Novel power capture optimization based sensorless maximum power point tracking strategy and internal model controller for wind turbines systems driven SCIG

Abstract

Under the trends to using renewable energy sources as alternatives to the traditional ones, it is important to contribute to the fast growing development of these sources by using powerful soft computing methods. In this context, this paper introduces a novel structure to optimize and control the energy produced from a variable speed wind turbine which is based on a squirrel cage induction generator (SCIG) and connected to the grid. The optimization strategy of the harvested power from the wind is realized by a maximum power point tracking (MPPT) algorithm based on fuzzy logic, and the control strategy of the generator is implemented by means of an internal model (IM) controller. Three IM controllers are incorporated in the vector control technique, as an alternative to the proportional integral (PI) controller, to implement the proposed optimization strategy. The MPPT in conjunction with the IM controller is proposed as an alternative to the traditional tip speed ratio (TSR) technique, to avoid any disturbance such as wind speed measurement and wind turbine (WT) characteristic uncertainties. Based on the simulation results of a six KW-WECS model in Matlab/Simulink, the presented control system topology is reliable and keeps the system operation around the desired response.

Keywords

power optimization / wind energy conversion system / maximum power point tracking (MPPT) / fuzzy logic / internal model (IM) controller

Introduction

Under the trends to using renewables energy sources as alternatives to the traditional ones, the Moroccan state aims to decrease greenhouse gas emissions by 15% by 2030 by increasing the amount of renewable energy to 52% where a great part will be provided by wind energy [¹].

The optimization and the injection into the grid of the energy produced from these sources was a challenge discussed in many papers [²–⁶]. The wind power or the wind energy conversion system (WECS) is considered as the most viable and advanced type of renewable energy sources until present, due to its competitiveness and its rate of increasing development. Its aim consists of producing the electrical energy from the kinetic energy contained in the wind field. Recently, the quality and the price of the energy of this source are very much affected, especially due to the optimization mode of the WECS operation and the appearance of the new advanced control strategy, such as, intelligent strategy in conjunction with the power converters. Two main kinds of wind turbines are found in the market: the fixed and the variable speed WT. Compared to the former, the latter has many advantages such as, increased energy capture, operation at maximum power point over a wide range of wind speed, high quality of the produced power, and minimized mechanical stress on the components of turbine. It is proved that variable speed wind turbine produces 10%–15% more power output and less mechanical stress in comparison with the operation at a fixed speed [⁴].

To operate a WT at its high level of efficiency, an MPPT strategy is needed [⁷–¹⁴]. Three main kinds of MPPT strategies of WECS can be found in the literature, the TSR, the power signal feedback (PSF), and the hill climbing searching technique (HCS) [¹⁵–¹⁷], where the major differentiation between each one is based on its attempt to use sensors of measuring parameters and the WT characteristics. The TSR strategy regulates the rotational speed of the generator to follow wind speed changes, in order to track the TSR at its optimal value. This technique is simple, but it is based on the WT characteristics and the wind speed measurement, which are difficult to obtain with accuracy. The PSF strategy makes it possible to track the reference power versus rotational speed stored in a look-up-table. As a result, this technique is reliable compared to the previous one. It does not require the wind speed measurement, but it is based on the rotational speed—power characteristic. The HCS strategy allows climbing the operating point of the WECS to the maximum value based on the mechanical power versus rotational speed characteristic of WT. This technique is found to be simple for implementation. It needs less information from the system compared to the previous strategies, but it requires much improvement which concern the methods of searching and tracking the optimal operating point (OPP). Recently, different modified versions of this strategy has been proposed aiming to improve the tracking and overcome the undesirable oscillations of the system responses around the OPP [²,⁹,¹⁷]. In Ref. [¹⁸], the authors propose an HCS MPPT algorithm for small wind energy conversion systems to overcome the problems related to the conventional HCS such as rapidity/efficiency trade-off and wrong directionality under rapid wind change, but due to the turbulent wind speed, the results obtained may not be satisfactory. In Ref. [¹⁹], the authors present a modified HSC strategy for a WT based permagnet magnetic synchronous generator (PMSG) where the DC side current is used as a perturbation variable and the DC-link voltage slope information is used to enhance the tracking speed and the stability of the algorithm. In Ref. [²⁰], a novel MPPT based control of interior permanent-magnet synchronous generator that incorporates an algorithm to minimze the losses is proposed. The algorithm proposed uses the estimated active power output of the generator as its input and generates command speed so that the power produced is maximized. In Ref. [²¹], an adaptive MPPT is proposed for a small scale WT to extract more energy from the turbulent wind. The MPPT proposed combines the computational behavior of the HSC, the TSR, and PSF control strategies in order to track the peak power fast. In Ref. [²²], an MPPT based on fuzzy control for a WT driven PMSG is proposed. The MPPT proposed makes it possible to locate the system operation points along the maximum power curves based on the inverter DC-link voltage. In Ref. [²³], the authors propose an optimized strategy based on fuzzy logic of wind generator based on the dual-stator induction generator. In Ref. [²⁴], the authors propose an improved MPPT strategy based on fuzzy logic that estimates wind speed from the mechanical power. The MPPT proposed reduces the speed variation range of the wind generator which leads to the downsizing of the PWM and takes into account the system losses. In Ref. [²⁵], an improved MPPT based on fuzzy control for a WT driven direct drive PMSG is proposed. The MPPT proposed makes it possible to vary the duty ratio of a switched-mode rectifier and thus maximizes the energy from the system.

