DFIG sliding mode control fed by back-to-back PWM converter with DC-link voltage control for variable speed wind turbine

Abstract

This paper proposes an indirect power control of doubly fed induction generator (DFIG) with the rotor connected to the electric grid through a back-to-back pulse width modulation (PWM) converter for variable speed wind power generation. Appropriate state space model of the DFIG is deduced. An original control strategy based on a variable structure control theory, also called sliding mode control, is applied to achieve the control of the active and reactive power exchanged between the stator of the DFIG and the grid. A proportional-integral-(PI) controller is used to keep the DC-link voltage constant for a back-to-back PWM converter. Simulations are conducted for validation of the digital controller operation using Matlab/Simulink software.

Keywords

doubly fed induction generator (DFIG) / wind turbine / back-to-back pulse width modulation (PWM) / DC-link voltage / sliding mode control

Introduction

The wind energy systems using a doubly fed induction generator (DFIG) have some advantages due to variable speed operation and four quadrants active and reactive power capabilities compared with fixed speed induction generators. The stator of DFIG is connected direct to the grid and the rotor links the grid by a bi-directional converter. The rotor converter aims at the active and reactive power control between the stator and AC supply of the DFIG [1].

DFIG-based wind generation is the state-of-the-art wind generator technology. The stator of a DFIG is connected directly to the grid while the rotor of a DFIG is connected through the rotor-side converter (RSC), the DC-link and the grid-side converter (GSC) to the grid [2].

Vector control technology is used to control the generator, and the rotor of DFIG is connected to an AC excitation of which the frequency, phase, and magnitude can be adjusted. Therefore, constant operating frequency can be achieved at variable wind speeds [3].

This paper adopts the vector transformation control method of stator-oriented magnetic field to realize the decoupling control of the stator active and reactive power using sliding mode control (SMC).

Sliding mode theory, stemmed from the variable structure control family, has been used for the induction motor drive for a long time. It has for long been known for its capabilities in accounting for modeling imprecision and bounded disturbances. It achieves robust control by adding a discontinuous control signal across the sliding surface, satisfying the sliding condition [4].

The power converter connected to the line is usually used for both last drive cases as the well known three phase diode bridge rectifier. In this converter, the power can only flow from the utility AC side to the DC side and the line current is not continuous. Because this type of AC-DC conversion does not control line current harmonics, the displacement power factor is poor and the DC side voltage is not constant [5].

To remedy these disadvantages, a reversible converter is used to replace the diode-bridge rectifier and to permit a reversible power line flow which allows the energy recovered from the rotor-side of DFIG to be fed back to the grid. To maintain constant the DC-link voltage, it can be regulated by the proportional-integral-(PI) controller.

In this paper, the SMC method is applied to control the active and reactive power of the DFIG based on wind energy using a back-to-back PWM converter with DC-link voltage control.

Wind turbine model

The aerodynamic power, which is converted by a wind turbine, P_t is dependent on the power coefficient C_p. It is given by Ref. [6]. As

(1)P_{\mathrm{t}}={\displaystyle \frac{\mathrm{1}}{\mathrm{2}}}\pi C_p\rho R^{\mathrm{2}}{v}^{\mathrm{3}},

where \rho is the air density, Ris the blade length, and \nu is the wind speed. The turbine torque is the ratio of the output power to the shaft speed {\mathrm{\Omega }}_t:

(2)C_t={\displaystyle \frac{P_t}{{\mathrm{\Omega }}_t}}.

The turbine is normally coupled to the generator shaft through a gearbox whose gear ratio G is chosen in order to set the generator shaft speed within a desired speed range. Neglecting the transmission losses, the torque and shaft speed of the wind turbine, referred to the generator side of the gear box, are given by

(3)C_g={\displaystyle \frac{C_t}{G}}\mathrm{a}\mathrm{n}\mathrm{d}{\mathrm{\Omega }}_t={\displaystyle \frac{{\mathrm{\Omega }}_{mec}}{G}},

where {\mathrm{\Omega }}_{mec} is the generator shaft speed.

A wind turbine can only convert just a certain percentage of the captured wind power. This percentage is represented by C_p(\beta ,\lambda )which is a function of the wind speed, the turbine speed and the pith angle of specific wind turbine blades.

