A grid-connected variable-speed wind generator driving a fuzzy-controlled PMSG and associated to a flywheel energy storage system

Electric Power Systems Research 180 (2020) 106137

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A grid-connected variable-speed wind generator driving a fuzzy-controlled PMSG and associated to a flywheel energy storage system

T

M. Mansoura,b, M.N. Mansourib, S. Bendoukhaa,*, M.F. Mimounib a

Electrical Engineering Department, College of Engineering at Yanbu, Taibah University, Saudi Arabia Research Unit of Industrial Systems Study and Renewable Energy, Electrical Engineering Department, National Engineering School of Monastir, University of Monastir, Avenue Ibn El Jazzar, 5019 Monastir, Tunisia

b

ARTICLE INFO

ABSTRACT

Keywords: VSWG PMSG MPPT Pitch control FESS Fuzzy control

In this paper, we propose a variable speed-wind energy conversion system based on a permanent magnetic synchronous generator (PMSG). A complete system model with multiple controllers is proposed and simulated. Two controllers are proposed and examined for regulating the current from the PMSG, the first is a simple PI controller and the second uses a fuzzy component to improve the tracking performance. A flywheel energy storage system (FESS) is associated to the proposed variable speed wind generator (VSWG). The FESS is linked at the DC bus stage in order to regulate the power supplied to the grid. In simple terms, if the generated power exceeds the demand, the excess is stored by the FESS for use when a shortage occurs. In this scenario, the VSWG is controlled to capture the maximum wind energy by means of the maximum power point tracking (MPPT) method. To maintain this operation as the turbine speed increases above the rated speed, we implement a pitch angle controller. The FESS is based on a squirrel-cage induction machine (IM) coupled to a flywheel. A controlled grid converter allows for the exchange of active and reactive powers with the grid. A proportional integral (PI) based grid connection is proposed that controls the current and voltage amplitudes as well as the frequency passed onto the grid. The aim of the converter control is to achieve a decoupled active and reactive power control suitable for operation at a unitary power factor. The dynamic model of the proposed system is simulated using the Matlab–Simulink package. The obtained results are presented and discussed to illustrate the performance of the overall proposed system.

1. Introduction The worldwide energy demand has been steadily rising ever since records began. Over the last few decades, light has been shed on the adverse effects of the production and consumption of energy on the environment. This led to a rise in the demand for renewable energy harnessed from natural phenomena such as the wind, the sun, and the tidal waves. These sources of renewable energy attracted more attention once it became clear that the world's reserves of the most major energy source (oil) are in constant decline. Although many countries around the world have made commitments to deploy large renewable energy systems, their integration into existing power grids and cooperation with the ancillary services of the grid still pose a challenge. Most of the renewable energy systems in use today are decentralized and thus do not support ancillary services, which are necessary for the proper operation of the grid. Ancillary services are responsible for controlling the grid voltage and frequency as well as reactive power

⁎

compensation and other essential tasks. From the view point of the grid, if the integrated renewable energy systems do not participate in these ancillary service than their inclusion is more harmful than beneficial. In order to maintain the stability of the power grid, the penetration rate of these decentralized sources is restricted. This is particularly the case with those sources that are highly unpredictable and suffer from extreme fluctuations such as wind generators. In order to successfully integrate a wind generator into the grid and ensure its participation in the ancillary services, it is necessary that the system is able to feed isolated loads [1]. Since the main problem with wind generators is the high coupling between the generated power and the actual wind speed, which is usually highly fluctuating, one interesting solution is the use of an energy storage system (ESS) that controls the power flow between the generator and the grid. The main objective of an ESS is to balance the power production and consumption by comparing the generated power to the grid demand. When the generated power exceeds the demand, the extra power is stored in the system, and once the

Corresponding author. E-mail address: [email protected] (S. Bendoukha).

https://doi.org/10.1016/j.epsr.2019.106137 Received 20 December 2018; Received in revised form 5 November 2019; Accepted 29 November 2019 Available online 19 December 2019 0378-7796/ © 2019 Elsevier B.V. All rights reserved.

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Fig. 1. The overall structure of the proposed wind energy conversion system which comprises a VSWG connected with a FESS and integrated directly to the grid.