An intelligent MPPT strategy is proposed in this paper, as an alternative to the previous strategies, based on fuzzy logic control. This strategy is based upon online monitoring and judgment of the mechanical power-rotational speed characteristic of the WT without requiring its characteristics even in presence of the high turbulence of the wind to find the optimal rotational speed in such manner that the produced energy is maximized.

Among drive machines, SCIG is very suitable for the WECS because it is cheap, simple in construction, easy to maintain, and easily replaceable [²⁶]. The SCIG control system can be implemented through different approaches: scalar or vector control, direct or indirect field orientation. Indirect vector control is the strategy commonly adopted to implement the MPPT strategy due to its robustness, its ability to achieve a decoupling control of the electromagnetic torque and the rotor flux, and its weak sensitivity from the machine parameters than the conventional scheme [²⁶]. The vector control technique makes it possible to control the drive machine via controlling the electromagnetic torque, by the stator current, through the machine side converter. This technique is implemented in this paper by three IM controllers. The structure of the IM controller includes the model of the plant to be controlled. An improvement of its structure is introduced in this paper in order to overcome the uncertainties related to the aerodynamic torque. The grid side converter makes it possible to regulate the voltage of the DC link and the reactive power exchanged between the machine and the grid to accomplish the grid code requirements. This task is not the objective of this work. It can be referred to in other papers [²⁶]. The performances of the topology proposed, the MPPT proposed in conjunction with the vector control technique referred in the rest of the paper as MPPT-FLC, are investigated by the simulation results of the entire system by using the Matlab/Simulink software.

Modelling of the wind energy conversion system

Due to the fluctuation and unpredictable nature of wind speed, the WECS is subjected to many complex aerodynamic phenomena, and its system control implementation poses a great challenge. Figure 1 shows a representative diagram of the WECS. It contains a rotor that transforms the motion of wind flow to a mechanical motion of rotation available at the drive train, a gearbox that adapts the rotational speed of the rotor to that of the generator, a SCIG machine that transforms the motion of rotation to an electric power, and a back-to-back converter that realizes the system control. The power electronics consists of two three-phase PWM (pulse width modulation) converters with a constant DC link voltage.

WT modelling

The amount of power that may be extracted from the wind by the WT is given by Eq. (1) [²⁷].

(1)P_r={\displaystyle \frac{\mathrm{1}}{\mathrm{2}}}\rho A{C}_p(\lambda ,\beta )v^{\mathrm{3}}.

The aerodynamic torque exerted by the wind on the WT is defined by Eq. (2).

(2)T_r={\displaystyle \frac{P_r}{{\Omega }_r}}={\displaystyle \frac{\mathrm{1}}{\mathrm{2}\lambda }}\rho AR{C}_p(\lambda ,\beta )v^{\mathrm{2}},

where

(3)\lambda ={\displaystyle \frac{R{\Omega }_r}{v}}.

The C_p(λ,β) coefficient describes the power extraction efficiency of the WT. It is a nonlinear function of \lambda and β. The value of this coefficient depends on both the aerodynamic parameters of the WT and the aerodynamic characteristic of the site. Theoretically, this coefficient may take the value of 0.59, which is called the Betz limit, but in practice its value is limited between 0.4 and 0.5 [²⁸].

Many expressions of the power coefficient can be found in Ref. [²⁶]. In this paper, the following expression is used [²⁹].