Although this equation seems simple, C_p is dependent on the ratio \lambda between the turbine angular velocity {\mathrm{\Omega }}_tand the wind speed \nu. This ratio is called the tip speed ratio:

(4)\lambda ={\displaystyle \frac{{\mathrm{\Omega }}_{t}R}{\nu }}.

C_p can be described in Ref. [7]. As

(5)C_p(\beta ,\lambda )=[0.5-0.0167(\beta -2)]sin\left({\displaystyle \frac{\pi (\lambda +0.1)}{18.5-0.3(\beta -2)}}\right)-0.00184(\lambda -3)(\beta -2).

A typical relationship between C_p, \beta and \lambda is shown in Fig. 1.

It is observed apparently from Fig. 1 that there is a value of \lambda for which C_p is maximum and that maximize the power for a given wind speed. The peak power for each wind speed occurs at the point where C_p is maximized. To maximize the generated power, it is, therefore, desirable for the generator to have a power characteristic that will follow the maximum C_{p\_\max } line.

The maximum value of C_p (C_{p\_\max }=0.5) is achieved for \beta =\mathrm{2} degree and for {\lambda }_{opt}=\mathrm{9.2}. The reference mechanical power value must be set, as in Ref.[8], to

(6)P_{m\_ref}={\displaystyle \frac{\mathrm{1}}{\mathrm{2}}}{\displaystyle \frac{C_{p\_max}}{{\lambda }_{opt}^3}}\rho \pi R^{\mathrm{5}}{\displaystyle \frac{{\mathrm{\Omega }}_{mec}^{\mathrm{3}}}{G^{\mathrm{3}}}}.

The electromagnetic torque reference value also must be set to

(7)C_{em\_ref}={\displaystyle \frac{P_{m\_ref}}{{\mathrm{\Omega }}_t}}={\displaystyle \frac{\mathrm{1}}{\mathrm{2}}}{\displaystyle \frac{C_{p\_\max }}{{\lambda }_{opt}^3}}\rho \pi R^{\mathrm{5}}{\displaystyle \frac{{\mathrm{\Omega }}_{mec}^2}{G^{\mathrm{3}}}}.

DFIG model

The general electrical state model of the induction machine obtained using Park transformation is given in Ref. [9].

Stator and rotor voltages

(8)$$\begin{gathered} \{{\mathit{U}}_{s\mathit{d}}={\mathit{R}}_s{\mathit{i}}_{s\mathit{d}}+{\displaystyle \frac{d}{d\mathit{t}}}{\mathit{\varphi }}_{s\mathit{d}}-{\omega }_s{\mathit{\varphi }}_{s\mathit{q}}, \\ {\mathit{U}}_{s\mathit{q}}={\mathit{R}}_s{\mathit{i}}_{s\mathit{q}}+{\displaystyle \frac{d}{d\mathit{t}}}{\mathit{\varphi }}_{s\mathit{q}}+{\omega }_s{\mathit{\varphi }}_{s\mathit{d}}, \\ {\mathit{U}}_{r\mathit{d}}={\mathit{R}}_r{\mathit{i}}_{r\mathit{d}}+{\displaystyle \frac{d}{d\mathit{t}}}{\mathit{\varphi }}_{r\mathit{d}}-({\omega }_s\mathrm{-}\omega ){\mathit{\varphi }}_{r\mathit{q}}, \\ {\mathit{U}}_{r\mathit{q}}={\mathit{R}}_r{\mathit{i}}_{r\mathit{q}}+{\displaystyle \frac{d}{d\mathit{t}}}{\mathit{\varphi }}_{r\mathit{q}}+({\omega }_s\mathrm{-}\omega ){\mathit{\varphi }}_{r\mathit{d}}. \end{gathered}$$

Stator and rotor fluxes

(9)$$\begin{gathered} \{{\mathit{\varphi }}_{s\mathit{d}}{\mathit{L}}_s{\mathit{i}}_{s\mathit{d}}+\mathit{M}{\mathit{i}}_{r\mathit{d}}, \\ {\mathit{\varphi }}_{s\mathit{q}}={\mathit{L}}_s{\mathit{i}}_{s\mathit{q}}+\mathit{M}{\mathit{i}}_{r\mathit{q}}, \\ {\mathit{\varphi }}_{r\mathit{d}}={\mathit{L}}_r{\mathit{i}}_{r\mathit{d}}+\mathit{M}{\mathit{i}}_{s\mathit{d}}, \\ {\mathit{\varphi }}_{r\mathit{q}}={\mathit{L}}_r{\mathit{i}}_{r\mathit{q}}+\mathit{M}{\mathit{i}}_{s\mathit{q}}. \end{gathered}$$