generated power drops below the demand, the stored power is used to compensate for the shortage. In addition, the ESS can be controlled to provide power regulation and load voltage control. Conventional electrochemical batteries are not suitable for the application at hand [1] as they generally only store small amounts of energy and cannot support the number of required cycles [2]. Ideally, the required storage system must be highly dynamical in order to keep up with the high fluctuations in the generated and consumed powers in real time [3]. Over the last few years, numerous research studies and industrial investigations have been dedicated to flywheel based ESSs (FESS) due to their many advantages including high dynamics, long lifetime and ecological nature [4]. It should be noted that flywheels have been around for a very long time but have only recently been discovered for use in the wind energy sector. Although the FESS can only store energy for a short while, it is generally sufficient as in reality, wind generators are mostly installed at high wind locations where the wind speed fluctuation, and by extension the generated power fluctuation, has a high frequency. In [5], the authors developed an appropriate method to predict and quantify the ability of an ESS with the aim of increasing the wind generator's penetration into the power grid. The FESS has been shown in the literature to successfully adapt the generated power to the demand [6,7]. A comprehensive review of recent FESS applications in the fields of hybrid vehicles, railways, wind energy, hybrid power, power networks, marine, space, etc. can be found in [8]. Another comprehensive review of FESS-based systems with particular focus on the wind energy sector is given in [9]. In general, wind generator systems can be classified into two main categories; fixed speed and variable speed. For variable speed wind generators (VSWG), the energy generator and the storage system can be coupled at the DC bus using power electronics [10]. In this configuration, FESS is used to control the DC-bus voltage through a balancing of the power generation and consumption. Once the DC-bus voltage is regulated, a power converter connects the VSWG to the grid and performs the required frequency and voltage control. In recent years, attempts have been made to connect the VSWG to a FESS in order to stabilize the power supplied to the grid. In [11], a VSWG-FESS system is proposed based on a PMSG. The study established a direct torque control (DTC) strategy and used computer simulations to assess the feasibility and performance of the system. In [12], an IM-based FESS was integrated with a doubly-fed induction generator (DFIG) based VSWG and two control strategies were evaluated: direct torque control (DTC) and direct power control (DPC). A similar system was considered in [13], where the authors developed an adaptive controller based on theoretical models of the VSWG. Although the DFIG has its own advantages including its low price and light weight, studies have concluded that in the long run the PMSG is superior. Unlike the PMSG, the DFIG may not be coupled directly with the rotor shaft of the turbine. A gear box is required to adapt the rotational speed of the turbine to the operating speed of the asynchronous generator within the DFIG. The main problem with gearboxes is the high associated cost of maintenance as well as the high failure

rate, which affects the operation of the whole system [14]. Since the PMSG has a variable speed, it can be connected directly to the rotor shaft. Recent studies have examined the integration of PMSG-based turbines directly to the grid including [15]. In this paper, we aim to develop a complete wind generator system that can be integrated directly into the grid. The considered VSWG is based on a variable speed PMSG machine and is attached at the DC-bus level to a low-speed FESS comprising of a flywheel connected to a classical squirrel cage induction machine (IM). The FESS aims to smooth fluctuations observed in the power to be injected into the grid and regulate the power flow from the VSWG to the grid, which undergoes an LR filter to ensure a good quality voltage. The main concerns of the study are the control strategies for different parts of the VSWG and the FESS as well as the overall efficiency and dynamical performance of the system. For instance, a fuzzy-PI controller is proposed to regulate the direct and quadrature components of the PMSG stator currents. The fuzzy component is shown to improve the tracking performance and remove fluctuations in the currents. A comprehensive block diagram of the proposed system is depicted in Fig. 1. 2. Variable-speed wind generator (VSWG) 2.1. Wind turbine Before we present the main findings of this study, let us give a brief description of the complete system we are interested in. We start with our model of the wind turbine. The literature related to the aerodynamics of a wind turbine is extensive and a comprehensive summary is found in [16]. The aerodynamic power of a wind turbine rotor is generally accepted to be

Pt =

1 2

Rt2 v 3Cp ( , ),

(2.1)

−3

where ρ (kg m ) is the air density, Rt (m) is the turbine radius, v (m s−1) is the wind speed and Cp ( , ) is the power coefficient. The power coefficient of the rotor is an important property that indicates the aerodynamic efficiency of the turbine. It is dependent on the pitch angle β as well as the speed ratio of the tip λ. The latter represents the ratio between the tangential velocity of the rotor blade tip and the speed of wind leading to

=

Rt v

t

(2.2)

with Ωt being the mechanical turbine speed (rad/s). As shown in [17], the mechanical torque generated by the turbine is equal to

Tt =

1 2

Rt3 v 2Ct ( , ),

(2.3)

where Ct ( , ) denotes the torque coefficient of the turbine given by

Ct ( , ) = 2

Cp ( , )

.

(2.4)

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In this context, the reference pitch angle can be defined as

ref

=

0

=

2

(

for 0 < tn)

t

+

0

for

t

tn ,

t

>

tn

(2.7)

with β0 (°) being the initial (optimal) pitch angle of the blades. A Matlab–Simulink block diagram for the adopted control system for the pitch angle is depicted in Fig. 4. 2.2. PMSG modeling Let us now move towards the PMSG. Perhaps the most widely used dynamical model for a PMSG is the Park model. A simplified model is obtained by ignoring the homopolar component of the flux distribution and taking into account only the fundamental harmonic. The resulting model in terms of its stator currents is described by the dynamic equations

Fig. 2. The power coefficient characteristics versus the speed ratio λ and the pitch angle of the blades β.

