9 the Inertial Response of Induction Machine Based Wind Turbine

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The Inertial Response of Induction-Machine-Based Wind Turbines Alan Mullane , Member, Member, IEEE, and Mark O’Malley , Senior Member, Member, IEEE 

 Abstract—The inertial response of a generator is influenced by the sensitiv sensitivity ity of the generato generator’s r’s electro electromag magneti neticc torque torque to changes changes in the power system frequency. This paper deals with the inertial respons responsee of wind turbines turbines employin employing g inductioninduction-mac machine hine-bas -based ed generat generators. ors. A model model of a field-orie field-oriented nted contro controlled lled doubly doubly fed induction induction generat generator or based based on a fifth-orde fifth-orderr induction induction-gen -genera erator tor model is described. The proposed model is implemented in a reference frame that allows the factors affecting the inertial response of a doubly doubly fed inductio induction n gener generato atorr to be easil easily y exam examine ined. d. A comparison between the inertial response of a squirrel-cage and doubly doubly fed inductioninduction-mac machinehine-base based d wind-turb wind-turbine ine generato generatorr is performed using the developed models. It is found that the inertial response of a doubly fed induction generator employing field-oriented control is strongly influenced by the rotor current-controlle current-controllerr bandwidth.  Index Terms—AC generato generators, rs, current current control control,, digital digital signal signal proprocessors, induction generators, power systems, transient analysis, variable-speed drives, wind energy, wind power generation.

NOMENCLATURE Current (A). Pola Polarr mome moment nt of iner inerti tiaa (kg (kg m ). Gains. Inductance (H). Refe Refere renc ncee fram framee angu angula larr vevelocity (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 . Appl Applie ied d mech mechan anic ical al torq torque ue . Electromagnetic torque . Time constant (s). Voltage oltage ( ). Subscripts and Superscripts

Reference value. Direct, quadrature axis component. Rotor, stator. Manuscrip Manuscriptt received received August August 27, 2004; 2004; revised revised Novembe Novemberr 30, 2004. 2004. This work  was supported by Sustainable Energy Ireland (SEI) through the National Development opment Plan and has been conducte conducted d in the Electricity Electricity Research Research Center, Center, Univer Univer-sity College Dublin, Dublin, Ireland, which is supported by Electricity Supply Board (ESB), ESB National Grid, Commission for Energy Regulation, Cylon Controls, and Enterprise Ireland. Paper no. TPWRS-00461-2004. The authors are with the Electricity Research Centre, Department of Electronic and Electrical Engineering, University College Dublin, Dublin 4, Ireland (e-mail: [email protected]; [email protected]; [email protected]). [email protected]). Digital Object Identifier 10.1109/TPWRS.2005.852081 10.1109/TPWRS.2005.852081

I. INTRODUCTION

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ENERA ENERATORS TORS and loads connected connected to power power systems systems worldwide rely on the strict regulation of system frequency in order to operate correctly. In the standard operation of a power power system, system, the frequency frequency is regulate regulated d within within strict limits 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 genera generatio tion n and load load connec connected ted to the power power system system.. A genera generator tor or load can be considered to contribute to system inertia if a change 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 partial loss of supply is the typical initiator of a frequency event. In this case, the combined inertial response of all remaining electrical electrical machines machines connected connected to the system is the main factor factor that determines the initial rate of fall of frequency [1 [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 isolated 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 [2]. In order to quantify the inertial response 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 the electromag electromagnetic netic torque that influences influences the inertial inertial response response of  a particular generator. If the electromagnetic torque is affected by changes in the system frequency, then an inertial response will be observed. observed. In convent conventional ional synchronous synchronous generators 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 into power power system systemss is ensuri ensuring ng that that an increa increasin sing g number number of nonconv nonconventio entional nal generation 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

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MULLANE AND O’MALLEY: INERTIAL RESPONSE OF INDUCTION-MACHINE-BASED WIND TURBINES

to quantify the effect of the increased penetration of such generators. Many authors have identi fied 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 of  problems 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 identi fied 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 signi ficant 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 inertial 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-based WTG, 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 designs using the DFIG and the multipole synchronous machine. The  fi xed-speed design in Fig. 1 utilizes a squirrel-cage induction machine connected directly to the power system, while the DFIG and multipole synchronous machine design both employ a back-to-back converter in the connection of the electrical machine to the power system. The back-to-back ac/dc/ac converter 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 a  fixedspeed 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 standard configuration does not contribute to system inertia. It can

Fig. 1.

