Page 1

Rotor-side Cascaded PI Controller Design and Gain

Tuning for DFIG Wind Turbines

Michael K. Bourdoulis, Student Member, IEEE, and Antonio T. Alexandridis, Member, IEEE

Department of Electrical and Computer Engineering

University of Patras

Rion, Patras, 26500, Greece

{bourdoulis, a.t.alexandridis}@ece.upatras.gr

Abstract—A novel and efficient solution to the problem of

designing and tuning the gains of cascaded PI controllers used in

DFIG wind systems is addressed in the present paper. The

overall design takes into account the nonlinear dynamic model of

the system while the analysis of the inner-loop controllers leads to

some new concepts, namely that of the effective time constant,

which in turn leads to a gain tuning rather independent from the

system parameters. The controller structure is completed by

exploiting the time-scale separation assumption in the design of

the outer-loop controller. This approach provides the possibility

to obtain a simple systematic method for tuning the outer-loop

controller gains, based on the well-analyzed in the literature

second order transfer function. Hence a more robust control

scheme with some essentially enhanced stability and transient

properties results, as it is clearly verified by extensive simulation

tests.

Keywords-DFIG wind turbines; cascaded controllers; PI

controller; controller gain tuning

I.

INTRODUCTION

Climate changes and CO2 emission reduction concerns

have lead electricity grids to take on a distributed generation

structure based on high local renewable energy sources (RES)

penetration. Among the RES connected at the distributed

generation system, variable-speed wind turbines play a key role

due to their size and increased capabilities [1]. Their main task

is to control active and reactive power and especially under

normal operation conditions to provide the optimal or

maximum energy available from the wind. Nowadays, this is

achieved by using large turbines, in the scale of MW, operating

at the variable-speed mode. Variable speed technique is used to

continuously track the generator rotor speed at its optimal value

as it is determined by the real wind speed in a manner that

guarantees the maximum mechanical power extraction [2].

In the frame of variable-speed wind turbine operation,

Doubly-Fed Induction Generator (DFIG) wind turbines are

widely used, for up to 3MW individual generator ratings

[1],[2]. They provide a possibility of variable-speed regulation

of about ±30% around the synchronous speed. To fulfill the

aim of maximum power tracking, an effective, stable and fast

controller scheme acting on the induction generator rotor side

has to be applied.

Vector or Field Oriented Control (FOC) is the standard

technique used for the control design of induction machines

[2],[3]. In this mode the system frame is aligned with the rotor

or the stator flux (field orientation). Especially for DFIGs, the

standard method used [2]-[5] is the stator-FOC (S-FOC). This

prerequires the system model to be represented in the

synchronously rotating dq reference frame. The benefits of this

dq reference model are that both the coupling stator and rotor

coils as well as the steady state variables and inputs (currents,

fluxes and voltages) become constant. As a result, two

controlled inputs are appeared, corresponding to the d and q

components of the rotor voltage, on which usually PI

controllers are implemented. The structure of two cascaded

controllers is used at each input, with the inner-loops regulating

the d and q current components while exact cancelation

networks for decoupled operation are utilized [5],[6]. The

dominant controller design method used for the inner-loop

controller gains is directly dependent from the generator

parameters. The outer-loop PI controllers provide the reference

current values and they are tuned to have a slower response

than those of the inner-loop, a feature typical for cascaded

controllers, known as time-scale separation assumption. Thus,

the two outer-loop PI controllers are used to regulate the

generator’s rotational speed at the optimum (corresponding to

the maximum wind power extraction) and the stator’s reactive

power [4],[5].

Nevertheless, the cascaded controller design is a

challenging problem since the DFIG wind turbine is a

nonlinear system with parameters that may change during the

system operation; there does not exist a systematic and efficient

way of tuning the outer- as well as the inner-loop gains in a

manner relaxed from the accurate system parameters.

In this paper, an alternative cascaded controller design and

tuning method suitable for DFIG wind turbines is proposed. In

particular, firstly the inner-loop controller is substantially

relaxed from the system parameters since the controller design

and gain tuning is based on the concept of the effective time

constant. By introducing this concept, we obtain a controller

with enhanced characteristics which however does not depend

its stability properties on the accurate system parameter values.

Secondly, the outer-loop PI controller is slightly modified in a

way that permits its analysis as a second-order linear system.