The power coefficient curves Cp ( , ) as a function of λ for different values of β are depicted in Fig. 2. Next, we examine the model of the mechanical shaft transmitting the energy from the rotor to the generator. Realistic models are complicated and lengthy. However, a simplified model can be obtained by considering only the electrical characteristics of the system. The total inertia JT (kg m2) observed on the generator shaft can be given by

JT

d t = Tt dt

Tem

f

t

Ts,

di sd 1 = (vsd dt Ls disq 1 = (vsq dt Ls

1 1 + bs

ref

t i sq ),

Rs i sq

t i sd

Ls p

p

t a ),

(2.8)

where Rs (Ω) represents the phase resistance of the stator winding, Ls (H) denotes the cyclic inductance of the stator, ϕa (Wb) is the flux induced by the permanent magnet, and the subscripts sd and sq denote the direct and quadratic components of the stator current or voltage, respectively. The constant p refers to the number of pairs of poles. The electromagnetic torque is, then, equal to

(2.5)

where Tt (N m) denotes the torque of the turbine, Tem (N m) represents the electromagnetic torque, Ts (N m) is the dry friction torque and f (N m s rad−1) is a constant coefficient accounting for the effects of viscous friction. In order to guarantee that the turbine rotor rotates at its optimal speed, careful attention must be paid to the pitch angle of the blades. A widely accepted control strategy for the pitch angle works by increasing the pitch angle once the rotational speed of the rotor exceeds the rated mechanical speed Ωtn in order to reduce the torque Tt of the turbine. The curve depicted in Fig. 3 shows the speed limit of the turbine. Most wind turbines used in reality have a variable speed, where an actuator is used to control the pitch angle of the blades with the aim of lowering the power coefficient Cp and ensuring the value of the power is constantly achieved. A linearized first order model was used in [5,6] whereby the mechanical torque Tt is directly proportional to the rotational speed of the turbine Ωt. This electromechanical actuator can be modeled as

=

Rs isd + Ls p

(2.9)

Tem = p a i sq . 2.3. Wind generator control

In order to make the most out of the VSWG, care must be paid to its control. The overall VSWG controller structure is depicted in Fig. 5. As shown in Fig. 5, The controller relies heavily on our measurement of the turbine speed Ωt. The general idea is that if the wind power is below the rated power of the turbine, we use the maximum power point tracking (MPPT) to determine the reference torque of the PMSG. On the other hand, if the wind power surpasses the rated value, pitch control of the turbine blades is required. The remaining part of the PMSG controller works by identifying reference values for the stator currents and using PI regulators to control the converter with the aim of regularizing the stator currents. The general aim of our VSWG control is to obtain the maximum possible efficiency for the VSWG, which is achieved by minimizing the losses for any given load. As shown in [20] and subsequent studies, the torque of the generator can be controlled simply by altering the quadrature component of the current while zeroing the direct component. In order to control the power of the VSWG it suffices to the specify the correct PMSG electromagnetic torque Tem. Generally, we can approach this by selecting the reference value Tem,ref in two respects [21]. When the turbine is operating at maximum power, our objective is to improve the aerodynamic output of the turbine, which corresponds to the maximum power coefficient. Using maximum power point tracking (MPPT), we can define the reference electromagnetic torque as

(2.6)

with s being the Laplace operator and τb being a time constant [18,19].

Tem,ref =

PMPPT

=K

t

2 t,

(2.10)

where the MPPT power is given by

PMPPT = Fig. 3. The reference pitch angle of the blades versus the turbine speed.

Rt5 Cp,max 2

3 opt

3 t

=K

3 t.

(2.11)

Note that the optimal speed ratio λopt is used to achieve the maximum 3

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Fig. 4. Pitch angle control system implemented in the Matlab–Simulink environment.

power coefficient Cp,max, which yields the maximum power. Also note that care must be taken to ensure that the turbine power is never higher than rated power of the generator. The second important aspect of the VSWG control is ensuring that the generated power remains constant and equal to the rated power even in case of strong winds, which is fulfilled by the pitch angle control strategy.

2.4.2. Fuzzy-PI controller Although the PI controllers discussed in the previous subsection are simple and robust, the resulting currents still contain fluctuations, which may have an impact on the grid. In this section, we implement a fuzzy-PI controller that achieves better current. The important thing about fuzzy logic is that it approaches an engineering problem from a human-like perspective such that decisions are made based on vague and incomplete data but still lead to valid conclusions. Fuzzy logic works in three steps. First, the crisp inputs are converted by means of a fuzzification process into fuzzy values. Fuzzy values linguistic and include, for instance, the adjectives: high, low, fast, slow, etc. In the second step, simple fuzzy rules derived from a specific rule base are applied by means of an inference mechanism. Finally, the results are defuzzified to obtain crisp output values. Perhaps the earlier fuzzy based controller is that of Mamdani and Assilian [23], where they selected the generic rules

2.4. PMSG control 2.4.1. PI controller One of the important tasks in any wind generator system is the regularization of the direct and quadrature current components of the PMSG stator. The torque control strategy adopted in [22] and other studies uses two separate current regulators for isd and isq. For simplicity, we start with two simple proportional integral (PI) controllers with similar integral and proportional parameters. This is based on the fact that the transfer functions on the two d and q axes are identical for a non-salient PMSG. The current regulators are used to supply the reference voltages vsd,ref and vsq,ref , which undergo an inverse Park transformation to supply the reference voltages (uwa1, uwb1, and uwc1) to the pulse width modulation (PWM) block to generate the cyclic ratios for the switches of the first converter.