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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 between the machine stator and the power system. This converter ensures that the system frequency is decoupled from the frequency at the stator of the synchronous generator. Therefore, in its standard con figuration, 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 multipole synchronous machine-based WTG will, therefore, not contribute to system inertia and will not provide an inertial response when the system frequency changes. In the case of the fixedspeed 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 straightforward in the case of the squirrel-cage induction-machine design as the operation of this machine is well documented [ 14]. In addition, computer models that accurately represent the operation of such machines are well established [15] and may be used to quantify the inertial response of a particular design employing this technology. The combination of a wound rotor induction 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 induction 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 the WTG 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  fi eld-oriented control (FOC) [16]. This control strategy is well established in the  field of variable-speed drives [17] and, when applied to the DFIG design, allows for independent control of the electromagnetic torque and stator reactive power. FOC is usually implemented in a digital signal processor (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.

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 electromagnetic torque. Inclusion of a flexible shaft model will not affect this relationship but will result in an additional dynamic in any observed inertial response. When simulating the operation of a squirrel-cage induction machine, such as that used in a  fi xed-speed WTG, the rotor voltage components and are zero.

III. INDUCTION-MACHINE  M ODEL

IV. FOC MODEL

The equations describing the operation of the squirrel-cage induction machine as found in  fixed-speed wind turbines can be written in a rotating reference frame using the transformation [14] and neglecting magnetic saturation as

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 associated 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 reference 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, usually appears 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 independently 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 typically 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

(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 and rotor resistances referred to the stator, and are the and -axis stator fl ux linkages, and and are the - and -axis rotor  fl ux 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  fl ux linkages as

(2)

where is the per-phase stator inductance, is the rotor inductance per-phase referred to the stator, and is the mutual inductance per-phase and . The developed electromagnetic torque is given by

(5) (6)

(3) with the equation relating the speed of rotation of the machine to the electromagnetic and applied mechanical torque given by

(7)

(4) where is the polar moment of inertia of the machine and prime mover referred to the induction-machine shaft, and is the

(8)

MULLANE AND O’MALLEY: INERTIAL RESPONSE OF INDUCTION-MACHINE-BASED WIND TURBINES

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 equation 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 component 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

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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 implementation, 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 electromagnetic torque set point according to (10), with derived from a stator reactive power set point. The usual approach to modeling a WTG employing an FOC DFIG is to use the standard 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  a  fi eld-oriented doubly fed induction generator. The two additional states result from the introduction of the two current controllers (17) and (18). A model constructed in this manner could then be used to examine the in fluence of changes in system frequency on the electromagnetic torque and subsequent inertial response of a WTG employing an FOC DFIG. V. EQUIVALENT M ODEL OF  FOC DFIG Many FOC DFIG models that have been presented use an induction-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 approach of separate machine and controller models results in unnecessarily increased model order and complexity, as the cancellations and order reduction could be assumed from the onset and an equivalent model of an FOC DFIG, thus, developed. If  the three-phase voltages corresponding to and are generated 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 the final 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)

(17) (23) (18) where and are the reference - and -axis rotor currents, is the -axis proportional gain, is the -axis inte-

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.

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Equivalent FOC DFIG model.

TABLE I 2-MW WTG INDUCTION-MACHINE P ARAMETERS

Fig. 3. Frequencytrace following the loss of 300 MW of generation, measured on Republic of Ireland system on a winter evening with approximately 2900 MW of system demand.

tion (9), which calculates based on the required torque . In addition, can be calculated based on a stator reactive power set point. With the reference frame speed of the equivalent FOC DFIG model given by (11), the equations relating the stator voltages to are now given by (24) (25)

VI. RESULTS AND  D ISCUSSION 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 effect on 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 in finite 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 using the parameters from a 2-MW WTG-based induction machine

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 to be easily adjusted by varying and . Due to the general lack of WTG parameter data in the public domain, operational values for and are diffi  cult 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 signi ficant 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 rotational speed of both the squirrel-cage and FOC DFIG-based WTG

MULLANE AND O’MALLEY: INERTIAL RESPONSE OF INDUCTION-MACHINE-BASED WIND TURBINES

Fig. 4.

Current-controller response

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s. Fig. 6. Squirrel-cage and FOC DFIG electromagnetic torque in response to frequency event.

Fig. 5. event.