In Section II the DFIG model in the dq synchronously

rotating frame is provided. Then, in Section III the DFIG rotor-

side control tasks are presented in the S-FOC frame. The

proposed control scheme is presented in Section IV, where the

978-1-4673-6392-1/13/$31.00 ©2013 IEEE

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inner- and outer-loop controller design and tuning methods are

established. Finally, in Section V the performance of the

closed-loop system is evaluated through extensive simulation

results, while in Section VI some conclusions are addressed.

WRIG

Drive Train

Gear Box

Grid

Back?to?back ac/dc

converters with dc?link

and R?L filter

Fig. 1. The DFIG wind system.

II.

DFIG MODELING

A DFIG, as shown in Fig. 1, consists of a wound rotor

induction generator (WRIG) with its stator connected directly

to the grid and its rotor connected to the grid through a

frequency converter, comprising of two back-to-back ac/dc

converters with a dc-link, and an R-L filter at the grid-side.

Under balanced three-phase ac conditions, the dynamic

model of the DFIG with states and inputs in the dq

synchronously rotating frame can be written as [7]

dsdss qss ds

R IU

λ

?

ω λ=−+

(a)

qs qss dss qs

R IU

λ

?

ω λ=++

(b)

()

drdrsr qrr dr

Vp R I

λ

?

ω ω λ=−−+

(c) (1)

()

qr qrsr drrqr

Vp R I

λ

?

ωω λ=+−+

(d)

errm

TJbT

ω

?

ω=++

(e)

ds s ds

L I

L I

m dr

L I

L I

drr dr m ds

L I

L I

qss qsm qr qrr qrm qs

L I

L I

λ

λ

λ

λ

=

=

+

+

=

=

+

+

(2)

3

2

()

m

e qs dr

I

λ

ds qr

I

λ

s

L

L

Tp

=−

(3)

3

2

3

2

3

2

3

2

()()

()()

sd ds q qss q dsd qs

r dr dr qr qrr qr drdr qr

P U IU IQ U IU I

PV IV IQV IV I

=+=−

=+=−

(4)

where d and q subscripts stand for the d- and q-axis

components, r and s subscripts stand for rotor and stator, U and

V stand for the constant grid voltage and the controlled voltage,

? stands for flux, I stands for current, p stands for the number

of pole pairs, ?r stands for the rotational speed of the generator

rotor, R stands for ohmic resistance, L stands for inductances

and Lm is the mutual inductance, J is the total moment of inertia

at the rotor of the induction generator, b is the damping

coefficient, Te and Tm are the electrical and mechanical torque

at the rotor, while P and Q stand for active and reactive power.

The dot over a symbol stands for the time derivative of the

corresponding variable.

III. DFIG OPERATION IN THE S-FOC FRAME AND ROTOR-

SIDE CONTROL TASKS

It is well-known that the DFIG and its controllers is

realized into the standard frame of S-FOC technique for the

DFIG wind power systems. This technique continuously

identifies a synchronously rotating flux axis for the DFIG. The

aim of applying S-FOC, i.e. accurate identification on the stator

flux axis, is the independent regulation of the electric torque

and the stator flux via the two orthogonal rotor current

components Idr and Iqr, respectively.

To implement the S-FOC technique, let the reference frame

be aligned with the d-axis component of the stator flux, that

means ?qs=0. This reduces the electromagnetic torque

expression (3) to

3

2

m

e ds qr

I

λ

s

L

L

Tp

= −

(5)

It is obvious that for a constant value of ?ds the

electromagnetic torque depends only on the q-axis component

Iqr of the rotor current.

On the other hand, the mechanical power captured from the

wind by the turbine is given by [8]

()

23

wind

1

2

,

mp

P R Cu

ρπλ β

=

(6)

where ? is the air density, R is the radius of the turbine blades,

uwind is the wind speed and Cp is the power coefficient of the

wind turbine, ? is the blade pitch angle and ? is the tip-speed

ratio.

In order to achieve maximum active power extraction, the

maximum value of Cp should be achieved for some constant

?=?opt. This can be achieved through the optimal rotational

speed of the generator, provided by

,

opt

R

g

r optwind

n

u

λ

ω

=

(7)

where ng is the gear ratio due to the existence of a gearbox.

Thus, the wind speed uwind determines through (7) the rotor

generator speed that corresponds to the maximum wind power

extraction. As a result, the rotor-side one controller task is to

adapt the generator speed ?r to a reference

,

ref

rr opt

ωω=

.

