Comparative Study on the performance of Fuzzy … Energy and Power...Comparative Study on the...

Comparative Study on the performance of Fuzzy-PID

and MRAC-PID Controllers based on DPC with SVM

for DFIG using MPPT Strategy

F. Amrane and A. Chaiba

LAS Research Laboratory

Department of Electrical Engineering.

University of Setif 1, Setif, Algeria.

E-mail : [email protected]; [email protected].

Abstract—In this paper, we realized a comparative study of

hybrid controllers Fuzzy-PID and MRAC-PID for doubly fed

induction generator (DFIG) based on Direct Power Control with

a fixed switching frequency proposed for wind generation

application. First, a mathematical model of the doubly-fed

induction generator written in an appropriate d-q reference

frame is established to investigate simulations. In order to control

the DFIG, active and reactive power controllers and space-vector

modulation (SVM) are combined to replace the hysteresis

controllers used in the original DPC drive, a control law is

synthesized using PID controllers. We proposed two new control

strategies for controlling the rotor current, the first based on

RMCA and the second based on FLC. The performance of each

of them is based on the DPC algorithm are investigated and

compared to those obtained from the PID controller. Results

obtained in environment show that the

regulation of rotor currents via MRAC strategy is relatively

improved compared to that using FLC, namely the power error

and the quality of energy injected into the grid.

Keywords—Doubly fed induction generetor (DFIG), Direct

power control (DPC), Model Reference adaptive control

(MRAC), Space vector modulation (SVM), Fuzzy logic control

(FLC), maximum power point tracking (MPPT).

I. INTRODUCTION

The development of wind energy has grown significantly due to the diversity of exploitable areas and to the relatively attractive costs. Many of the wind turbines installed today are equipped with double fed induction machine (DFIG). However, most of these machines are connected directly to the network to avoid the presence of a converter. [1-2].

A DFIG consists of a wound rotor induction generator (WRIG) with the stator windings directly connected to a three-phase power grid and with the rotor windings mounted to a bidirectional back-to-back IGBT frequency converter. A schematic diagram of variable speed wind turbine system with a DFIG is shown in Fig. 1.

Control strategies of DFIG have been discussed in

literatures [3-5]. Control of DFIG through the Field Oriented

Control (FOC) which is performed by rotor currents control has

been developed in [6]. FOC method depends on parameters

variation and its power dynamics can be influenced by these

variations. Although, DFIG control using Input-Output

Feedback Linearization method can operate below and above

synchronous speed, but complication of control method and

dependence on parameters are its disadvantages.

Direct power control (DPC) strategy, as an alternative, has

been introduced to the DFIG based wind power generation, the

basic theory of DPC has been described in detail in [7], same as

the well-known direct torque control strategy, the basic DPC

has the demerits of large torque and current ripple and variable

switching frequency, a space vector modulation based constant

switching frequency DPC method is proposed in [8] to solve

the previous problems, and some compensation method is

proposed as well to improve the system performance. Further,

three improved DPC methods, with different control targets, for

DFIG control system have been discussed and implemented in

[9], it shows that these three strategies can be used to regulate

the active and reactive powers independently under both

normal and grid voltage-dip conditions with different steady

state and dynamic performance.

This paper is organized as follows; firstly the modeling of the turbine is presented in section II. In section III, the mathematical model of DFIG is given. Section IV presents Direct Power Control of DFIG which is based on the orientation of the stator flux vector along the axis ‘d’.

Fig.1. Schematic diagram of wind turbine system with a DFIG.

Ωmec

Gearbox

DFIG

Power

Grid AC/DC DC/AC

Pem

The power Converter

machine Side

The power Converter Grid Side

MPPT DPC Cp_max

Préf

Qref=0

Vα Vβ

Sα Sb Sc

SVM

PWM

Sα Sb Sc

International Conference on Automatic control, Telecommunications and Signals (ICATS15)University BADJI Mokhtar - Annaba - Algeria - November 16-18, 2015

1

In section V and section VI present Model Reference Adaptive Control and the model of Fuzzy logic control respectively, they are established to control the rotor currents after being compared by conventional regulators PID. In section VII, computer simulation results are shown and discussed. Finally, the reported work is concluded.