The electromagnetic torque is done as

(10)C_e=P{\displaystyle \frac{M}{L_s}}({\varphi }_{sd}{\mathit{i}}_{r\mathit{q}}-{\varphi }_{sq}{\mathit{i}}_{r\mathit{d}}),

and its associated motion equation is

(11)C_e-C_r=J{\displaystyle \frac{d\mathrm{\Omega }}{dt}}.

Control of generator and its associated converters

Figure 2 demonstrates the main circuit topology of a DFIG system with a back-to-back PWM converter, which is composed of a GSC, a RSC and a DC-link capacitor. Though a few schemes of control, the DC-link voltage of the back-to-back PWM converter have been studied [10].

In the back-to-back PWM converter of DFIG, the bidirectional power is transferred between the grid-side and the generator rotor-side.

GSC and DC-Link Voltage Control

Figure. 3 presents the GSC configuration.

Then there are the following relations

(12)$$\begin{gathered} \{v_{1n}\mathit{=}{\displaystyle \frac{1}{3}}(2{\mathit{v}}_1-v_2-v_3), \\ {v}_{2n}\mathit{=}{\displaystyle \frac{1}{3}}(-{\mathit{v}}_1+2v_2-v_3), \\ {v}_{3n}\mathit{=}{\displaystyle \frac{1}{3}}(-{\mathit{v}}_1-v_2+2v_3). \end{gathered}$$

According to the closing or the opening of the switches K_{\mathit{i}\mathit{j}}, the voltages of branch v_{\mathit{i}} can be equal to U_c or 0. Other variables such as S_{11}, S_{12} and S_{13} are introduced which take 1 if the switch K_{ij} is closed or 0 if it is blocked. Equation (12) can be rewritten as

(13)\left[\begin{array}{c}{v}_{\ln }\\ v_{2\mathrm{n}}\\ v_{3\mathrm{n}}\end{array}\right]={\displaystyle \frac{U_c}{3}}\left[\begin{array}{lll}2\hfill & -1\hfill & -1\hfill \\ -1\hfill & 2\hfill & -1\hfill \\ -1\hfill & -1\hfill & 2\hfill \end{array}\right]\left[\begin{array}{c}{S}_{11}\\ S_{21}\\ S_{31}\end{array}\right]

The rectified current can be written as

(14)i_{rec}=S_{11}{i}_{\mathit{a}}+S_{\mathrm{21}}{i}_{\mathit{b}}+S_{31}{i}_c,

where S_{\mathit{i}1} presents a logical signal deduced from the application of the control technique of PWM. In this paper, the moments of commutation are determined by a comparison with hysteresis between the grid currents i_{\mathit{a}\mathit{b}\mathit{c}} and the reference currents i_{\mathit{a}\mathit{b}\mathit{c}\mathit{\_}ref}.

The terminal voltage of the capacitor is calculated by

(15)C_f{\displaystyle \frac{d{U}_c}{dt}}=i_c=i_{rec}-i_f=S_{11}{i}_a+S_{21}{i}_b+S_{31}{i}_c-i_f.

Figure 4 depicts the control block diagram of a vector control strategy for the GSC.

The GSC is usually controlled with a vector control strategy with the grid voltage orientation [10]. This voltage frame corresponds to the axes d-q, which makes it possible to decouple the expressions from the active and the reactive power exchanged between the grid and the rotor-side. The control of active power and consequent control of the DC-link voltage are realized by the intermediary of reference active current i_{\mathit{d}\_ref} and the reactive power by the intermediary of reference reactive current i_{\mathit{q}\_ref}. To guarantee a unity power factor at the grid-side, the reference reactive current i_{q_ref.} is maintained to zero.

RSC Control

The RSC is used to control the stator active and reactive power of DFIG.