(4)C_p(\lambda ,\beta )=\left[\mathrm{0.73}\left({\displaystyle \frac{\mathrm{151}}{{\lambda }^{\text{'}}}}\right)-\mathrm{0.002}\beta -\mathrm{13.2}\right]\exp \left({\displaystyle \frac{-\mathrm{18.4}}{{\lambda }^{\text{'}}}}\right),

where

{\lambda }^{\text{'}}={[\mathrm{1}/(\mathrm{1}+\mathrm{0},\mathrm{008}\beta )-\mathrm{0},\mathrm{035}/({\beta }^{\mathrm{3}}+\mathrm{1})]}^{-\mathrm{1}}.

Mathematical model of SCIG

The behavior of the generator electric is required because the electrical power delivered by the generator needs to be measured, which is used to estimate the mechanical power needed by the MPPT. In addition, the internal model controller is based on the electrical model of the generator, which is the reason for the requirement of the electrical model of the system in this paper. The generator model can be simplified by a first order system with a small constant if its behavior is not required.

The modelling of the SCIG machine in dq frame is given by voltage Eqs. (5) and (6) [²⁶].

(5)\{\begin{array}{l}{v}_{sq}=r_s{i}_{sq}+L_s{\displaystyle \frac{d{\Phi }_{sq}}{dt}}+{\omega }_s{\Phi }_{sd},\\ v_{sd}=r_s{i}_{sd}+L_s{\displaystyle \frac{d{\Phi }_{sd}}{dt}}-{\omega }_s{\Phi }_{sq},\\ v_{rq}=\mathrm{0}=r_r{i}_{rq}+L_r{\displaystyle \frac{d{\Phi }_{rq}}{dt}}+{\omega }_s{\Phi }_{rd},\\ v_{rd}=\mathrm{0}=r_r{i}_{rd}+L_r{\displaystyle \frac{d{\Phi }_{rd}}{dt}}-{\omega }_s{\Phi }_{rq}\end{array}

with

(6)\{\begin{array}{l}{\Phi }_{sq}=L_s{i}_{sq}+L_m{i}_{rq}\\ {\Phi }_{sd}=L_s{i}_{sd}+L_m{i}_{rd}\\ {\Phi }_{rq}=L_r{i}_{rq}+L_m{i}_{sq}\\ {\Phi }_{rd}=L_r{i}_{rd}+L_m{i}_{sd}\end{array}.

The electromagnetic torque T_em and the active power P_e yields are expressed respectively by Eqs. (7) and (8).

(7)T_{\mathrm{e}\mathrm{m}}={\displaystyle \frac{\mathrm{3}}{\mathrm{2}}p{L}_{\mathrm{m}}}(i_{sq}{i}_{\mathrm{r}d}-i_{sd}{i}_{\mathrm{r}q}).

The active power yields are given by

(8)P_e={\displaystyle \frac{\mathrm{3}}{\mathrm{2}}}(v_{sd}{i}_{sd}+v_{sq}{i}_{sq}).

The electrical energy E extratcted from the system, which is the power of the system over a time periode, is given by Eq. (9).

(9)E={\displaystyle \int P_e}dt.

The drive train of the WT, which represents the coupling between the WT and the electrical machine, is considered rigid in this paper. The gearbox is considered ideal. The drive train model referred to as high shaft speed is given by Eq. (10) [²⁶].

(10)J_t{\displaystyle \frac{d{\Omega }_g}{dt}}={\displaystyle \frac{T_r}{i}}-T_{\mathrm{em}}

with Ω_g=BΩ_r.

Power optimization and control of the WECS

Power optimization from the WT

MPPT strategy

The mechanical power versus the rotational speed captured by the studied WT for different wind speeds is plotted in Fig. 2. It is clearly seen from Fig. 2 that the mechanical power extracted for each wind speed is maximum at a specific value of the rotational speed, which corresponds to an optimal rotational speed {\Omega }_r^{\mathrm{opt}}. All these rotational speed values, constituting the regime optimal of the WT called the optimal partial load operation, correspond to one optimal value called tip speed ratio (TSR) λ_opt. This regime is marked by the dotted line in Fig. 2. Therefore, it is necessary to operate the WT on this regime to harvest a maximum power from the wind. As a consequence, λmust be kept fixed at its optimal value of λ=λ_opt regardless of wind speed changes. Thereafter, the power coefficient, according to Eq. (4), will be thus at its optimal value C_p=C_p^{\mathrm{opt}}. The optimal value of the pitch angle is \beta =\mathrm{0} [³⁰].

According to Eq. ( 2), it is necessary that the rotational speed follow adequate wind speed changes in order to keep \lambda fixed at its optimal value, which is the task of the so called MPPT strategy. The MPPT strategy should be integrated into the WECS to enable the WT to follow accurately the wind speed.