Ri : IF x1 is G1i AND x2 is G2i , … AND xn is Gni, THEN y is Hi

(2.12)

for i = 1, 2, …, r, with xj being the observable variables of the controlled system, y being the control output, and Gij and Hi representing specifically chosen fuzzy sets. In recent years, fuzzy control has attracted the attention of many researchers in the field of power

Fig. 5. A block diagram describing the overall control structure of the variable-speed wind generator. 4

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Fig. 6. A block diagram of the proposed fuzzy-PI controllers.

generation from wind turbines. A fuzzy-PI optimal power controller was proposed in [24]. Other relevant studies include [25,26]. In order to regulate the currents isd and isq supplying to the grid, we replace the PI controllers from the previous subsection with Mamdani type controllers. Fig. 6 depicts the structure of the proposed fuzzy controllers. The required inputs for the fuzzy logic controllers are the current errors

ed = i sd,ref eq = isq,ref

isd, i sq

Table 1 Fuzzy logic control rules for the two current regulating controllers. e

Δe

(2.13)

N Z P

N

Z

P

N N Z

N Z P

Z P P

reference value for the d-component of the current. Both of these, in turn, are useful in identifying the IM's stator pulsation. The next stage of the controller uses PI regulators and decoupling to obtain the reference voltages to control the bus converter. The following subsections give a detailed description of the most important stages of the controller.

along with their variations Δed and Δeq. The outputs are the variations in the control voltages vsd and vsq . Since the two controllers are identical, it suffices to describe that of the direct current component isd. The fuzzy rules to be employed in the inference step are selected to allocate a fuzzy set of the control input u for each pair (ed, ed ) . The controllers contains three fuzzy sets for each input: negative (N), zero (Z), and positive (P) as depicted in Fig. 7. The 9 resulting fuzzy sets describing the output are summarized in the inference matrix listed in Table 1. In the proposed controllers, we use the max–min method for the inference stage and the center of gravity method for the defuzzification process. In the min–max method, the logical AND operator is represented by the minimum, the logical OR by the maximum, and the implication operator by the minimum. More details about these methods can be found in [27].

3.1. Modeling We start by modeling the flywheel and mechanical shaft. For a given inertia, the energy stored in the flywheel is proportional to the square of the rotational speed [29]. The relationship can be described by

Ef =

1 Jf 2

2 f

(3.1)

with Jf representing the inertia moment in (kg m2) and Ωf denoting the flywheel speed in (rad/s). The amount of energy required to store the rated power of the IM, denoted by Pn−IM, over a short storage period Δt is

3. Flywheel energy storage system (FESS) The FESS, as shown in Fig. 8 comprises a flywheel, an induction machine (IM) and a converter (rectifier/inverter) that controls the torque of the flywheel and, therefore, the exchanged power. The FESS has two main objectives; to regulate the DC bus voltage [6] and to regulate the power flow towards the mains [28]. A flywheel is comprised of a rotor that is accelerated to a high speed by means of electrical energy. The aim of incorporating the flywheel into the system is to use the conservation of energy law to convert and preserve the excess electrical energy from the generator as rotational energy for use when a shortage occurs. Typical flywheels come with a rotor that is made from a carbon–fiber composite and magnetic bearings in a vacuum enclosure. The controller depicted in Fig. 8 relies mainly on our measurement of the flywheel rotational speed as well as the reference IM power estimated by means of a PI regulator. The reference power is used to estimate the reference value for the q-component of the current while the speed is used to estimate the IM rotor flux and by extension the

Ef = Pn

IM

(3.2)

t.

By combining (3.1) and (3.2), we obtain the required inertia of the flywheel

Jf =

2Pn

IM 2 f

t

=

2Pn IM t 2 2 f ,max f ,min

,

(3.3)

where Ωf,max and Ωf,min represent the maximal and minimal speed limits of the flywheel, respectively. It is important to maintain the speed within the specified range in order to avoid any deterioration in the energy storage operation of the flywheel [30]. As for the mechanical shaft transferring the rotation, we can use the simple model described by

Jf =

d dt

f

= Tem

f

f,

(3.4)

where Tem (N m) is the electromagnetic torque and f′ (N m s rad−1) is a viscous friction coefficient. Similar to the PMSG described earlier in the paper, the classical squirrel-cage IM can be described by means of Park model, which considers the flux and currents yielding the system of differential equations Fig. 7. Membership functions (MFs) for the controller inputs e and Δe and the output v . 5

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Fig. 8. A block diagram of the control strategy of the FESS-IM.