II. MODEL OF THE TURBINE

The wind turbine input power usually is:

(1)

Where is air density; is wind turbine blades swept area in the wind; is wind speed.

The output mechanical power of wind turbine is:

(2)

Where Cp represents the wind turbine power conversion efficiency. It is a function of the tip speed ratio λ and the blade pitch angle β in a pitch-controlled wind turbine. λ is defined as the ratio of the tip speed of the turbine blades to wind speed. is given by:

(3)

Where R is blade radius, Ωt is angular speed of the turbine. Cp can be described as [10-11]:

( ( )) [ ( )

( )]

( ) ( ) (4)

Fig.2. Power coefficient variation Cp

In our work we use the wind profile, as shown in fig. 3:

Fig.3. Wind profile (Wind Speed).

The maximum value of ( ) is achieved

for degree and for . This point

corresponds at the maximum power point tracking (MPPT) [16]

After the simulation of the wind turbine using this wind profile, we test the robustness of our MPPT, we have as results the curve of power coefficient versus time; this latter

achieved the maximum value mentioned in Fig.6 ( ) despite the variation of the wind

Fig.4. Power coefficient (Cp).

III. MATHEMATICAL MODEL OF DFIG

The generator chosen for the conversion of wind energy is

a double-fed induction generator, DFIG modeling described in

the two-phase reference (Park). The general electrical state

model of the induction machine obtained using Park

transformation is given by the following equations, [12-13]:

Stator and rotor voltages:

. (5)

. (6)

( ) . (7)

( ) . (8)

Stator and rotor fluxes:

(9)

(10)

(11)

(12)

The electromagnetic torque is given by:

( ) (13)

And its associated motion equation is:

0 2 4 6 8 10 12 140

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

X: 8.107

Y: 0.4785

Vitesse relative Lambda.

Coef

ficien

t de

puiss

ance

.

Cp

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.86

7

8

9

10

11

12

13

Time (Secondes).

Win

d S

pe

ed

.

Wind Speed (m/sec).

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

Time (Secondes).

Pow

er C

oeffi

cien

t.

Cp

Cp_max=0.4785

=8.107


2

(14)

(15)

where: is the load torque is total inertia in DFIG’s rotor, Ω

is mechanical speed and G is gain of gear box.

The voltage vectors, produced by a three-phase PWM inverter, divide the space vector plane into six sectors, as shown in Fig. 5 [14].

Fig. 5 The diagram of voltage space vectors in α-β plan.

In every sector, each voltage vector is synthesized by the basic space voltage vector of the 2 sides of the sector and 1 zero vector. For example, in the first sector, Vaβ is a synthesized voltage space vector and is expressed by:

(16)

After projection the vectors , and we have:

‖ ‖ ( )

(

√

√ )

(

√

√ )

(17)

‖ ‖ ( )

(

√

√ )

(18)

(√ √ )

(19)

√

(20)

IV. DIRECT POWER CONTROL OF DFIG

In this section, the DFIG model can be described by the

following state equations in the synchronous reference frame

whose axis d is aligned with the stator flux vector as shown in

fig. 6, ( )and ( ) [7].

By neglecting resistances of the stator phases the stator

voltage will be expressed by:

(21)

Fig. 6 Stator and rotor flux vectors in the synchronous d-q Frame.

We lead to an uncoupled power control; where, the

transversal component irq of the rotor current controls the

active power. The reactive power is imposed by the direct

component ird as in shown in Fig. 7:

(22)

(23)

The arrangement of the equations gives the expressions of

the voltages according to the rotor currents (Fig. 5):

(

)

(

) (24)

(

)

(

)

(25)

(26)

(

)

(27)

with:

(28)

where:

are stator flux components, are rotor flux

components, are stator voltage components,

are rotor voltage components. are stator and rotor

resistances, are stator and rotor inductances, is

mutual inductance, is leakage factor, is number of pole

pairs, is the stator pulsation, is the rotor pulsation, is

the friction coefficient, and are stator and rotor time-

constant, and is the slid.