Taking into account (5), one can see that for any wind

speed uwind the controller should enforce Te to follow Tm by

regulating Iqr to a suitable

qr

I

, as can be realized by an inner-

loop PI q-axis current controller. This reference value

obviously comes from an outer-loop PI controller which

regulates

r

ω

such that DFIG meets maximum Pm

corresponding to the optimum Tm .

ref

ref

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In the same way, it can be easily shown that reactive stator

power can be regulated through the Idr inner-loop PI controller,

since Qs is dependent from Idr (one can combine (4) with (2) to

reach this relation). A common way to determine

enforcing ?ds to a desired reference value through an outer loop

PI controller. In this paper,

dr

I

is chosen to be constantly zero,

resulting to an almost constant but high value of the stator’s

reactive power.

ref

dr

I

is by

ref

IV. DFIG ROTOR-SIDE CONTROL SCHEME

Before presenting the proposed control scheme, the system

is transformed to an equivalent and appropriate form for the

analysis. Using (1), (2) and taking into account the reference

frame alignment at the stator flux, i.e.

following dynamic equations for the rotor currents can be

acquired

(

1

r dr drr slip qr

III

στ στ ω

+=−

0

qs qs

λ

?

λ

==

, the

)

r

dr

ds

mr

V

RL

σ τ

−

λ

?

+

?

(8)

()

1

qr

r

rqr qrr slip drslip ds

mr

V

R

I

?

II

L

σ τ

−

στ στ ω

= −

ωλ

+−+

(9)

where

2

m

1

sr

L L L

σ = −

,

rrr

L R

τ =

and

slipsr

p

ωωω=−

.

From the last expressions it is clear that the dynamics of

and

qr

I are coupled and they can be decoupled by introducing

the following two new control inputs,

dr

I

dr

u and

qr

u , as

()

1

r

dr

drr slip qr ds

mr

V

R

uI

L

σ τ

στ ωλ

?

−

=−+

(10)

()

1

qr

r

qrrslip drslipds

mr

V

R

uI

L

σ τ

στ ω= −ωλ

−

−+

(11)

Through (10) and (11), (8) and (9) are simplified to

r drdr dr

I

?

Iu

στ+=

(12)

rqrqrqr

I

?

Iu

στ+=

(13)

which represent two decoupled and identical first order

equations.

As shown in [6],

its derivative has a negligible average value. This leads to the

realization that the control input expressions can be simplified

to

ds

λ has a fairly constant value, ˆ

ds

λ , while

dr

drr slip qr

r

V

R

uI

στ ω=+

(14)

()

1

ˆ

qr

r

qrr slip drslip ds

mr

V

R

uI

L

σ τ

στ ω= −ωλ

−

−+

(15)

A. Rotor-side controllers’ structure

Due to the fact that equations (12) and (13) for

dynamics are decoupled first order differential equations, the

following PI current controllers for

dr

I and

qr

I

dr

u and

qr

u are proposed

0

()()

t

ref

dr

ref

drdrPdr drIdr dr

ukIIkIIdτ=−+−

?

(16)

0

()()

t

ref

qr

ref

qr qr Pqrqr Iqrqr

ukIIkIIdτ=−+−

?

(17)

where

representing the proportional and integrator gains, respectively.

Pdr

k ,

Pqr

k and

Idr

k ,

Iqr

k are positive scalars

The d-axis current reference,

zero [6]. On the other hand, the q-axis current reference,

is provided by a slightly modified outer-loop PI controller as

follows

ref

dr

I , is chosen to be equal to

ref

qr

I ,

0(

?

)

t

ref

qr

ref

rPrIr

Ikkd

ωω

ωωωτ = −+−

(18)

where

proportional and integrator gain, respectively, while

generator’s rotor rotational speed reference provided by (7).

P kω and

Ikω are positive scalars representing the

ref

r

ω

is the

B. Inner-loop Controller Tuning

It is obvious from (12) and (13) that the dynamics of the

rotor currents are identical to each other when the new control

inputs given by (10) and (11) are applied with inner-loop

controllers provided by (16) and (17). Thus the d and q

subscripts are omitted for remainder of the tuning analysis

providing the following expressions of the current dynamics

and the inner-loop controllers

rrrr

I

?

Iu

στ+=

(19)

0

()()

t

ref

r

ref

rr PrrIrr

ukIIkI I dτ=−+−

?