In the full load operation, the WECS is controlled by a pitch angle controller to limit the produced energy to the rated value [²²,³¹].

MPPT based on fuzzy logic control

The goal of the proposed MPPT is to quickly and continuously adapt the rotational speed of the WT to wind speed changes in such a way that the WT operates at its higher level of aerodynamic efficiency at all times, i.e., C_p=C_p^{\mathrm{opt}}. The proposed MPPT has many advantages. It does not need the WT characteristics and the wind measurement, and it requires poor measurement information from the system compared to the traditional one.

Based on the estimation and monitoring of the produced mechanical power versus rotational speed, at any wind speed, the MPPT-FLC strategy makes it possible to maintain the operation of the WECS at λ=λ_opt. The aim of the MPPT-FLC is to drive fast and without oscillations the operating point to the peak of the characteristic. This is done by increasing or decreasing the rotational speed of the generator according to the rate sign of the characteristic as depicted in Fig. 3. If{\displaystyle \frac{\Delta P_r}{\Delta {\Omega }_r}}>\mathrm{0}, the MPPT increases Ω_r by an adequate step given at its output \Delta {\Omega }_r^{*} according to Eq. (16). In the opposite cases if , the MPPT-FLC strategy decreases the rotational speed by an adequate step.

The mechanical power is estimated based on the electrical power measurement of Eq. (11).

(11){{\displaystyle P}}_{\mathrm{r}}=\eta {{\displaystyle P}}_{\mathrm{e}}

where \eta is the efficiency of the drive train to the generator.

The rotational speed and the mechanical power change at the kth iteration are given respectively by Eqs. (12) and (13).

(12)\Delta {\Omega }_r(k)={\Omega }_r(k)-{\Omega }_r(k-\mathrm{1}),

(13)\Delta P_r(k)=P_r(k)-P_r(k-\mathrm{1}).

The structure of the MPPT strategy is given in Fig. 4. The inputs to the MPPT areΔQ_r andΔP_r, which are given by Eqs. (11) and (12). The output from the MPPT is the adaptive step change of the rotational speed \Delta {\Omega }_r^{*}. Finally, the rotational speed that maximizes the extracted power is obtained by Eq. (14).

(14){\Omega }_r^{*}(k)={\Omega }_r(k-\mathrm{1})+\Delta {\Omega }_r^{*}(k).

Fuzzy logic inference, a reliable tool to control and optimize the complex system, is proposed by Zadeh [³²]. Its main feature is the use of linguistic variables rather than numerical variables in system control. The process of a fuzzy controller is composed by fuzzification, fuzzy rules, and defuzzification.

1)Fuzzification

The inputs/output variables of the system should be expressed in fuzzy set notations using linguistic variables. The notations used for ΔP_r, ΔQ_r and \Delta {\Omega }_r^{*} are negative big (NB), negative medium (NM), negative small (NS), negative (N), zero (Z), positive (P), positive small (PS), positive medium (PM), and positive big (PB). The membership functions of the inputs and output variables are gaussian symmetric for the positive and negative regions of all variables. In addition, the universe of discourse is devised into seven fuzzy sets in order to cover the range of operation of variables. The fuzzy universe of the input and output values of the controller are chosen equal by means of scale factors.

\{\begin{array}{l}\Delta P_r=-\mathrm{1},-\mathrm{0.67},-\mathrm{0.34},\mathrm{0},\mathrm{0.34},\mathrm{0.67},\mathrm{1},\\ \Delta {\Omega }_r=-\mathrm{1},-\mathrm{0.67},-\mathrm{0.34},\mathrm{0},\mathrm{0.34},\mathrm{0.67},\mathrm{1},\\ \Delta {\Omega }_r^{*}=-\mathrm{1},-\mathrm{0.67},-\mathrm{0.34},\mathrm{0},\mathrm{0.34},\mathrm{0.67},\mathrm{1.}\end{array}

2)Fuzzy rules

After the fuzzification step of the inputs, a fuzzy inference engine is defined by a set of IF-THEN rules to link the inputs to the output. Based on the exact and accurate knowledge of the WECS behavior, these heuristic rules are expressed in fuzzy domain as shown in Table 1.

3)Defuzzification

This step consists of transforming the output linguistic variables to crisp values to obtain the desired rotational speed of the generator. The center of gravity method [³⁰] is used to find the value of the rotational speed step change.