Stator Axis: Is fixing

Rotor Axis

d-q Frame

θr

θs

0

θm

Sector1 Sector3

Sector4 Sector6

Sector5

β

α

Sector2

V2 (110) V3 (010)

V4 (011)

V5 (001) V6 (101)

V1 (100)

V0 (000)

V7 (111)

Vαβ

T1/Ts*V1

T2/Ts*V2


3

Fig. 7 The doubly fed induction generator simplified model.

V. MODEL REFERENCE ADAPTIVE CONTROL

The system studied in this paper is based on a first-order linear

plant approximation given by [15-17]:

( ) ( ) ( ) (29)

where x(t) is the plant state, u(t) is the control signal and a and

b are the plant parameters. The control signal is generated

from both the state variable and the reference signal r(t),

multiplied by the adaptive control gains K and Kr such that

( ) ( ) ( ) ( ) ( ) (30)

where K(t) is the feedback adaptive gain and Kr(t) the feed

forward adaptive gain. The plant is controlled to follow the

output from a reference model

( ) ( ) ( ) (31)

where is the state of the reference model and and

are the reference model parameters which are specified by the

controller designer. The object of the algorithm is for

→0 as →∞, where is the error signal. The

dynamics of the system may be rewritten in terms of the error

such that

( ) ( ) ( ( )) ( )

( ( )) ( ) (32)

Using Equations (27), (28) and (29), it can be seen that for

exact matching between the plant and the reference model, the

following relations hold

(33)

(34)

Where (K) E

denotes the (constant) Erzberger gains [18].

Equations (33) and (34) can be used to express Equation (35)

as:

( ) ( ) ( ) (

) (35)

For general model reference adaptive control, the adaptive

gains are commonly defined in a proportional plus integral

formulation

( ) ∫

(36)

( ) ∫

(37)

Where and are adaptive control weightings representing

the adaptive effort. is a scalar weighted function of the error

state and its derivatives, , where can be chosen

to ensure the stability of the feed forward block.

The equivalent scheme of MRAC for adjusting rotor currents

of DPC in this work is shown in fig. 8.

Fig. 8 The Simulink scheme of MRAC for rotor currents.

Fig. 9 The proposed DPC of a DFIG based on MRAC

VI. DISEIGN OF FLC CONTROLLER

The fuzzy controller used in this work has two inputs

and one output.

The fuzzy rule base consists of a collection of linguistic

rules of the form [4]

Rule 1: if is NB, and is NB then is NB.

Rule 2: if is NM, and is NB then is NB

Rule 3: if is NS, and is NG then is NS.

Rule 49: if is PB, and is PB then is PB.

These inferences can be made in a more explain as shown in

table.1 [4].

+-

+-

--

+-

+-

+-

irq

ird

Vrd

Vrq Ps

Qs

Rr +p*(Lr-Lm^2/Ls)

1

Rr +p*(Lr-Lm^2/Ls)

1

Ls*ωs

Vs^2

Lm*Vs g*

Lm*Vs

Ls -

Ls -

Lm*Vs

g*ωs*(Lr - (Lm^2/Ls))


--

Pref

Qref

Adaptive

Controller

Vrq_ref

Vrd_ref

ird_meas



irq_meas

Lm*Vs

Ls -

Ls - Lm*Vs

g* Lm*Vs

Ls

Ls*ωs

Vs^2

Ps

Qs

Irq_ref

ird_ref Error

ird_ref

Error

irq_ref

+-

+-

--

--

--

+-

-- +

-

+-

+-

--

+-

+-

+-

ird_meas

irq_meas

Adaptive

Controller +-

PID

PID

Error

Irdq

Irdqref

Vrdq*

Kerror

1/S

1/S

α

β

G

G1

+

+

+


4

TABLE.1. FUZZY INFERENCE TABLE.

NB NM NS EZ PS PM PB

NB NB NB NB NM NS NS EZ NM NB NM NM NM NS EZ PS

dS1,2 NS NB NM NS NS EZ PS PM

EZ NB NM NS EZ PS PM PM

PS NM NS EZ PS PS PM PB

PM NS EZ PS PM PM PM PB

PB EZ PS PS PM PB PB PB

The equivalent scheme of Fuzzy Logic control (FLC) for

adjusting rotor currents of DPC in this work is shown in figure

10.

