9 the Inertial Response of Induction Machine Based Wind Turbine

8/13/2019 9 the Inertial Response of Induction Machine Based Wind Turbine

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1496 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 20, NO. 3, AUGUST 2005

The Inertial Response of Induction-Machine-BasedWind Turbines

Alan Mullane, Member, IEEE,and Mark OMalley, Senior Member, IEEE

AbstractThe inertial response of a generator is influenced bythe sensitivity of the generators electromagnetic torque to changesin the power system frequency. This paper deals with the inertialresponse of wind turbines employing induction-machine-basedgenerators. A model of a field-oriented controlled doubly fedinduction generator based on a fifth-order induction-generatormodel is described. The proposed model is implemented in a ref-erence frame that allows the factors affecting the inertial responseof a doubly fed induction generator to be easily examined. Acomparison between the inertial response of a squirrel-cage anddoubly fed induction-machine-based wind-turbine generator isperformed using the developed models. It is found that the inertialresponse of a doubly fed induction generator employing field-ori-

ented control is strongly influenced by the rotor current-controllerbandwidth.

Index TermsAC generators, current control, digital signal pro-cessors, induction generators, power systems, transient analysis,variable-speed drives, wind energy, wind power generation.

NOMENCLATURE

Current (A).Polar moment of inertia (kg m ).Gains.Inductance (H).Reference frame angular ve-

locity (rad/s).Synchronous speed (rad/s).Rotor electrical angular velocity(rad/s).Rotor angular velocity (rad/s).Flux linkage (Wb).Machine pole number.Differential operator.Resistance .Applied mechanical torque

.Electromagnetic torque .Time constant (s).

Voltage ( ).Subscripts and Superscripts

Reference value.

Direct, quadrature axis component.

Rotor, stator.

Manuscript received August 27, 2004; revised November 30, 2004. This workwas supported by Sustainable Energy Ireland (SEI) through the National Devel-opment Plan and has been conducted in the Electricity Research Center, Univer-sity College Dublin, Dublin, Ireland, which is supported by Electricity SupplyBoard (ESB), ESB National Grid, Commission for Energy Regulation, CylonControls, and Enterprise Ireland. Paper no. TPWRS-00461-2004.

The authors are with the Electricity Research Centre, Department of Elec-tronic and Electrical Engineering, University College Dublin, Dublin 4, Ireland(e-mail: [email protected]; [email protected]).

Digital Object Identifier 10.1109/TPWRS.2005.852081

I. INTRODUCTION

GENERATORS and loads connected to power systems

worldwide rely on the strict regulation of system fre-

quency in order to operate correctly. In the standard operation

of a power system, the frequency is regulated within strict limits

by adjusting the electrical supply to meet the demand. If supply

and demand are not matched, the system frequency will change

at a rate initially determined by the total system inertia. System

inertia comprises the combined inertia of most of the spinning

generation and load connected to the power system. A generator

or load can be considered to contribute to system inertia if achange in system frequency causes a change in its rotational

speed and, thus, its kinetic energy. The power associated with

this change in kinetic energy is fed to or taken from the power

system and is known as the inertial response. The sudden par-

tial loss of supply is the typical initiator of a frequency event.

In this case, the combined inertial response of all remaining

electrical machines connected to the system is the main factor

that determines the initial rate of fall of frequency [1]. In order

that the power system frequency is not overly sensitive to the

supply-demand imbalance, it is extremely important that a large

proportion of generation and load connected a power system

contributes to system inertia by providing an inertial response.

Provision of inertial response is particularly important in iso-lated networks or networks with weak interconnection such as

that of Ireland, where the largest online unit can represent up to

25% of total generation [2]. In order to quantify the inertial re-

sponse of an electrical machine connected to a power system, it

is necessary to examine whether a change in system frequency

will result in a change in its rotational speed and kinetic energy.