•ω

s

denotes the stator pulsation (rad/s).

Finally, the electromagnetic torque generated by the flywheel is given by

Tem = p

M (i sq Lr

isd

rd

rq ).

(3.6)

3.2. Control of the FESS associated to a VSWG Let us, now, show how the FESS-IM can be controlled. Based on Fig. 1, the evolution of the DC bus voltage can be described by

Fig. 9. A block diagram of the control strategy for the flywheel energy storage system.

di sd = dt disq = dt d rd = dt d rq = dt

Rsr isd + Ls

s i sq

M Ls Lr Tr

+

Mp Ls Lr

Rsr i sq Ls

s i sd

M isd Tr

1 Tr

M i sq Tr

(

rd

s

+( p

s f ) rd

p

+

rd

f

rd

+

Mp Ls Lr

rq

M Ls Lr Tr

+ rq

du dc 1 = (i1 + i2 + i3). dt C

1 vsd, Ls +

We use a PI controller to regulate the DC bus voltage. The controller identifies the power ΔP required to maintain the DC bus voltage at some reference value, which we denote by udc,ref. The idea behind the adopted control strategy is depicted in Fig. 9. We denote the reference grid active power by Pr,ref and the optimal active power generated by the VSWG by Pwg. In order to ensure the power supplied to the grid remains at Pr,ref, we can simply define the active power exchanged between the FESS and the grid as

1 vsq, Ls

f ) rq ,

1 Tr

rq .

(3.5)

Pf ,ref = Pr ,ref

The parameters used in (3.5) are described below:

• L and L denote the cyclic proper inductances of the stator and the rotor (H). • M denotes the mutual inductance between the stator and the rotor (H).

is the dispersion coefficient of the machine. • =1 R and R are the resistances of the stator and rotor (Ω), respectively. • R = R + (Ω). • ϕ and ϕ are the direct and quadratic components of the rotor flux • (Wb), respectively. and i are the direct and quadratic components of the stator • icurrents (A), respectively. and v are the direct and quadratic components of the stator • vvoltages (V), respectively. • p′ is the number of pairs of poles in the system. M2 Ls Lr

r

s

sr

rd

M2 Lr Tr

s

rq

sd

sq

sd

sq

Pwg + P.

(3.8)

If Pf,ref > 0, then the generated power is in more than the demand and thus we need to store the excess energy in the FESS. Alternatively, if Pf,ref < 0, then the generated power is less than the demand and the shortage can be compensated for by the FESS. For the control of the FESS IM, we use a vector torque controller obtained by cascading a flux oriented control (FOC) strategy with an external power loop [31]. Over the last decade, a vast number of studies have attempted to develop the most successful vector control structures taking into account most industrial constraints, particularly mechanical, thermal and energy constraints. In our work, we implement a vector control of the IM by applying rotor flux oriented control constraints on the rotor voltage equilibrium equations of (3.5). By linking the d-axis of the Park reference frame to the rotor flux vector

r

s

(3.7)

( 6

rq

= 0,

d rq dt

)

= 0 , we obtain the reduced model

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di sd Rsr = isd dt Ls disq = s i sd dt d rd M = isd dt Tr

+

s i sq

M Ls Lr Tr

+

Mp Ls Lr

Rsr i sq Ls 1 Tr

rd

f

rd

+

operation of the converters. It also allows us to gain a comprehensive understanding of the total dynamical behavior of the system. In the Park model, the modulated voltages (AC side) of the three converters are related to the DC bus voltage udc according to the formulas

1 vsd, Ls

+

1 vsq, Ls

rd .

vsd udc u wd1 vsq = 2 u wq1 ,

(3.9)

The electromagnetic torque in (3.6) becomes

Tem

M = p i sq Lr

rd .

vsd u u wd2 , = dc u wq2 vsq 2

(3.10)

vod udc u wd3 voq = 2 u wq3

In the structure depicted in Fig. 1, the rotor flux estimator is

M isq (s ) r ,estimated| = 1 + Tr s

(3.11)

and the stator pulsation is calculated as s

=p

f

+

M i sq . Tr rd

(3.12)

Before we move on to the modeling of the power converters and the grid powers, we need to address some practical considerations. In our system, we assume that the rotational speed of the flywheel is 3000 rpm whereas that of the IM is 1500 rpm. Hence, to keep up with the maximum speed of the flywheel, it is imperative that the IM operate in its flux-weakening region (from 1500 to 3000 rpm), over which the rated power of the IM remains available. According to [6], the FOC-controlled power is of the form

Pf

Tem

=p

f

M isq Lr

f.

rd

1 (i sd u wd1 + i sq u wq1), 2 1 i2 = (isd u wd2 + i sq u wq2), 2 1 i3 = (i rd u wd3 + i rq u wq3), 2 i1 =