The two inputs and output are normalized by their respective scaling factors k₁, k₂, and k₃. These parameters are used as scale factors in order to normalize the basic universe of the inputs and output whitin the range of [–1, 1]. Their values are determined manually in this paper based on the variation of the variable region, thus the scaling factor equals the maximum value of the basic universe of the variable. Therefore, the input scaling factor transforms a crisp input into the normalized input in order to keep its value within the normalized universe and the output scaling factor provides a transformation of the defuzzified crisp output from the normalized universe of the controller into a real output, which is the rotational speed. However, there are specific techniques that can be used to tune the value of these factors such as Ziegler-Nichols and Generic methods, which are not the interest of this paper.

Vector control of the SCIG

IM controller

The principle of the IM controller is based on the model of the system to be controlled. Its structure introduces a low pass filter in cascade with the inverse system model to add a pole to the controller, which is chosen such that the closed-loop system retains its asymptotic tracking properties. The low pass filter used is of first order with a time constant \alpha, which correspons to the order of the system [³³]. The structure of this controller is improved by inserting a feedback loop formed by a gain G and an integrator at its output. These elements provide another degree of freedom inserted by the gain G to speed up the disturbance rejection of the system, and a zero offset of steady state error is garuanted by the integrator. One of the advantages of this controller is that its structure makes it possible to eliminate the effects of any kind of perturbations, such as, nonlinearities, uncertainties, represented as a disturbance as shown in Fig. 5, and makes it possible to overcome the linearization process. Hence, its performances are valid for all operating conditions of the system. Unlike the linear controllers where its principle is based on a linearized model of the system to be controlled, their performances are limited only to the defined operating point of linearization.

The controller is proposed, as an alternative to PI, to implement the MPPT-FLC strategy. Its structure is given in Fig. 5 which consists of a PID tracker, an integrator, and an inner feedback gain G. The added integrator allows two tasks: eliminating the steady state error coming from the disturbance and showing a PID tracker structure rather than a PI tracker in the work [³³]. The aim of the tracker is to track the desired response y_r, whereas the objective of the integrator and the loop formed by the gain G is to reject the perturbation effect (the aerodynamic torque in the case of the speed controller for example). The aerodynamic torque applied to the WT is represented as a disturbance due to its high complexity feature when designing the controller (IM1). Therefore, its effect is eliminated by the loop formed by the gain G (or the introduced degree of freedom) and the integrator. In addition, the aerodynamic torque is not inserted into the system model but is inserted as a disturbance treated by the inernal loop and the integrator. So the objective of the proposed controller desgined depends on the method of taking into account these objectives when desingnig its structure. As can be seen from Fig. 5, the aim of the PID tracker is to track the desired response y_r (without including the aerodynamic torque model). Hence, the aerodynamic torque effect is rejected by the inserted gain G and the integrator. In contrast, this parameter is linearized when desingning the PI controller where its effect is taken into account in its system model, and thus its effect is eliminated by the controller.

The parameters of the PID tracker are given, based on the plant model and the introduced gain, by the relation [³³]

(15)C(s)={\displaystyle \frac{\alpha }{s}}{[P^{-\mathrm{1}}(s)+G]}^{-\mathrm{1}}=K_p+{\displaystyle \frac{K_i}{s}}+K_{d}s,

where P(s)={\displaystyle \frac{M(s)}{s}}, and α is the bandwidth of the controller, which is chosen to track the desired response.

The inner feedback loop (formed by G) is set in such a manner to match the dynamics of the plant with those of the controller. Therefore, the pole created by G is set to match the pole of the IM controller in the transfer function from the disturbance d(s) to the output signal of the plant y(s).

(16){\displaystyle \frac{y(s)}{d(s)}}={\displaystyle \frac{s}{s+\alpha }}{\displaystyle \frac{\mathrm{1}}{P{(s)}^{-\mathrm{1}}+G}}.

Finally, G can be calculated to make the previous expression as

(17){\displaystyle \frac{y(s)}{d(s)}}=K\left[{\displaystyle \frac{s}{{(s+\alpha )}^{\mathrm{2}}}}\right],

where K is a constant.

Decoupled control of the generator

The SCIG is controlled by using the oriented rotor flux technique i.e., orienting the rotor flux around the d component of the reference frame.

(18)\{\begin{array}{l}{\Phi }_{rq}=\mathrm{0},\\ {\Phi }_{rd}={\Phi }_r,\\ {\displaystyle \frac{d{\Phi }_{rd}}{dt}}=\mathrm{0.}\end{array}

This control technique consists of controlling independently the electromagnetic torque and rotor flux by using the machine side converter. Two inner feedback loop are used to control the electromagnetic torque and another is used for the rotor flux control. Each inner loop is implemented by an IM controller, based on the following parameters:

1)Parameters of rotational speed IM controller (IM 1)

The rotational speed control loop is used to provide the electromagnetic torque reference based on the rotational speed reference given at the output of the MPPT strategy.