As electrical machines operate on the principle of an opposing

electromagnetic and mechanical torque, changes in rotational

speed may only occur as a result of a change in one or both

of these variables. If the mechanical torque provided by the

prime mover is considered constant during the frequency event,

then it is the influence of changes in system frequency on theelectromagnetic torque that influences the inertial response of

a particular generator. If the electromagnetic torque is affected

by changes in the system frequency, then an inertial response

will be observed. In conventional synchronous generators,

the electromagnetic torque is sensitive to changes in system

frequency, and thus, an inertial response is naturally observed

[3]. However, the continuing penetration of renewable energy

into power systems is ensuring that an increasing number

of nonconventional generation systems are being connected

to power systems. Of the commercially available renewable

energy conversion systems, wind-turbine generators (WTGs)

are proving most successful, and thus, there is a distinct need

0885-8950/$20.00 2005 IEEE


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MULLANE AND OMALLEY: INERTIAL RESPONSE OF INDUCTION-MACHINE-BASED WIND TURBINES 1497

to quantify the effect of the increased penetration of such

generators. Many authors have identified that in the absence of

measurements, adequate computer models of WTGs must be

developed in order to investigate the many effects of increased

penetration of wind energy into power systems [4][6]. It has

been further stated that the development of realistic models

is one of the main factors that will facilitate the solution ofproblems associated with the increased penetration [7], [8].

Computer models of WTGs have appeared with many authors

concentrating on the popular doubly fed induction-generator

(DFIG)-based design, where the models have been used to

assess the general performance of WTGs employing such

generators [9], [10]. More recently, these models are being

used to assess the performance of DFIGs during voltage sags,

as this has been identified as a potential challenge for this type

of technology [11]. An assessment of the inertial response of

a WTG employing a DFIG has only recently appeared [12].

For the DFIG model presented in [12], it was stated that this

electromagnetic torque is decoupled from the power system

frequency, and hence, there is no contribution to system inertia.The authors state, however, that the control scheme of the DFIG

can have a significant influence on the dynamic performance

of WTGs with the DFIG topology. This paper will develop a

computer model of a modern WTG suitable for examining in-

ertial response. This paper will concentrate on the DFIG-based

design. A computer model of the generator and its control

system will be developed based on a fifth-order model of the

squirrel-cage induction machine. The developed model will

be implemented in a manner that allows the factors affecting

the inertial response of a DFIG to be easily examined. Using

the developed models, the inertial response of a DFIG will be

compared with the response of a squirrel-cage machine-basedWTG, and the factors affecting the inertial response of a DFIG

will be examined.

II. WTGs

Various WTG systems have been developed and connected to

power systems worldwide. Three of the most popular topologies

are outlined in Fig. 1, namely, the fixed-speed design employing

a squirrel-cage induction machine and the variable-speed de-

signs using the DFIG and the multipole synchronous machine.

Thefixed-speed design in Fig. 1 utilizes a squirrel-cage induc-

tion machine connected directly to the power system, whilethe DFIG and multipole synchronous machine design both em-

ploy a back-to-back converter in the connection of the electrical

machine to the power system. The back-to-back ac/dc/ac con-

verter allows power at arbitrary frequencies to be supplied to the

system at the system frequency and enables the WTG to operate

at variable speed. A variable-speed WTG allows for increased

energy capture at low wind speeds when compared with afixed-

speed design, allows for smoother power production, and, due

to the presence of a power-converter, allows for control of the

reactive power exchange with the power system [13]. While it

may be possible to observe an inertial response from some of

the commercially available WTGs, the multipole synchronous

machine design is an example of a generator that in its stan-dard configuration does not contribute to system inertia. It can

Fig. 1. Fixed-speed, DFIG, and multipole synchronous WTG topologies.

be seen from Fig. 1 that for the multipole synchronous machine

design, the back-to-back converter provides the only path be-

tween the machine stator and the power system. This converter

ensures that the system frequency is decoupled from the fre-

quency at the stator of the synchronous generator. Therefore, inits standard configuration, changes in system frequency will not

be seen at the stator of the machine; thus, there will be no change

in electromagnetic torque. In its standard configuration, a multi-

pole synchronous machine-based WTG will, therefore, not con-

tribute to system inertia and will not provide an inertial response

when the system frequency changes. In the case of the fixed-

speed and DFIG designs, there is a direct connection between

the power system and the machine stator. In order to quantify

the inertial response of such WTGs, it is necessary to examine

in detail the relationship between the system frequency and the

electromagnetic torque of these machines. This task is straight-

forward in the case of the squirrel-cage induction-machine de-sign as the operation of this machine is well documented [ 14].

In addition, computer models that accurately represent the op-

eration of such machines are well established [15] and may be

used to quantify the inertial response of a particular design em-

ploying this technology. The combination of a wound rotor in-

duction machine together with the back-to-back converter that

comprisesthe DFIG of modern variable-speed WTGs represents

a relatively new technology compared with the squirrel-cage in-

duction machine. As a result, computer models of DFIGs are

less well established than their squirrel-cage counterpart. The

back-to-back converter in a DFIG also incorporates complex

controllers that must be incorporated into the computer model.