(20)

The Laplace transformations of (19) and (20) can be easily

calculated and manipulated to arrive at

( )

s

2

(1)

rPr Ir

ref

rrPrIr

I k s

+

k

Isksk

στ

+

=

++

which can be equivalently written in the following form

( )

s

1

( )1

r

ref

r ir

I

H ss

I

τ

=

+

(21)

where

arbitrary time constant resulting from the arbitrary selected

value of

Ir

k , while ( )H s represents a transfer function given

by

ir

τ

is calculated as 1

irIr

k

τ =

and represents an

1

2

1

1

( )

T s

T s

H s

+

+

=

(22)

with

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4th International Conference on Power Engineering, Energy and Electrical Drives

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POWERENG 2013

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1r

T

στ=

and

2

Pr

Ir

k

k

T

=

(23)

Transfer function (22) can represent a lead or lag

compensator if

12

TT

>

or

12

TT

<

unitary if

12

TT

=

and constitute the conventional design [6].

From the definition of

as

Pr

k becomes larger the transfer function

lag compensator. Obviously, for small values of

may represent a lead compensator.

, respectively, or even it can be

1T and

2T it is clear that, for a given

H s determines a

Ir

k ,

( )

Pr

k , ( )H s

As one can see from (21),

multiplier - amplifier - on the time constant

the effective time constant,

( )

H s acts as a dynamic

τ [9]. Defining

ir

eff

ir

τ

, as

( )

eff

ir ir

H s

ττ=

(24)

a lead operation of

frequencies, while at low frequencies

hand, a lag operation of

frequencies while, again, at low frequencies

shown in Fig. 2. A lag operation of

in increased damping of transients since it provides an effective

time constant

ir

τ

smaller at high frequencies, where transients

occur. On the other hand, a lead operation of

to result in poorly damped transients since it provides an

effective time constant

ir

τ

greater at high frequencies.

Therefore, lag operation is adopted since it is expected to

enhance transient performance.

( )

H s increases the value of

eff

ir

τ

at high

eff

ir ir

ττ=

; on the other

τ

at high

ττ=

( )

H s reduces the value of

eff

ir

eff

ir ir

, as

( )

H s is expected to result

eff

( )

H s is expected

eff

( )H ω

1

1

2

Τ

Τ

2

1

Τ

1

1

Τ

ω

Fig. 2. Asymptotic Bode plot for magnitude absolute value (lag operation).

Hence, for lag operation of ( )

H s ,

2T should be determined

as

2rr

Ta στ=

with 1

ra >

Taking into account (23), the arbitrary selection of

related with

Ir

k , σ and

Pr

k may be

rτ as follows

PrrrIrr Ir

kakk

στστ=>

(25)

Remark 1. If

transfer function with controller gains dependent from the

exact system parameters σ and

coincides with the standard technique used [6]. The proposed

design allows a small integral gain

manner that ensures reduced sensitivity at steady-state and the

flexibility to select

Pr

k large enough corresponding to some

arbitrary

1

r

α > . This approach permits a rather independent

controller design from the accurate values of the system

parameters. Simultaneously, since the time constant

clearly decreased when transients occur, a faster response and

decay than that of the initially selected

1

r

α = then

eff

irir

ττ=

, (21) reduces to a first order

rτ , and the proposed design

Ir

k to be selected in a

eff

ir

τ

is

ir

τ is expected.

C. Outer-loop Controller Tuning

Since the S-FOC technique used results in a stator flux ˆ

which is fairly constant, the electromagnetic torque expression

(5) can be written as

ds

λ

3

2

ˆ

m

e ds qr

I

λ

s

L

L

Tp

= −

and is directly dependent from the q-axis rotor current. Tuning

the inner-loop current controller to be faster enough than the

outer-loop, then one can consider

separate time-scale assumption. Thus, the simplified block

diagram of Fig. 3 is valid.

ref

qr qr

II

=

by using the

ref

qrqr

II

≡

+−

+−

eT

m

T

1

+

Jsb

r

ω

ref

r

ω

3

2

ˆ

m

ds

s

L

pL

λ

+−

Ik

s

ω

P kω

Fig. 3. Block diagram of the subsystem and its controller.

Considering the mechanical torque,

the following transfer function is acquired for the closed-loop

system

m

T , as a disturbance,

2

3

2

L

ˆ

3

2

3

2

ˆˆ

m

dsI

sr

ref

r

mm

dsP dsI

ss

L

p

J L

k

L

b

J

p

J L

p

J L

sksk

ω

ωω

λ

ω

ω

λλ

=

?

?

?

?

?

?

