of the proposed control strategy.

Figure 14 show stator and rotor voltage-current. It can be observed from Figure 14a, that the stator voltage-current are symmetric to ensure a unity power factor at the connection point of the stator with the electrical grid.

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Figure 11. Generator rotational speed

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Figure 12. Stator active and reactive powers

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Figure 13. dq rotor currents, rotor active and reactive powers and total active and reactive powers

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(a) stator voltage-current

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(b) rotor voltage-current

Figure 14. Voltage-current

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Figure 15. Power coefficient Cp and speed ratio λ

Figure 15 shows respectively power coefficient Cp versus time and speed ratio λ versus time. As remarked, power coefficient Cp pursues its maximal values offering maximal mechanical power to the DFIG rotor. In addition, speed ratio λ is at its optimal value equal to 7.07 at β equal to 2°.