These give the DFIG its variable-speed capability and allow theWTG to operate effectively over a wide range of wind speeds.


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The choice of control strategy incorporated can vary between

WTGs, but the most widely reported controller associated with

the DFIG of a WTG is field-oriented control (FOC) [16]. This

control strategy is well established in thefield of variable-speed

drives [17] and, when applied to the DFIG design, allows for

independent control of the electromagnetic torque and stator re-

active power. FOC is usually implemented in a digital signalprocessor (DSP) that constantly monitors the operation of the

WTG and adjusts the operation of the ac/dc/ac converter. In

order to fully assess the effect of changes in system frequency

on the electromagnetic torque and subsequent inertial response

of a WTG employing a DFIG, models of the machine, converter,

and the control system must be developed.

III. INDUCTION-MACHINE MODEL

The equations describing the operation of the squirrel-cage

induction machine as found infixed-speed wind turbines can be

written in a rotating reference frame using the transformation

[14] and neglecting magnetic saturation as

(1)

where and are the - and -axis stator voltages, and

and are the - and -axis rotor voltages. and are

the - and -axis stator currents, and and are the - and

-axis rotor currents. and are the per-phase stator androtor resistances referred to the stator, and are the -

and -axis statorflux linkages, and and are the - and

-axis rotor flux linkages. is the speed of rotation of the

frame, and is the rotor electrical angular velocity. The rotor

electrical angular velocity is related to the rotational speed of

the machine through the relationship , where

is the number of machine poles. The stator and rotor currents

can be expressed in terms of the dq flux linkages as

(2)

where is the per-phase stator inductance, is the rotor in-

ductance per-phase referred to the stator, and is the mutual

inductance per-phase and . The developed

electromagnetic torque is given by

(3)

with the equation relating the speed of rotation of the machine

to the electromagnetic and applied mechanical torque given by

(4)

where is the polar moment of inertia of the machine and primemover referred to the induction-machine shaft, and is the

mechanical torque provided from the prime mover also referred

to the induction-machine shaft. Equations (1)(4) comprise a

fifth-order model of an induction machine. The two mass shaft

model often included in WTG simulations is not modeled here,

as the primary aim of this paper is to examine the effects of

changes in system frequency on the decelerating electromag-

netic torque. Inclusion of a flexible shaft model will not af-fect this relationship but will result in an additional dynamic

in any observed inertial response. When simulating the opera-

tion of a squirrel-cage induction machine, such as that used in

afixed-speed WTG, the rotor voltage components and

are zero.

IV. FOC MODEL

The induction-machine model presented in Section IV may

also be used to simulate the operation of a doubly fed induction

machine, in which case and are nonzero. In addition to

the machine model, a model of the power converter and its asso-

ciated controls must also be included. The controller of a DFIG

is typically configured to allow for adjustment of the speed of

rotation of the WTG. The typical means of achieving control of

the WTG speed is to control the electromagnetic torque . As

can be seen from (1)(4), the equations describing the dynamics

of an induction machine comprise a set of differential equations

linking stator and rotor currents and voltages with torque, speed,

and angular position. Control of the electromagnetic torque

can appear complicated because of the intricate coupling of

these quantities. However, through appropriate choice of refer-

ence frame, the task can be simplified, upon which control of the

field-oriented quantities allows for independent control of the

electromagnetic torque. This technique, known as FOC, usuallyappears in the context of squirrel-cage induction machine fed

using a DSP controlled series-connected back-to-back converter

[18]. In the squirrel-cage case, a rotating frame is implemented

in the DSP such that the electromagnetic torque can be inde-

pendently controlled by controlling the stator current. While an

FOC squirrel-cage design controls torque by controlling stator

current, the controlled back-to-back converter of a DFIG is typ-

ically connected through slip rings to the rotor windings, and

independent torque control is usually achieved through control

of the rotor current. With this objective in mind, a model of the

FOC can be developed for the DFIG by rewriting equations (1)

with as the differential operator as

(5)

(6)

(7)

(8)


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The expression for electromagnetic torque (3) can also be

rewritten in terms of rotor current as

(9)

Examining (9), it can be seen that in order to have control over

the electromagnetic torque, it is desirable to have , in

which case in the reference frame of the DSP, the torque equa-tion reduces to

(10)

allowing the electromagnetic torque to be controlled by ad-

justing . By imposing on (5)(8), one gets the

necessary conditions to ensure that can be derived. It

can be seen that if the speed of rotation of the reference frame

of the DSP is chosen as

(11)

then (5) will reduce to

(12)

which has a solution and as required. Thus,

if the reference frame is chosen according to (11), then (10) will

represent the torque equation in the reference frame of the DSP,

and if a means of controlling can be found, then can be

controlled.