Active and Reactive DFIG Indirect Power Control

A d-q reference frame synchronized with the stator flux is employed. By setting the quadratic component of the stator to the null value as in Ref. [6],

(16){\varphi }_{sd}={\varphi }_s\mathrm{a}\mathrm{n}\mathrm{d}{\varphi }_{sq}=\mathrm{0}

The torque is simplified as

(17)C_e=P{\displaystyle \frac{M}{L_s}}{\mathit{i}}_{r\mathit{q}}{\varphi }_{s\mathit{d}}.

By neglecting the stator resistance {\mathit{R}}_s, Eq. (8) gives

(18){\mathit{U}}_{\mathrm{s}\mathit{d}}=\mathrm{0}\mathrm{a}\mathrm{n}\mathrm{d}{U}_{sp}=U_{\mathrm{s}}.

By choosing this reference frame, stator voltages and fluxes can be rewritten as

(19)$$\begin{gathered} \{{\mathit{U}}_{s\mathit{d}}=\mathrm{0};{\mathit{V}}_{s\mathit{q}}={\mathit{V}}_s={\omega }_s{\mathit{\varphi }}_{s\mathit{d}}, \\ {\varphi }_{sd}={\varphi }_s={\mathit{L}}_s{\mathit{i}}_{sd}+\mathit{M}{\mathit{i}}_{r\mathit{d}};{\mathit{\varphi }}_{r\mathit{d}}={\mathit{L}}_r{\mathit{i}}_{r\mathit{d}}+\mathit{M}{\mathit{i}}_{s\mathit{d}}, \\ {\mathit{\varphi }}_{s\mathit{q}}=\mathrm{0}={\mathit{L}}_s{\mathit{i}}_{s\mathit{q}}+\mathit{M}{\mathit{i}}_{r\mathit{q}};{\mathit{\varphi }}_{r\mathit{q}}={\mathit{L}}_r{\mathit{i}}_{r\mathit{q}}+\mathit{M}{\mathit{i}}_{s\mathit{q}}. \end{gathered}$$

The active and reactive power of the stator can be written according to the rotor currents as

(20)P_s=-V_s{\displaystyle \frac{M}{L_s}}{i}_{rq},

(21)Q_s={\displaystyle \frac{V_{\mathrm{s}}^{\mathrm{2}}}{{\omega }_s{L}_s}}-V_s{\displaystyle \frac{M}{L_s}}{i}_{rd}.

The arrangement of the equations gives the expressions of the rotor voltages according to the rotor currents

(22){\dot{i}}_{\mathrm{r}d}=-{\displaystyle \frac{\mathrm{1}}{\sigma T_{\mathrm{r}}}}{i}_{rd}+g{\omega }_{\mathrm{s}}{i}_{\mathrm{r}q}+{\displaystyle \frac{\mathrm{1}}{\sigma L_{\mathrm{r}}}}{V}_{\mathrm{r}d},

(23){\dot{i}}_{\mathrm{r}q}=-{\displaystyle \frac{\mathrm{1}}{\sigma }}\left({\displaystyle \frac{\mathrm{1}}{T_{\mathrm{r}}}}+{\displaystyle \frac{M^{\mathrm{2}}}{L_{\mathrm{s}}{T}_{\mathrm{s}}{L}_{\mathrm{r}}}}\right)i_{rq}-g{\omega }_{\mathrm{s}}{i}_{\mathrm{r}d}+{\displaystyle \frac{\mathrm{1}}{\sigma L_{\mathrm{r}}}}{V}_{\mathrm{r}q},

with

\sigma =\mathrm{1}-{\displaystyle \frac{M^{\mathrm{2}}}{L_s{L}_r}},T_r={\displaystyle \frac{L_r}{{\mathit{R}}_r}},g={\displaystyle \frac{{\omega }_s-\omega }{{\omega }_s}},T_s={\displaystyle \frac{L_s}{{\mathit{R}}_s}}.

SMC theory

The design of the control system is demonstrated for a nonlinear system as described in Ref.[11].

(24)\dot{x}=f(x,t)+B(x,t)u(x,t),

where x\in {\mathbf{R}}^n is the state vector, f(x,t)\in {\mathbf{R}}^n, B(x,t)\in {\mathbf{R}}^{n\times m} and u\in {\mathbf{R}}^m are the control vectors. From Eq. (24), it is possible to define a set S of the state trajectories x such as

(25)S=\{x(t)|{\sigma }_s(x,t)=\mathrm{0}\},

where

(26){\sigma }_s(x,t)={[{\sigma }_{s\mathrm{1}}(x,t),{\sigma }_{s\mathrm{2}}(x,t),\cdots ,{\sigma }_{sm}(x,t)]}^T

and {[\cdot ]}^{\mathrm{T}} denotes the transposed vector, while S is called the sliding surface.