Based on Eq. (10), it is found that

(19)P_r(s)={\displaystyle \frac{T_{\mathrm{em}}}{{\Omega }_g}}=-{\displaystyle \frac{\mathrm{1}}{J_{t}s}},

where the aerodynamic torque is considered as a disturbance d(s)=T_r(s) and will be rejected by the gain G_r. The parameters of the controller are determined based on Eq. (20).

(20)\{\begin{array}{l}{K}_{\mathrm{pr}}=\mathrm{0},\\ K_{\mathrm{ir}}={\alpha }_r{G}_r,\\ K_{dr}=-{\alpha }_r{J}_t,\\ G_r={\alpha }_r{J}_t.\end{array}

2)Parameters of stator current IM controller (IM 2 and IM 3)

Based on Eqs. (5) and (6), the stator voltage is expressed by

(21)\{\begin{array}{l}{v}_{sq}=r_s{i}_{sq}+\left(L_s-{\displaystyle \frac{L_m^{\mathrm{2}}}{L_r}}\right){\displaystyle \frac{d{i}_{sq}}{dt}}+L_s{\omega }_s{i}_{sd}=v_{sq}^{\text{'}}+L_s{\omega }_s{i}_{sd},\\ v_{sd}=r_s{i}_{sd}+L_s{\displaystyle \frac{d{i}_{sd}}{dt}}-{\omega }_s\left(L_s-{\displaystyle \frac{L_m^{\mathrm{2}}}{L_r}}\right)i_{sq}=v_{sd}^{\text{'}}-{\omega }_s\left(L_s-{\displaystyle \frac{L_m^{\mathrm{2}}}{L_r}}\right)i_{sq}.\end{array}

with

(22)\{\begin{array}{l}{v}_{sq}^{\text{'}}=r_s{i}_{sq}+\left(L_s-{\displaystyle \frac{L_m^2}{L_r}}\right){\displaystyle \frac{d{i}_{sq}}{dt}},\\ v_{sd}^{\text{'}}=r_{sd}{i}_{sd}+L_s{\displaystyle \frac{d{i}_{sd}}{dt}}.\end{array}

Based on Eq. (21), two IM controllers are derived in order to control the q and d current components of the stator current independently. The two terms on the right side of Eq. (21), considered as disturbances, are rejected by G_sq and G_sd respectively. The parameters of controller IM 2 and IM 3 are given respectively by Eqs. (24) and (25), based on the transfer functions of Eq. (23).

(23)\{\begin{array}{l}{P}_{sq}={\displaystyle \frac{i_{sq}}{v_{sq}^{\text{'}}}}={\displaystyle \frac{\mathrm{1}}{(L_s-L_m^{\mathrm{2}}/L_r)s+r_s}},\\ P_{sd}={\displaystyle \frac{i_{sd}}{v_{sd}^{\text{'}}}}={\displaystyle \frac{\mathrm{1}}{L_{s}s+r_s}}.\end{array}

(24)\{\begin{array}{l}{K}_{\mathrm{ps}q}={\alpha }_{sq}{r}_s,\\ K_{\mathrm{is}q}={\alpha }_{sq}{G}_{sq},\\ K_{dsq}={\alpha }_{sq}(L_s-L_m^{\mathrm{2}}/L_r),\\ G_{sq}={\alpha }_{sq}(L_s-L_m^{\mathrm{2}}/L_r)-r_s,\end{array}

(25)\{\begin{array}{l}{K}_{\mathrm{ps}d}={\alpha }_{sd}{r}_s,\\ K_{\mathrm{is}d}={\alpha }_{sd}{G}_{sd},\\ K_{dsd}={\alpha }_{sd}{L}_s,\\ G_{sd}={\alpha }_{sd}-r_s.\end{array}

3)References calculation

The set point of IM 1 controller is {\Omega }_g^{*} derived from the MPPT-FLC strategy, by{\Omega }_g^{*}=B{\Omega }_r^{*}. The output from the controller is the desired electromagnetic torque T_{\mathrm{em}}^{*}.

The set point of IM 2 and IM 3 is derived from {\Phi }_{rd}^{*} by Eq. (26).

(26)i_{sd}^{*}={\displaystyle \frac{{\Phi }_{rd}^{*}}{L_m}},

where {\Phi }_{rd}^{*}={\displaystyle \frac{U_s}{f_n}} with U_S being the nominal voltage of the converter and f_n being the nominal frequency of the grid.