(3.13)

if

f

rd,ref

=

Pr ,IM Lr if p Mi sq,max f ,mes

f

5. Modeling and control of grid powers

fn ,

>

fn ,

The power expected from the coupling VSWG-FESS assembly and transmitted on DC bus is applied to converter 3 (Fig. 1) whose order must ensure the control of the active and reactive power injected to the grid characterized by a voltage vr and frequency f = 50 Hz. Similar to [35], we select a reference frame rotating synchronously with the grid voltage space vector, which yields the dynamic model described by

(3.14)

where ϕrd,n is the rated value of the direct component of the flux, i sq,max is the maximum stator q current, Ωf,mes is the measured speed of the IM rotor, and Ωfn is the nominal speed of the IM. Based on (3.13), we may express the reference electromagnetic torque as

Tem =

Pf ,ref

=p

f ,mes

M isq,ref Lr

rd,ref

(3.15)

and consequently, the reference current is

i sq,ref =

Lr pM

Pf ,ref rd,ref

.

f ,mes

(4.2)

where ird and irq denote the Park components of the modulated currents at the output of converter 3. It is important at this stage to note that since the switching frequency is not taken into consideration in this equivalent model, the voltage and current harmonics cannot be predicted.

In [32,33] and numerous subsequent studies, it was shown that fluxweakening control of the IM may be accomplished by the simple laws rd, n

(4.1)

with (u wd1 u wq1)T , (u wd2 u wq2 )T , and (u wd3 u wq3 )T being the Park components of the reference voltages of converters 1, 2, and 3, respectively, and vod and voq are the Park components of the modulated voltages at the output of converter 3. By disregarding the converter losses and equating the average power on the DC side with the active power on the AC side for each of the three converters yields the currents

vrd = vod

Rird

vrq = voq

Rirq

dird +L dt dirq L L dt L

r i rq , r i rd ,

(5.1)

where L and R are the grid inductance and resistance, respectively, and ωr denotes the grid frequency. The active power Pr and reactive power Qr delivered to the grid are given by

(3.16)

Finally, current references are obtained by means of an FOC algorithm. In the flux-oriented reference frame, measurements of the stator currents and rotor speed are used to estimate the space vector position of the rotor flux. In addition, a suitable full dynamic saturated machine model is adopted for the IM in order to allow operation in the IM's fieldweakening region with speeds below and above the base value. A block diagram of the FESS-IM controller is depicted in Fig. 8.

vr = vrd + j0.

4. Modeling of power converters

Substituting in (5.2) yields the reduced powers

Pr = vrd i rd + vrq i rq, Qr = vrq ird vrd i rq .

(5.2)

Since the d-axis of the chosen reference frame is oriented along the grid voltage, the grid voltage vector is simply

Pr = vrd i rd , Qr = vrd i rq .

In the modeling of the power converters we make use of the instantaneous average value method [34]. This modeling strategy is interesting as it adaptively selects a suitable integration step thereby alleviating the necessity of choosing a step lower than the period of

(5.3)

(5.4)

Based on (5.4), it is easy to regulate the power supplied to the grid by selecting the reference values of the grid current direct and quadrature

7

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Fig. 10. The overall control structure for converter 3.

components as

Pr ,ref , vrd Qr ,ref = . vrd

ird,ref = irq,ref

(5.5)

Hence, the active and reactive powers can be controlled by controlling the direct and quadrature current components, respectively. We use two separate control loops for the active and reactive power as in [36]. Keep in mind that the desired reference value for the reactive grid power is Qr,ref = 0kVAR. The current controllers will provide a voltage reference for the converter which is compensated by adding compensation terms. Both of the controllers applied here are PI-based. A block diagram summarizing the overall control structure of converter 3 is depicted in Fig. 10. In this structure, converter 3 is controlled to compensate a reactive power into the grid.

Fig. 12. The mechanical turbine speed Nt.

6. Simulation results and discussions In this section we put the models and control schemes proposed in this paper to the test using numerical simulations carried on Matlab–Simulink. The overall system comprises of a PMSG-based VSWG associated with an IM-based FESS connected to the AC grid. A realistic wind speed profile taken over time window of 300 s is considered as depicted in Fig. 11. For simplicity, we have omitted most of the parameters from our discussion and listed them in Appendix A. The

Fig. 13. The power coefficient Cp of the wind turbine.

initial flywheel speed is assumed to be 2250 rpm. The VSWG is controlled to capture the maximum wind energy. When the rotational speed is less than the nominal value of 25 rpm as shown in Fig. 12, the conversion system operates the MPPT control law (2.10), the power coefficient is at its maximum Cp = 0.44 as depicted in Fig. 13, and the blades are at their optimal angle β = −2 (Fig. 14). Conversely, if the wind speed exceeds the turbine's nominal value, the VSWG crosses over to nominal operation with a reduced power coefficient as shown in Fig. 13, constant rotational speed and generated

Fig. 11. A realistic wind speed profile taken over a 300 s time window.