A means of controlling can be established by examining

(7) and (8) with the condition

(13)

(14)

It can be seen from (13) that the machine rotor current compo-

nent as seen by the DSP is a function not alone of but

also and . The dependence of on and can be

removed if the -axis applied rotor voltage is designed as

(15)

where is an auxiliary signal in the reference frame of the

DSP. A similar analysis for the -axis yields

(16)

The auxiliary signals and are available as outputs from

the - and -axis proportional-integral (PI) current controllers

(17)

(18)

where and are the reference - and -axis rotor currents,is the -axis proportional gain, is the -axis inte-

gral gain, is the -axis proportional gain, and is the

-axis integral gain. Equations (15)(18) comprise a model of a

field-oriented controller for a DFIG. In a practical implementa-

tion, the outputs of the current controllers and are usedto

calculate the applied rotor voltages according to (15) and (16).

The reference signal is derived from a required electromag-

netic torque set point according to (10), with derivedfrom a stator reactive power set point. The usual approach to

modeling a WTG employing an FOC DFIG is to use the stan-

dard induction-machine model presented in Section IV, which is

included within most power system simulation tools. The FOC

is then modeled using (15)(18) with the reference frame speed

calculated using (11). Using this approach together with a

fifth-order machine model results in a seventh-order model of

afield-oriented doubly fed induction generator. The two addi-

tional states result from the introduction of the two current con-

trollers (17) and (18). A model constructed in this manner could

then be used to examine the influence of changes in system fre-

quency on the electromagnetic torque and subsequent inertial

response of a WTG employing an FOC DFIG.

V. EQUIVALENTMODEL OFFOC DFIG

Many FOC DFIG models that have been presented use an in-

duction-machine model as described in Section IV coupled with

a model of the FOC as described in Section V. The very design

of an FOC DFIG, however, acts to cancel much of the coupling

and dynamics contained in an induction machine in order that

the torque be controlled by alone. Therefore, using the ap-

proach of separate machine and controller models results in un-

necessarily increased model order and complexity, as the can-

cellations and order reduction could be assumed from the onset

and an equivalent model of an FOC DFIG, thus, developed. Ifthe three-phase voltages corresponding to and are gen-

erated by the DSP and power-converter circuitry according to

(15) and (16), then in the reference frame of the controller, the

following simple relationships hold:

(19)

(20)

with (5) yielding thefinal dynamic equation in the equivalent

FOC DFIG model

(21)

This equivalent sixth-order differential equation-based FOC

DFIG model can be represented in block diagram format, as

shown in Fig. 2(a). If the closed-loop response of the current

control loops are represented by the transfer functions

(22)

(23)

then the reduced-order FOC DIFG model can be redrawn,

as shown in Fig. 2(b), where and. Fig. 2(b) includes the set-point calcula-


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Fig. 2. Equivalent FOC DFIG model.

Fig. 3. Frequencytrace following the loss of 300 MW of generation, measuredon Republic of Ireland system on a winter evening with approximately2900 MW of system demand.

tion (9), which calculates based on the required torque .

In addition, can be calculated based on a stator reactivepower set point. With the reference frame speed of the equiva-

lent FOC DFIG model given by (11), the equations relating the

stator voltages to are now given by

(24)

(25)

VI. RESULTS AND DISCUSSION

The inertial response of both squirrel-cage and FOC

DFIG-based WTGs may be assessed by applying a frequency

deviation to the developed models and examining its effecton the rotor rotational speed , the electromagnetic torque

, and electrical power. The frequency deviation that is used

for the assessment is shown in Fig. 3. This frequency trace

was measured on the Irish electricity system and shows the

frequency dropping to approximately 49.3 Hz, which occurred

following the loss of 300 MW of generation. The total system

demand at the time of the event was approximately 2900 MW. It

was assumed that the WTG was connected to an infinite busbar,

and thus, the system voltage at the point of connection of the

wind turbine remains constant during the frequency event.