From Eqs. (6)–(18), it can be found that i_{rq}=-{\displaystyle \frac{L_m}{L_r}}{i}_{sq} , and i_rd=0, thus, the reference electromagnetic torque is obtained from Eq. (7) as

T_{\mathrm{em}}^{*}={\displaystyle \frac{\mathrm{3}p{L}_m^{\mathrm{2}}}{\mathrm{2}{L}_r}}{i}_{sd}^{*}{i}_{sq}^{*}.

Finally, the set point of IM 3 controller is given by Eq. (27).

(27) i_{sq}^{*}={\displaystyle \frac{\mathrm{2}{L}_r}{\mathrm{3}p{L}_m^{\mathrm{2}}}}{\displaystyle \frac{T_{\mathrm{em}}^{*}}{i_{sd}^{*}}}.

The rotor θ_r and grid θ_slip angle are given respectively by Eqs (28) and (29).

(28){\theta }_{\mathrm{r}}=\int p\mathrm{d}\theta ,

(29){\theta }_{\mathrm{slip}}={\int \omega }_{\mathrm{slip}},

where {\omega }_{\mathrm{slip}}={\displaystyle \frac{r_{\mathrm{r}}}{L_{\mathrm{r}}}}{\displaystyle \frac{i_{\mathrm{s}q}}{i_{\mathrm{s}d}}}.

The rotation angle used to implement the park and reverse transformation is given by Eq. (30),

(30){\theta }_{\mathrm{e}}={\theta }_{\mathrm{r}}+{\theta }_{\mathrm{slip}},

(28){\theta }_e={\displaystyle \int {\Omega }_e}dt={\displaystyle \int (p{\Omega }_g+{\omega }_{\mathrm{slip}})}dt={\theta }_r+{\theta }_{\mathrm{slip}},

where {\omega }_{\mathrm{slip}}={\displaystyle \frac{r_r}{L_r}}{\displaystyle \frac{i_{sq}}{i_{sd}}}.

The overall structure control of the WECS-based on SCIG is given in Fig. 6.

Results and discussion

In this section, the performances of the proposed topology are evaluated. In order to investigate the performances very well, the system is subjected to different scenarios of wind speed, a step change from 7 m/s to 9 m/s, and a very turbulent wind speed profile of 7 m/s medium wind speed. The parameters of the simulated system and the controllers used are given respectively in Tables 2 and 3. The optimal values of the power coefficient and the TSR of the studied WT are respectively C_p^{\mathrm{opt}}=\mathrm{0.47} and λ_opt=7. The reference value of the rotational speed used for the WT is derived from Eq. (3), based on the WT characteristic and the wind speed measurement, where the measurement of the wind speed is obtained using an anemometer located at the top of the tower.

The developed MPPT-FLC strategy is compared with the optimal parameters of the WECS and the HSC strategy. Note that in the HSC strategy, a simple PI controller is utilized in the filed orientation control technique of the generator.

The MPPT-FLC is tested first under a step change of wind speed. The wind step and the simulation results are shown in Fig. 7. Due to the step wind speed, the MPPT-FLC reacts rapidly to maintain the power coefficient of the system around its optimal value of C_p=0.47. Besides, the rotational speed and the mechanical power reach rapidly their steady state values of around 20 rad/s and 2 kW respectively, as shown in Fig. 7(d), (b) and (c). At t=30 s the wind speed changes from 7 to 9 m/s, and accordingly, the rotational speed and the mechanical power reach their optimal values of about 25 rad/s and 4.3 kW respectively. However, as can be seen from the Fig. 7, C_p drops at t=30, due to the transient changes of the wind speed, and comes back to its optimal value quite fast (at a time less than 1 s). The MPPT-FLC enables the rotational speed of the WT to follow well the wind speed in order to keep C_p at its optimal value.

The MPPT-FLC is subjected now to a realistic wind speed profile, as depicted in Fig. 8, to examine its performances. Despite the fast fluctuations of the wind speed profile, the MPPT-FLC enables the rotational speed of the generator to follow well the optimal value as displayed in Fig. 9. According to system response in Fig. 10, the operation of the system is kept around its optimal level of efficiency over the wind speed profile. Indeed, the power coefficient follows well the nominal value of C_p^{\mathrm{opt}}=\mathrm{0.47} at all times. It can be concluded that the proposed strategy is able to operate the WECS around its high level of efficiency despite of high fluctuations of wind speed.