+++

(26)

It is obvious that the last transfer function’s form allows the

control designer to reach the following desired closed-loop

transfer function with ζ damping factor,

and unity static gain

n

ω natural frequency

2

n

22

n

2

r

ref

rn

ss

ω

ζω

ω

ω

ω

=

++

(27)

where

2

n

3

2

ˆ

m

dsI

s

L

p

J L

k

ω

ωλ

=

and

3

2

ˆ

2

m

n dsP

s

L

b

J

p

J L

k

ω

ζωλ

=+

.

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Applying for example the 2% criterion [10], the desired

settling time

sT is connected to ζ and

n

ω through

4

sn

T

ζω=

.

Also, for the desired damping factor

loop controller gains are calculated as

des

ζ

choice, the outer-

8

T

2

3

1

ˆ

ds

λ

s

P

sm

L

b

J

J

p L

k

ω

?

?

?

?

?

?

=−

(28)

22

des

2

3

1

ˆ

ds

λ

16

ζ

s

I

m

s

L

J

p L

k

T

ω

=

(29)

Remark 2. Usually, the outer-loop controller gains are selected

either empirically or by using complicated methods such as the

Symmetric Optimum Method [11]. In our case a simple gain

tuning method is proposed based on a flexible criterion used in

a well-known linear system technique [10]. Again, a design

lightly dependent from the system parameters is achieved.

V.

SIMULATION RESULTS

In this section, the effectiveness of the proposed design and

analysis is verified through extensive simulation results. The

response of a 2MW DFIG is simulated for the case of step

changes in the wind speed, as shown in Fig. 4. All the

parameters of the simulated system are provided in Table I. For

100

the inner-loop proportional gain is selected to be

10

Idr Iqr

kk

==

and through (25)

outer-loop controller gains are calculated for

ζ=

and ˆ

3.17

ds

λ =

through (28) and (29) to be equal

to

87.84

and

70.3

. The inner-loop low frequency

time constant is equal to 0.1sec while the high frequency

effective time constant is equal to 0.001sec. Two cases are

examined: i) with input including simplified decoupling as

given by (14), (15) and ii) without taking into account

decoupling, i.e.

drr dr

VR u

=

and

ra =

1.033

PdrPqr

kk

==

, while the

5sec

sT =

,

0.707

des

P kω=

Ikω=

qrr qr

V R u

=

.

TABLE I. 2MW DFIG WIND SYSTEM PARAMETERS

Symbol Quantity Value

s R

stator resistance 0.01 ?

r R

rotor resistance 0.00842 ?

sL

stator inductance 0.005305 H

rL

L

p

R

rotor inductance

0.0053137 H

m

mutual inductance

pole pairs

blade radius

rotor friction

coefficient

rotor inertia

0.0051839 H

3

35 m

b

0.00015 N*m*sec/rad

J

765.6 kg*m2

g n

β

ρ

λ

gearbox ratio 62.5

0o pitch angle

air density 1.2 kg/m3

6.325

opt

optimal tip-speed-ratio

s

ω

grid angular frequency 2?50 rad/sec

2

ds

2

qs

UU

+

grid voltage 700 V (rms)

05 1015 20 25 30 35404550

8

9

10

11

12

time (sec)

uwind (m /sec)

Fig. 4. Wind speed profile.

0

5 1015 20253035 40 4550

90

95

100

105

110

115

120

125

130

time (sec)

?

r, ?

r r e f ( r a d / s e c )

?r with decoupling

?r without decoupling

?rref

Fig. 5. DFIG rotor angular speed vs. its reference.

05 1015 2025 3035 404550

3.16

3.17

3.18

3.19

?ds (Wb)

05 1015 2025 3035 404550

-4

-2

0

2x 10

-3

time (sec)

?qs (Wb)

with decoupling

without decoupling

Fig. 6. Stator flux component responses.

05 1015 202530 35 404550

-50

0

50

100

150

Idr (A)

05 10 1520 2530 35 4045 50

0

500

1000

1500

time (sec)

Iqr (A)

with decoupling

without decoupling

Fig. 7. Rotor current component responses.

The response of the rotor rotation speed versus its reference

is provided in Fig. 5. Figures 6 and 7 provide the responses of

the d- and q-axis stator flux and rotor current components,

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POWERENG 2013

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respectively. It is clear that the cascaded controller design as

provided in Section IV is fully confirmed for the case where

decoupling networks are utilized. The d-axis flux component is

approximately constant at the ˆ

λ value selected, while the q-

axis flux component is effectively regulated to zero. The flux

and current responses appear to have a fast and smooth

transient for the case (i), while for case (ii) the system

robustness permits convergence to the steady-state equilibrium

after some oscillations with a slower transient.

ds

The stator and rotor active and reactive power responses are

provided in Fig. 8 and 9, respectively. As expected, the rotor

reactive power is minimized while the stator reactive power

experiences a large but almost constant at steady state value.