Both the fifth-order squirrel-cage induction-machine model

described in Section IV and the equivalent FOC DFIG model

described in Section VI were implemented in Simulink usingthe parameters from a 2-MW WTG-based induction machine

TABLE I2-MW WTG INDUCTION-MACHINEPARAMETERS

listed in Table I. The accelerating mechanical torque

provided from the wind-turbine rotor was adjusted in the model

such that the WTG was operating at its rated power when the

frequency event occurred. It was assumed that a small increase

in generated electrical power above the rated value could be

tolerated for a short period following the frequency event. It

was also assumed that the WTG is largely insensitive to small

variations in rotational speed, and thus, was held constant

during the frequency event. During normal operation of a WTG,the signal is supplied from an external control loop, which

adjusts the speed of the WTG in order that maximum energy

is extracted at below rated wind speeds, and power smoothing

is achieved at and above rated wind speed. As the wind speed

was assumed constant during the frequency event, the reference

torque remained constant during the event. In order to make

a comparison between the inertial response of the squirrel-cage

and FOC DFIG design, the rotational speed of the FOC DFIG

was adjusted to match that of the squirrel-cage machine. A

first-order current-controller response was assumed for the FOC

DFIG model .

This assumption allows the current-controller bandwidth tobe easily adjusted by varying and . Due to the general

lack of WTG parameter data in the public domain, operational

values for and are dif ficult to obtain. Current controller

responses having time constants in the region of 5 ms have

been reported in ac/dc/ac converters similar to those found in

modern variable speed WTGs [21], [22]. For this examination,

however, slow current-controller time constants of

s were deliberately chosen to demonstrate a choice of FOC

DFIG parameters that results in a significant inertial response.

The resulting closed-loop current-controller response is shown

in Fig. 4, where it can be seen that the current reaches 63% of

its reference value in approximately 5 s. Fig. 5 shows the effect

of the measured system frequency deviation on the rotationalspeed of both the squirrel-cage and FOC DFIG-based WTG


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Fig. 4. Current-controller response s.

Fig. 5. Squirrel-cage and FOCDFIG rotational speed in response to frequencyevent.

model. It can be seen from Fig. 5 that for both the squirrel-cage

induction machine and the FOC DFIG, the rotational speed de-

creases with the system frequency. The reason for the decrease

in rotational speed is due to the change in electromagnetic

torque that occurs as a result of the reduction in system fre-

quency. The effect of the reduction in system frequency on

the electromagnetic torque can be seen in Fig. 6, where an

increase in decelerating torque can be observed in response to

the reduction in system frequency. The inertial response thatresults from the decrease in rotational speed and release of

kinetic energy can be seen by observing the electrical power

generated in Fig. 7, where an increase in generated electrical

power can be observed immediately following the frequency

event. The reduction in rotational speed in Fig. 5 and resulting

inertial response is brought about by the increased deceler-

ating electromagnetic torque seen in Fig. 6 and caused by the

reduction in system frequency. If the electromagnetic torque

were not sensitive to changes in the system frequency, then an

inertial response would not be observed.

The inertial response of the FOC DFIG observed above re-

sulted from the particular choice of current-controller parame-

ters. The relationship between these controller parameters andthe sensitivity of the electromagnetic torque of an FOC DFIG

Fig. 6. Squirrel-cage and FOC DFIG electromagnetic torque in response tofrequency event.

Fig. 7. Squirrel-cage and FOC DFIG-generated electrical power in responseto frequency event.

to changes in the system frequency can be understood by exam-

ining the block diagram representation of the FOC DFIG model

in Fig. 2(b). This diagram shows that the electromagnetic torque

of an FOC DFIG is a function of and . Changes in ei-

ther of these variables will affect the electromagnetic torque. In

the model presented in Fig. 2(b), the frequency deviation entersthe model through a deviation in the term (25). This causesa

change in , which in turn affects the electromagnetic torque.

As can be seen in Fig. 2(b), the torque control loop that adjusts

accounts for variations in , in order that the steady-state

value of equals the reference value . The speed of this

adjustment is determined by the bandwidth of the -axis cur-

rent controller that greatly affects the influence of changes in

on the electromagnetic torque and subsequent inertial re-

sponse of an FOC DFIG. For the current controller chosen here,

the bandwidth is adjusted by varying the parameter . To in-

vestigate the influence of current-controller bandwidth on the

inertial response of an FOC DFIG further, two additional values

of were chosen, resulting in varying current-controller band-widths. Using the three controller settings, the electromagnetic


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Fig. 8. FOC DFIG electromagnetic torque in response to frequency event forvarious current-controller settings.

Fig. 9. FOC DFIG generated electrical power in response to frequency eventfor various current-controller settings.

torque and generated electrical power were observed in response

to the frequency event used earlier.