To bring the state variable to the sliding surfaces, the following two conditions have to be satisfied:

(27){\sigma }_{\mathrm{s}}(x,t)=\mathrm{0},{\dot{\sigma }}_{\mathrm{s}}(x,t)=\mathrm{0.}

The control law satisfying the precedent conditions is presented as

(28)$$\begin{gathered} \{u=u^{eq}+u^n, \\ {u}^n=-k_{f}sgn({\sigma }_s(x,t)), \end{gathered}$$

where u^{eq} can be obtained by considering the condition for the sliding regimen, {\sigma }_s(x,t)=\mathrm{0}. The equivalent control keeps the state variable on sliding surface, once they reach it.

The sgn function is defined, as shown in Refs. [11,12], by

(29)

The controller described by Eq. (28) presents high robustness, insensitive to parameter fluctuations and disturbances, but it has high-frequency switching (chattering phenomena) near the sliding surface due to sgn function involved. These drastic changes of input can be avoided by introducing a boundary layer with width ϵ [11]. Thus replacing sgn({\sigma }_s(x,t)) by sat({\sigma }_s(x,t)) (saturation function), in (28), Eq. (30) can be obtained.

(30)u=u^{eq}-k_{f}sat({\sigma }_s(x,t))

where ϵ>\mathrm{0}:

(31)

Application of SMC to DFIG

The rotor currents i_{rq} and i_{rd} are the images, respectively, of the P_s and the Q_s, which must follow their references.

Quadratic rotor current control with SMC

The sliding surface representing the error between the measured and reference quadratic rotor current is given by

(32){\sigma }_{\mathrm{s}}(i_{\mathrm{r}q})=e=i_{\mathrm{r}q}^{*}-i_{\mathrm{r}q},

(33){\dot{\sigma }}_{\mathrm{s}}(i_{\mathrm{r}q})={\dot{i}}_{\mathrm{r}q}^{*}-{\dot{i}}_{\mathrm{r}q}.

Substituting the expression of {\dot{i}}_{\mathrm{r}q} Eq. (23) in Eq. (33), Eqs. (34) and (35) can be obtained.

(34)\dot{\sigma }(i_{\mathrm{r}q})={\dot{i}}_{\mathrm{r}q}^{*}-\left[-{\displaystyle \frac{\mathrm{1}}{\sigma }}\left({\displaystyle \frac{\mathrm{1}}{T_{\mathrm{r}}}}+{\displaystyle \frac{M^{\mathrm{2}}}{L_{\mathrm{s}}{T}_{\mathrm{s}}{L}_{\mathrm{r}}}}\right)i_{\mathrm{r}q}-g{\omega }_{\mathrm{s}}{i}_{\mathrm{r}d}+{\displaystyle \frac{\mathrm{1}}{\sigma L_{\mathrm{r}}}}{V}_{\mathrm{r}q}\right].

And

(35)V_{rq}=V_{rq}^{eq}+V_{rq}^n.

During the sliding mode and in permanent regime, there is

(36){\sigma }_{\mathrm{s}}(i_{\mathrm{r}q})=\mathrm{0},{\dot{\sigma }}_{\mathrm{s}}(i_{\mathrm{r}q})=\mathrm{0},V_{\mathrm{r}q}^{\mathrm{n}}=\mathrm{0.}

where the equivalent control is

(37)V_{\mathrm{r}q}^{\mathrm{e}q}=\left[{\dot{i}}_{\mathrm{r}q}^{}+{\displaystyle \frac{\mathrm{1}}{\sigma }}\left({\displaystyle \frac{\mathrm{1}}{T_{\mathrm{r}}}}+{\displaystyle \frac{M^{\mathrm{2}}}{L_{\mathrm{s}}{T}_{\mathrm{s}}{L}_{\mathrm{r}}}}\right)i_{\mathrm{r}q}+g{\omega }_{\mathrm{s}}{i}_{\mathrm{r}d}\right]\sigma L_{\mathrm{r}}.