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Fig. 14. The time evolution of the actual pitch angle β and the reference angle βref.

Fig. 17. Electromagnetic coupling Tem of the standard PI and fuzzy PI controllers.

examine the performance of the PI controller and the extent of the improvement achieved by the added fuzzy component, Figs. 15–17 depict the time evolution of the stator currents isd and isq and the electromagnetic torque of the PMSG Tem, respectively, with both the PI and fuzzy-PI controllers. The current responses indicate that the two controllers are adequate. However, As shown in Fig. 15, less ripple is observed in the stator current isd when the fuzzy-PI controller is activated. The current converges to zero in a short time and remains within a smaller range. The second current component isq shown in Fig. 16 is more important as it is directly required to the electromagnetic torque. Again, an important observation can be made regarding the current dynamics. The fuzzy-PI controller shows faster tracking of the reference currents and a lower offset after the current settles. This effect is more noticeable during setpoint changes as the standard PI controller experiences an apparent overshoot that is not observed in the fuzzy case. This can be attributed to the fact that the response time of the PI controller is design dependent whereas the fuzzy controller has a variable response time allowing it to adapt quickly to changes in the setpoint. The overall envelop of the electromagnetic torque as shown in Fig. 17 is a mirrored (upside down) replica of the current isq. Hence, the same observations hold. As expected, one can easily observe the strong correlation of the PMSG speed with the actual wind speed. Fig. 18 confirms that the MPPT strategy succeeds at maintaining the wind power at its optimal value even as the turbine speed exceeds the nominal value. Throughout the simulations, the active power reference Pr,ref is selected as a multistep function as shown in Fig. 19 and the reactive power reference Qr,ref is assumed to be equal to zero as in Fig. 20. As mentioned earlier, setting Qr,ref to zero aims to compensate for the

Fig. 15. The direct component of the stator current isd for the standard PI and fuzzy PI controllers.

Fig. 16. The quadrature component of the stator current isq for the standard PI and fuzzy PI controllers.

power values, and an increased pitch angle β to lower the turbine torque. Fig. 14 shows the observed increase in the pitch angle at high wind speeds. The pitch angle seems to follow the reference value closely. Fig. 15 shows the power supplied by the wind generator. Note that the negative sign refers to power being generated (produced) as opposed to consumed. Also note that these limited power results correspond to the wind speed being in excess of its nominal value of 750 KW. These results indicate the successful pitch angle and MPPT controls of the turbine blades. Next, we assess the proposed controller for the VSWG. In order to

Fig. 18. The active power Pwg of the wind generator system.

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Fig. 22. The active power of the flywheel energy storage system Pf and the corresponding reference value Pf,ref.

Fig. 19. The active power of the grid Pr along with the corresponding reference Pr,ref.

Fig. 23. The rotational speed of the flywheel (Nf).

Fig. 20. The reactive power of the grid Qr along with the corresponding reference value Qr,ref.

Fig. 24. The electromagnetic torque of the squirrel cage induction machine Tem. Fig. 21. The DC bus voltage udc.

see a fluctuation in Pf with positive values corresponding to power being stored in the flywheel and negative values corresponding to power being supplied to the grid to compensate for shortages. This high fluctuation coincides with the fluctuation in the power generated by the VSWG and causes the flywheel to change its speed over time. The rotational speed of the Flywheel Nf is shown in Fig. 23. As expected, the speed increases as energy is transferred to the flywheel and decreases as the flywheel is unloaded. Fig. 24 depicts the IM electromagnetic torque Tem which again fluctuates in a close to identical manner to the FESS power Pf. The reference and actual direct rotor fluxes are depicted in Fig. 25. The actual flux tracks the reference value almost exactly as can be seen in the figure. It is important to mention that the IM is in fact operating in the flux-weakening region. Another

reactive power. In addition to the reference values, Figs. 19 and 20 also show the actual active and reactive powers of the grid, respectively. These results indicate a good tracking performance of both active and reactive powers. Since the reactive power is kept at zero, the system operates with a unitary power factor. We have, consequently, proven the ability of the VSWG-FESS to compensate the reactive power. The aim of the FESS is to regulate the power supplied by the generator to the grid by stabilizing the DC bus voltage as shown in Fig. 21. The DC bus voltage remains constant at 1500 V, which demonstrates the success of the FESS in achieving its main objective. Fig. 22 depicts the active power of the FESS Pf along with its reference value Pf,ref. We