Fig.10 The Simulink scheme fuzzy logic control for rotor currents.

Fig.11 The proposed DPC of a DFIG based on FLC

The overall system is described in detail, as shown in Fig.12.

Fig. 12 Global System.

VII. SIMULATION RESULTS

CASE I ( HYBRID MRAC-PID USING MPPT):

Fig. 13 Stator Active power Ps.

Fig. 14 Stator Reactive power QS.

Fig. 15 FFT analysis of spectrum THD of stator current is_abc (0.74%)

CASE II (HYBRID FLC-PID USING MPPT):

Fig. 16 Stator Active power Ps.

Fig. 17 Stator Reactive power QS.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

-4000

-3000

-2000

-1000

0

1000

Ps meas MRAC (W).

Ps ref (W).

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8-1000

0

1000

2000

3000

4000

Qs meas MRAC (Vra).

Qs ref (Var).

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

-4000

-3000

-2000

-1000

0

1000

Ps meas FLC (W).

Ps ref (W).

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8-1000

0

1000

2000

3000

4000

Qs meas FLC (Var).

Qs ref Var).

Sta

tor

Acti

ve P

ow

er

PS_M

RA

C (W

).

Sta

tor

Acti

ve P

ow

er

PS_FLC

(W

).

Sta

tor

Reactiv

e P

ow

er

QS_M

RA

C (V

ar)

.

Sta

tor

Reactiv

e P

ow

er

QS_FLC

(V

ar)

.

Time (seconds).

Time (seconds).

Time (seconds).

Time (seconds).

Vdc

Doubly Fed

Induction

Generator (DFIG)

Park :

abc/dq

Rotor Side

Converter

(RSC)

3

2

Space Vector

Modulation

(SVM)

Direct Power

Control (DPC)

Park Inverse

dq/abc+

Concordia

abc/αβ

3

2 3

2

Bloc

3

Bloc

1 Bloc

2

Fig. (9-11) Fig.5 Fig.7

Pref

Qref

Vrq_ref

Vrq_ref

Irdq_meas



Irdq_meas

Lm*Vs

Ls -

Ls - Lm*Vs

g* Lm*Vs

Ls

Ls*ωs

Vs^2

Ps

Qs

Irdq_ref

Irdq_ref Error

Error

+-

+-

--

--

--

+-

-- +

-

+-

+-

--

+-

+-

+-

+-

PID

PID

Irdq

Vrdq* 1/G1

1/G

1/G Z

1

Unit Delay

Fuzzy Logic

Controller

Fuzzif

icatio

n

Intefe

rence

Defu

zzif

icatio

n

1

1


5

Fig. 18 FFT analysis of spectrum THD of stator current is_abc (0.74%)

The DFIG used in this work is a 4 kW whose

nominal parameters are indicated in Table.2. And the wind

turbine used in this work is a 10kW whose parameters are

indicated in Table.3.

Fig.13 and Fig.16 present the stator active power and its

reference profiles injected into the grid using SVM for both

cases. It is clearly seen that the stator active power exactly

follows its reference to both cases; concerning the power error

is small using MRAC (Fig.13) for control of the rotor current

to the one using FLC (Fig.16). Fig.14 and Fig.17 show the

stator reactive power ant its reference using SVM for both

cases, we remark that the both reactive power equal to 0 Var,

that means the unity power factor. Using FLC-PID, we remark

the ripples in reactive power, is remarkable compared to

MRAC-PID, because the maximum of stator active power

equal to 4kW at 0.6sec, after that, the value of reactive power

becomes stable again equals to 0 Var.

Fig.15 and Fig.18 represent FFT analysis that helps us to

determine spectrum harmonics or the THD, which can

influence and disrupt the grid unless it has a low value. In our

work the THD of stator current using MRAC-PID and FLC-

PID equal to 0.74% (Fig.15 and Fig.18 respectively),

correspond in standard IEEE which should be lower than 5%.

VIII. APPENDIX

TABLE.2. PARAMETERS OF THE DFIG.