Therefore, the correction factor is given by

(38)V_{rq}^n={\mathit{k}}_{V_{rq}}sat({\sigma }_s(i_{rq})),

where {\mathit{k}}_{V_{rq}} is positive constant.

Direct rotor current control with SMC

The sliding surface representing the error between the measured and reference direct rotor current is given by

(39){\sigma }_s(i_{rd})=e=i_{rd}^{*}-i_{rd},

(40){\dot{\sigma }}_{\mathrm{s}}(i_{\mathrm{r}d})={\dot{i}}_{\mathrm{r}q}^{*}-{\dot{i}}_{\mathrm{r}d}.

Substituting the expression of {\dot{i}}_{\mathrm{r}q} Eq. (22) in Eq. (40), there is

(41){\dot{\sigma }}_{\mathrm{s}}(i_{\mathrm{r}d})={\dot{i}}_{\mathrm{r}d}^{}-\left(-{\displaystyle \frac{\mathrm{1}}{\sigma T_{\mathrm{r}}}}{i}_{\mathrm{r}d}+g{\omega }_s{i}_{rq}+{\displaystyle \frac{\mathrm{1}}{\sigma L_{\mathrm{r}}}}{V}_{rq}\right).

and

(42)V_{rd}=V_{rd}^{eq}+V_{rd}^n.

During the sliding mode and in permanent regime, Eq. (43) can be obtained.

(43){\sigma }_{\mathrm{s}}(i_{\mathrm{r}q})=\mathrm{0},{\dot{\sigma }}_{\mathrm{s}}(i_{\mathrm{r}d})=\mathrm{0},V_{\mathrm{r}d}^{\mathrm{n}}=\mathrm{0},

where the equivalent control is

(44)V_{\mathrm{r}d}^{\mathrm{e}\mathrm{q}}=\left({\dot{i}}_{\mathrm{r}d}^{}+{\displaystyle \frac{\mathrm{1}}{\sigma T_{\mathrm{r}}}}{i}_{rd}-g{\omega }_{\mathrm{s}}{i}_{\mathrm{r}q}\right)\sigma L_{\mathrm{r}}.

Therefore, the correction factor is given by

(45)V_{rd}^n={\mathit{k}}_{V_{rd}}sat({\sigma }_s(i_{rd})),

where {\mathit{k}}_{V_{rd}} is positive constant.

Simulation results

The complete control block diagram employing the SMC for stator active and reactive power control with DC-link voltage control is illustrated in Fig. 5. The DFIG used in this paper is a 4 kW, whose nominal parameters are indicated in Appendix. The block ‘MPPT’ represents the maximum power point tracking. The block ‘SMC’ represents the SMC of stator active and reactive power.

To verify the feasibility of the proposed control scheme, computer simulations were performed using Matlab/Simulink software. The block diagram was realized and executed on an Intel Celeron PC having 2.5 GHz CPU, 1GB DDR RAM. Figure 6 exhibits the random wind speed, Figure. 7 displays the turbine rotor speed, Figure. 8 shows the power coefficient variation C_p which is kept around its maximum value C_p=\mathrm{0.5}, and Figure. 9 presents the stator active power and its reference profile injected into the grid. The stator reactive power and its reference profile are presented in Fig. 10.

A very good decoupling is obtained between the stator active and reactive power. It is apparent that the actual stator active power follows its desired values using the proposed controller, and to guarantee a unity power factor at the stator side, the reactive power is maintained to zero. Figure 11 presents the stator current versus the time of the DFIG and its zoom. The amplitude of stator current increases when wind speed increases. Figure 12 shows the harmonic spectrum of output phase stator current obtained by using the Fast Fourier Transform (FFT) technique. Figure 13 presents the DC-link voltage and its zoom in startup. It can be observed from Fig. 13 that the DC voltage follows its reference with no overshoot and the settling time is very small. In addition, the DC-link voltage ripples are very small.

Conclusions

In this paper, the SMC of a DFIG has been presented, which has been used for reference tracking of active and reactive power exchanged between the stator and the grid by controlling the RSC. The RSC usually provides active and reactive power control of the generator while the GSC keeps the voltage of the DC-link voltage constant. The simulation results obtained by using the Matlab/Simulink tool show the effectiveness of the SMC in power control. In addition, the results give a good DC-link voltage control which indicates that this DC-link voltage remains constant at all fluctuation of the wind speed.

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