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the zoomed in snapshots on the right hand sides of the two figures, the currents are out of phase with respect to the voltages, which implies that the power supplied by the VSWG to the grid is purely active. We see that the voltages and currents are in opposition of phase, which indicates the power flow from the VSWG-FESS to the grid. It is clear that the integration of the FESS has enabled us to smooth the net power injected into the grid despite the highly stochastic nature of the wind. 7. Conclusions and future work This study has investigated the integration of a squirrel cage IMbased FESS with an online PMSG-based VSWG to regulate the power flowing into the power grid. We have presented the complete system with multiple control strategies and simulated its response and overall performance using the Matlab/Simulink environment. The efficiency of the VSWG is maximized by means of an MPPT-optimized power generation as well as a pitch angle controller, both of which rely on the measured rotational speed of the turbine. Traditionally, the PMSG current is regulated by means of a standard PI controller. In our investigation, we proposed a modified fuzzy-PI controller and compared its performance to the standard one. We showed that the fuzzy component is capable of improving the tracking performance of the PMSG current and attenuating the current fluctuations. The second main objective of the study was to investigate the regulation of power flowing into an online grid by means of the FESS. The FESS stores any excessive power generated by the VSWG to compensate for shortages when the wind speed drops. The proposed control strategy for the FESS requires online measurement of the flywheel rotational speed and the reference FESS-IM power estimated from the measured voltage by means of a dedicated PI regulator. The ultimate aim of the controller is to control the DC bus converter (converter 2 in Fig. 8) using pulse-width modulation (PWM) to stabilize the voltage. In addition, a proportional integral (PI) based grid connection is proposed that controls the current and voltage amplitudes as well as the frequency passed onto the grid. The converter has been controlled to achieve a decoupled active and reactive power control suitable for operation at a unitary power factor. Simulation results based on a 300 s window of a realistic wind profile have been presented. The results confirm the feasibility and performance of each of the control schemes proposed in this study including the FESS, the VSWG, and the power grid. The overall dynamical performance of the system proved the ability of the FESS to regulate the power supplied to the grid. In this study, we have not carried out an economic evaluation of the proposed system. However, it has been shown in numerous studies throughout the literature that wind energy is becoming cheaper and cheaper. In fact, a comprehensive study carried out in [37] found that

Fig. 25. The direct component of the flywheel rotor flux ϕrd and the corresponding reference value ϕrd,ref.

Fig. 26. The quadrature component of the flywheel rotor flux ϕrq. The reference value ϕrd,ref has been omitted as it is simply zero.

interesting observation is that the magnitude of the direct flux component is a function of the speed. Fig. 26 shows the quadrature component of the IM rotor flux. The two figures together give an indication of the decoupling effect between the direct and the quadratic rotor flux components of the IM. Finally, Figs. 27 and 28 show the grid voltage and current waveforms, respectively. The left sides of the figures show the time evolutions over the complete 300 second window. The three waveforms are in fact perfect sine waves with a constant amplitude independent of the wind speed and a constant frequency of 50 Hz. In addition, as shown in

Fig. 27. Grid voltages vra , vrb , and vrc (left) and a snapshot taken over the range 200–200.05 s (right).

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Fig. 28. Grid current ira, irb, and irc (left) and a snapshot taken over the range 200–200.05 s (right).

• Filter resistance, R = 0.01 Ω. • Filter inductance, L = 1 mH.

the cost of a single KW of wind power is estimated to be 2$. Studies have also considered the cost comparison of a FESS with other types of storage such as pumped hydroelectric storage, flow batteries, lithium batteries, hydrogen-based storage, etc. To the best of our knowledge, the general consensus seems to be that the cost of the FESS is comparable to other types [38,39]. A detailed study of the economic aspects of the proposed system is the subject of our future work.

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Conflict of interest None declared. Appendix A. Simulation parameters 1. Win turbine: Wind turbine radius, Rt = 24 m. Number of blades = 3. Nominal rotational speed, Ntn = 25 rpm. Optimal tip speed ratio, λoptimal = 5. Maximum power factor, Cp,max = 0.44. Density of air, ρ = 1.22 kg m−3. Dry friction torque, Ts = 953 N m. Viscous friction coefficient, f = 0 N m s rad−1. Total inertia of the mechanical transmission (turbine + PMSG), JT = 105 kg m2. 2. PMSG: Nominal power, Pn,PMSG = 750 kW. Nominal rotational speed, Nn,PMSG = 25 rpm. Number of pole pairs, p = 42. Stator resistance, Rs = 0.01 Ω. Self-inductance, Ls = 7.79 mH. Permanent magnetic flux, ϕa = 7.3509 N m/A. 3. IM and flywheel: Nominal powe, Pn,IM = 660 kW. Nominal voltage, Vn = 690 V. Nominal rotational speed, Nn,IM = 1500 rpm. Number of pole pairs, p′ = 2. Stator resistance, Rs = 14.6 mΩ. Rotor resistance, Rr = 23.8 mΩ. Stator inductance, Ls = 30.6 mH. Rotor inductance, Lr = 30.3 mH. Mutual inductance, M = 29.9 mH. FESS inertia (flywheel + IM), Jf = 1097.95 kg m2. Viscous friction coefficient, ff = 0.00646412 N m rad/s. 4. DC bus and filter: DC bus voltage, udc = 1500 V. Equivalent capacitance, C = 10 mF.

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