Rated Power: 4 Kwatts

Stator Resistance: Rs = 1.2Ω

Rotor Resistance: Rr = 1.8Ω

Stator Inductance: Ls = 0.1554 H.

Rotor Inductance: Lr = 0.1558 H.

Mutual Inductance: Lm = 0.15 H.

Rated Voltage: Vs = 220/380 V

Number of Pole pairs: P= 2

Rated Speed: N=1440 rpm

Friction Coefficient: fDFIG=0.00 N*m/sec

The moment of inertia J=0.2 kg*m^2

Slid: g=-0.04

TABLE.3. PARAMETERS OF THE TURBINE.

Rated Power: 10 Kwatts

Number of Pole pairs: P= 3

Blade diameter R= 3m

Gain: G=5.4

The moment of inertia Jt=0.00065 kg*m^2

Friction coefficient ft=0.017 N*m/sec

Air density: ρ=1.22 Kg/m^3

IX. CONCLUSION

In this work, two types of control have been proposed for

the control of the rotor current of the DFIG, using MRAC and

FLC respectively. The control of the DFIG should be more

robust because of the random shape of the winds. Using the

MPPT strategy for extracting maximum power and control of

the inverter is done via SVM. The results obtained using the

, have shown remarkable efficiency for

the both proposed methods, with a slight advantage of the

strategy MRAC compared with FLC, about the power error

and the THD of stator current injected to the grid.

X. REFERENCES

[1] R. Pena, et al., “Doubly Fed Induction Generator using Back-to-Back PWM Converter and Its Application to Variable-Speed Wind–Energy Generation”, IEE Proc. B, vol. 143, no.3, pp.231-241,1996.

[2] S. Muller, M. Deicke, R.W. D. Doncker, “Doubly fed induction generator systems for wind turbines”, IEEE Industry Application Magazine, Vol.8, No.3, pp. 26-33.2002.

[3] J. Ben Alaya, A. Khedher and M. F. Mimouni, " DTC, DPC and Nonlinear Vector Control Strategies Applied to the DFIG operated at Variable Speed", Journal of Electrical Engineering (.lEE), vol. 6, no II, pp. 744-753,2011.

[4] Ismail Bendaas, Farid Naceri and Sebti Belkacem, "Improving Asynchronous Motor Speed and Flux Loop Control by Using Hybrid Fuzzy-SMC Controllers", International Journal of Automation and Computing, vol 10, pp.361-367. 2014.

[5] Luna, F. K. A Lima, P. Rodriguez, E. H. Watanabe and R.Teodorescu, "Comparison of Power Control Strategies for DFIG Wind Turbines", IEEE Trans on Energy Conversion, pp. 2131-2136, 2008.

[6] AG. Abo-Khalil, G. Ahmed, "Synchronization of DFIG output voltageto utility grid in wind power system", Renewable Energy 44, pp. 193-198,2012.

[7] L. Xu, P. Cartwright. “Direct Active and Reactive Power Control of DFIG for Wind Energy Generation”, IEEE Trans. on energy conversion, vol.21,pp.750-758.

[8] D. W. Zhi, L. Xu. “Improved Direct Power Control of Doubly-Fed Induction Generator Based Wind Energy System”, IEMDC2007,pp.436-441.

[9] M. Guo, D. Sun, B. T. He, “Direct Power Control for Wind-Turbine Driven DFIG with Constant Switch Frequency”, ICEMS 2007,pp.1966-1971.

[10] Boukhezzar B, Robust Siguerdidjane H. Non linear control with

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[12] Gaillard A, Karimi S, Poure P, Saadate S. Fault tolerant back-to-back

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[13] Lie Xu Cartwright P. Direct active and reactive power control of DFIG

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[14] Zhi D, Xu L. Direct power control of DFIG with constant switching frequency and improved transient performance. IEEE Trans Energy Convers2007;22(1):110–8.

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[16] Youcef Bekakra, Djilani Ben Attous: ECTI Transactions on Electrical eng., Electronics, and Communications vol.11,pp 63-75 Feb (2013)

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[18] Khalil, H.K.: Nonlinear systems. Macmillan, New York,(1992).


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