The mechanical power harvested from the wind by the proposed MPPT-FLC, as demonstrated in Fig. 11, is much maximized because it fluctuates quickly according to the time and tracks well the reference mechanical power (The reference mechanical power is proportional to the cube of the wind speed as given by Eq. (1).). The power extracted is larger than the power produced by the HCS strategy.

The oscillations presented in the response of Figs. 9, 10 and 11 characterize the transient regime of the system governed particularly by the MPPT based on fuzzy control. The oscillations, at the start-up, as shown, for example in Fig. 10, introduce an amount of power loss. These undesirable oscillations are caused by the fast response of the fuzzy logic to the wind speed transient at the system launch, even if the mass of the used model is low. However, after about 3 seconds, the MPPT-FLC cancels the effect of these oscillations and enables the WECS to reach the steady state value whereas the oscillation in the steady state regime are caused specifically by the rapid fluctuation of wind speed and to the long time constant of the WT. For the HCS, the situation is even worse. If its operating point is not fixed at the launch, the system may never reach its permanent regime. For this reason, the operating point of the HSC strategy has been fixed until t=10 s (i.e., the rotational speed is fixed at {\Omega }_r^{*}=19 rad/s).

In terms of generated energy, Fig. 12 compares the electrical energy generated by the MPPT-FLC and the HCS strategy with the optimum energy generated by the WECS. As can be seen from Fig. 12, the energy generated by the MPPT-FLC is slightly lower compared to the optimal energy. Up to 20 s the energy produced by MPPT-FLC is a little lower than that obtained by the HSC. The reason for this is that the optimum operating point of the HSC is fixed manually at the start-up. From 20 s to 40 s the energy produced by the MPPT-FLC increases gradually and becomes slightly higher than that generated by the HCS. Therefore, it can be concluded from Fig. 12 that the MPPT-FLC is competitive and can extract a significant amount of energy compared to the HSC, and follow well the electrical energy extracted by the system. The delay from the energy produced by the MPPT-FLC to the reference value is caused by the long time constant of the electromechanical part of the system. In fact, at every change of wind speed, this time constant induces a delay to the system to follow the changes of wind speed by the proposed strategy. As a result, the system cannot profit freely from the kinetic energy contained in the wind.

As a conclusion, the proposed MPPT based fuzzy logic can estimate very well the reference rotational speed without knowing wind speed. In addition to this benefit, the proposed MPPT has the advantage that it may be easily adaptable to other models that operate in different environments.

It is observed, the incorporation of the proposed controller makes it possible to submit low error tracking indices over the wind speed profile compared with the PI controller. It can be concluded that the IM controller not only rejects the aerodynamic torque effect from the turbulence nature of the wind but also makes it possible to optimize the energy captured by tracking the reference rotor speed.

In order to compare the performaces of the two controllers, Fig. 13 gives the reference and the actual rotational speed of the generator when considering the reference rotational speed value based on the wind speed measurment. As can be seen, the controller proposed presents superior performances and no overshoot than the PI controller, which illustrates the ability of the controller proposed to reject the aerodynamic torque and to track rapidly the reference response.

Table 4 summarizes the results of the following tracking indices of the rotational speed given by the PI and the IM controllers:

(1)The integral of absolute error: IAE, given by \mathrm{IAE}={\displaystyle {\int }_{\mathrm{0}}^t\left|e(t)\right|}dt.

(2)The integral of square error: ISE, given by \mathrm{ISE}={\displaystyle {\int }_{\mathrm{0}}^t{e}^{\mathrm{2}}(t)}dt.

It can be concluded from Table 4 that the suggested controller submits low error tracking indices over the wind speed profile, and their values concurs well with those of the PI controller.

Conclusions

This paper presents an improved control structure of a small variable speed WECS. The control strategy is designed as a cascade technique to ensure the optimal operation of the WECS. An intelligent MPPT strategy, based on senseless of wind speed, to find the optimal operating point is designed in the outer loop, and an internal model controller is modeled for controlling indirectly the electromagnetic torque of SCIG in the inner loop. The MPPT strategy is proposed based on fuzzy logic control in order to extract a maximum mechanical power from the wind turbine, whereas the vector control technique (inner control loop) is realized by means of an IM controller because of its simplicity and its capability to reject the disturbance effect. The simulation results indicate that the proposed MPPT-FLC enables the WECS to extract more energy from the wind. Based on the recounted benefits, the MPPT based on the fuzzy logic strategy in conjunction with the IM controller makes it possible to make the WECS control system simple, reliable and more flexible.

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