It can be seen from Fig. 8 that as the time constant of the

closed-loop current-controller response is reduced, resulting in

an increase in current-controller bandwidth, the effect of the

change in system frequency on the electromagnetic torque is re-

duced. The inertial response observed as the increase in power

generation following the frequency event in Fig. 9 reduces as the

influence of the system frequency on the electromagnetic torque

reduces.

While a reduction in inertial response is observed with in-

creasing current-controller bandwidths, large current-controller

bandwidths ensure accurate control of electromagnetic torque.

Using this facility, the inertial response could be increased and

indeed made to resemble that of the squirrel-cage design by

actively decelerating the machine in response to a frequency

event. The extent of the deceleration and resulting inertial

response would be limited by machine and converter ratingsand also the WTG operating point, as deceleration may cause

Fig. 10. AC/DC/AC converter power in response to frequency event forvarious current-controller settings.

changes in captured aerodynamic power. Mechanical drive

train dynamics will also be affected by the choice of cur-

rent-controller bandwidths, where reduced current-controller

bandwidths ensure that changes in wind speed do not result

in rapid electromagnetic torque changes. With changing wind

speeds, the rotational speed will, thus, vary, and the captured

power will be filtered by the large WTG inertia, resulting in

smoother power production, more damped drive train mechan-

ical dynamics, and reduced drive-train mechanical stress.

The chosen controller parameters that result in varying iner-

tial responses will also result in varying power flows through

the ac/dc/ac converter. Referring to Fig. 1, changes in the power

flow through an ac/dc/ac converter may result in changes in thedc-link voltage. The dc-link voltage is regulated by Inverter II

through adjustment of the voltage at the terminals of Inverter II

such that the power flowing through Inverter I and onto the dc

link is matched by the powerflowing through Inverter II to the

power system. The regulation of dc-link voltage can, thus, be-

come problematic when there is a fast and large change in power

flowing onto the link or alternatively when Inverter II loses the

ability to deliver that power to the network that could occur,

for example, during a dip in network voltage. Fig. 10 shows the

power at the terminals of Inverter I for the three scenarios in-

vestigated above. It can be seen from the figure that the power

at the rotor terminals is 30 kW before the occurrence of the fre-quency event. This represents less than 2% of the rated turbine

power and is well within the rating of the power converter being

typically rated at 25%30% of the turbine rating [19]. As typ-

ical dc-link voltage responses would have setting times in the

region of 20 ms [20], it is also expected that the power varia-

tions shown in Fig. 10 would not result in excessive variations

of the dc-link voltage.

VII. CONCLUSION

It was found that if an FOC DFIG of a WTG is modeled in

a field-oriented reference frame, then the factors affecting theinertial response of the FOC DFIG can be readily identified. It


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was also found that upon using this approach, a more simpli-

fied equivalent model results than a model employing a sepa-

rate DFIG and FOC. The developed model was used to assess

the effects of increased penetration of WTGs on the inertia of

a power system where it is found that the inertial response of a

DFIG employing FOC depends on the bandwidth of the rotor

current controllers. In contrast to the FOC DFIGs complete de-coupling from system frequency reported by previous authors

[12], it was found that complete decoupling will only occur for

large current-controller bandwidths.

Controller structure and parameter details would have to be

provided in order to determine the inertial response of commer-

cially available WTGs. In addition to determining the inertial

response through simulation, measurements should be taken at

operational wind turbine generators to validate an expected in-

ertial response.

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1, pp. 119126, Feb. 2001.[16] A. Tapia, G. Tapia, J. Ostolaza, and J. Saenz,Modeling and controlof a wind turbine driven doubly fed induction generator,IEEE Trans.

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Alan Mullane (S01M03) received the B.E.degree in electrical and electronic engineering in1998 and the Ph.D. degree in electrical engineeringin 2003, both from the Department of Electrical andElectronic Engineering, University College Cork,Cork, Ireland.

In 2004, he joined the Electricity Research Centre,

University College Dublin, Dublin, Ireland, as aPostdoctoral Research Fellow. His research interestsinclude nonlinear modeling and control of dynamicsystems, with particular interest in simulation and

control of wind turbines and their integration into electrical networks.

Mark OMalley(S86M87SM96) received theB.E. and Ph.D. degrees from University CollegeDublin, Dublin, Ireland, in 1983 and 1987, respec-tively.

He is currently a Professor in University CollegeDublin and the Director of the Electricity Research

Centre,with research interestsin power systems,con-trol theory, and biomedical engineering.

9 the Inertial Response of Induction Machine Based Wind Turbine

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