Finally, in Fig. 10 a zoom on the transient response of both

rotor currents is presented for different values of the

parameter, for case (i). It becomes clear that, as expected, when

α increases the transient response is enhanced with more

smooth and smaller in magnitude transients, while the settling

time is unaffected.

r

α

r

051015 20 25303540 4550

0

0.5

1

1.5

2x 10

6

Ps (W)

05 101520 25 3035404550

-1

0

1

2

3x 10

5

time (sec)

Pr (W)

with decoupling

without decoupling

Fig. 8. Stator and rotor active power responses.

05 10 15 202530 3540 4550

-10

-9

-8

-7x 10

5

Qs (Var)

05 1015 2025 303540 45 50

-2

0

2

4x 10

4

time (sec)

Qr (Var)

with decoupling

without decoupling

Fig. 9. Stator and rotor reactive power responses.

9.5 1010.5 11 11.512 12.513 13.5

-100

0

100

200

Idr (A)

9.510 10.5 1111.5 1212.51313.5

600

800

1000

1200

time (sec)

Iqr (A)

?r=1

?r=25

?r=50

?r=100

Fig. 10. Transient response detail of rotor current components.

VI. CONCLUSIONS

A more flexible design and innovative tuning method for

the conventional cascaded rotor-side control system of a DFIG

is proposed. Through extensive simulation results, enhanced

and robust transient performance has been demonstrated even

in the case where decoupling inner-loop networks are omitted.

REFERENCES

[1] R. Teodorescu, M. Liserre, and P. Rodriguez, Grid Converters for

Photovoltaic and Wind Power Systems. West Sussex, UK: Wiley-

IEEE Press, 2011.

[2] G. Abad, G. Iwanski, J. López, L. Marroyo, and M.A. Rodríguez,

Doubly Fed Induction Machine: Modeling and Control for Wind

Energy Generation Applications. Hoboken, NJ: Wiley, 2011.

[3] R. Pena, J.C. Clare, and G.M. Asher, “Doubly fed induction generator

using back-to-back PWM converters and its application to variable

speed wind-energy generation,” Proc. IEE- Elect. Power Appl., vol.

143, no. 3, pp. 231–241, May 1996.

[4] A.D. Hansen, P. Sørensen, F. Iov, and F. Blaabjerg, “Control of

variable speed wind turbines with doubly-fed induction generators,”

Wind Eng., vol. 28, no. 4, pp. 411–434, June 2004.

[5] W. Qiao, W. Zhou, J.M. Aller, and R.G. Harley, “Wind Speed

Estimation Based Sensorless Output Maximization Control for a Wind

Turbine Driving a DFIG,” IEEE Trans. Power Electron., vol. 23, no.

3, pp. 1156–1169, May 2008.

[6] A. Yazdani, and R. Iravani, Voltage-Sourced Converters: Modeling,

Control, and Applications. Hoboken, NJ: Wiley, 2010.

[7] P.C. Krause, O. Wasynczuk, and S.D. Sudhoff, Analysis of Electric

Machinery and Drive Systems, 2nd Edition. Piscataway, NJ: Wiley-

IEEE Press, 2002.

[8] L. Yang, Z. Xu, J. Østergaard, Z.Y. Dong, and K.P. Wong, “Advanced

Control Strategy of DFIG Wind Turbines for Power System Fault

Ride Through,” IEEE Trans. Power Systems, vol. 27, no. 2, pp. 713–

722, May 2012.

[9] I.C. Konstantakopoulos, M.K. Bourdoulis, and A.T. Alexandridis,

“An Alternative PI Controller Design Approach for PWM- regulated

ac/dc three-phase Converters,” IEEE Intern. Conf. on Industrial Tech.

(ICIT 2012), pp. 955-960, Athens, Greece, Mar. 19-21, 2012.

[10] J.J. D’Azzo, and C.H. Houpis, Linear Control System Analysis and

Design: Conventional and Modern, 2nd Edition. McGraw-Hill, 1981.

[11] J.W. Umland, and M. Safiuddin, “Magnitude and symmetric optimum

criterion for the design of linear control systems: what is it and how

does it compare with the others?,” IEEE Trans. Ind. Appl., vol.26, no.

3, pp. 489- 497, May/Jun 1990.

738

4th International Conference on Power Engineering, Energy and Electrical Drives

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POWERENG 2013