Squirrel-cage and FOCDFIG rotational speed in response to frequency

model. It can be seen from Fig. 5 that for both the squirrel-cage induction machine and the FOC DFIG, the rotational speed decreases 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 frequency. 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 that results 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 decelerating 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 resulted from the particular choice of current-controller parameters. The relationship between these controller parameters and the sensitivity of the electromagnetic torque of an FOC DFIG

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

to changes in the system frequency can be understood by examining 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 either of these variables will affect the electromagnetic torque. In the model presented in Fig. 2(b), the frequency deviation enters the 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 current controller that greatly affects the influence of changes in on the electromagnetic torque and subsequent inertial response of an FOC DFIG. For the current controller chosen here, the bandwidth is adjusted by varying the parameter . To investigate 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 bandwidths. Using the three controller settings, the electromagnetic

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

Fig. 9. FOC DFIG generated electrical power in response to frequency event for 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 reduced. 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 increasing 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 ratings and also the WTG operating point, as deceleration may cause

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

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

changes in captured aerodynamic power. Mechanical drive train dynamics will also be affected by the choice of current-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 mechanical dynamics, and reduced drive-train mechanical stress. The chosen controller parameters that result in varying inertial 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 the dc-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  fl owing through Inverter I and onto the dc link is matched by the power fl owing through Inverter II to the power system. The regulation of dc-link voltage can, thus, become 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 investigated above. It can be seen from the  fi gure that the power at the rotor terminals is 30 kW before the occurrence of the frequency 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 typical dc-link voltage responses would have setting times in the region of 20 ms [20], it is also expected that the power variations 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 the inertial response of the FOC DFIG can be readily identi fied. It

MULLANE AND O’MALLEY: INERTIAL RESPONSE OF INDUCTION-MACHINE-BASED WIND TURBINES

was also found that upon using this approach, a more simplified equivalent model results than a model employing a separate 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 DFIG ’s complete decoupling 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 commercially available WTGs. In addition to determining the inertial response through simulation, measurements should be taken at operational wind turbine generators to validate an expected inertial response. REFERENCES [1] E. Welfonder, “Least-cost dynamic interaction of power plants and power systems,”   Control Eng. Practice , vol. 5, no. 9, pp. 1203–1216, 1997. [2] J. O’Sullivan and M. O’Malley,  “ Economic dispatch of a small utility with a frequency based reserve policy,”  IEEE Trans. Power Syst. , vol. 11, no. 3, pp. 1648–1653, Aug. 1996. [3] A. Ait-Kheddache and S. Ebron, “ Optimal load shedding methodologies in power systems,”  in   Proc. IEEE Conf. Southeastcon, 1988, pp. 269–272. [4] A. Feijoo and J. Cidras, “Modeling of wind farms in the load  flow analysis,”  IEEE Trans. Power Syst., vol. 15, no. 1, pp. 110–115, Feb. 2000. [5] Z. Saad-Saoud,  “ Models for predicting  fl icker induced by large wind turbines,”   IEEE Trans. Energy Convers. , vol. 14, no. 3, pp. 743 –748, Sep. 1999. [6] E. Welfonder, “Development and experimental identification of dynamic models for wind turbines,”  Control Eng. Practice, vol. 5, no. 1, pp. 63–73, Jan. 1997. [7] V. Akhmatov, H. Knudsen, and A. Nielsen,  “ Advanced simulation of  windmills in the electric powersupply,” Int. J. Elect. Power Energy Syst., vol. 22, no. 6, pp. 421–434, Aug. 2000. [8] M. Gustafsson andJ. Wiik, “Aggregation of wind park modelsfor studies on power system dynamics in weak networks,”  in  Proc. EWEA Special Topic Conf.: Wind Power 21st Century, Sept. 2000. [9] R.Pena, “Doubly fedinductiongeneratorusingback-to-back PWMconverters and its application to variable speed wind energy generation,” Proc. Inst. Elect. Eng., Electric Power Applications , vol. 143, no. 3, pp. 231–241, May 1996. [10] R. Datta and V. Ranganathan, “ Variable-speed wind power generation using doubly fed wound rotor induction machine—A comparison with alternative schemes,”  IEEE Trans. Energy Convers. , vol. 17, no. 3, pp. 414–421, Sep. 2002. [11] L. Holdsworth, X. Wu, J. Ekanayake, and N. Jenkins, “ Comparison of  fixedspeedand doubly-fedinductionwind turbines duringpowersystem disturbances,”  in   Proc. Inst. Elect. Eng., Gener. Transm. Distrib. , vol. 150, May 2003, pp. 343–352. [12] L. Holdsworth, J. Ekanayake, and N. Jenkins, “Power system frequency response from  fi xed speed and doubly fed induction generator based wind turbines,”  Wind Energy, vol. 7, pp. 21–35, 2004.

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Alan Mullane (S’01–M’03) received the B.E. degree in electrical and electronic engineering in 1998 and the Ph.D. degree in electrical engineering in 2003, both from the Department of Electrical and Electronic Engineering, University College Cork, Cork, Ireland. In 2004, he joined the Electricity Research Centre, University College Dublin, Dublin, Ireland, as a Postdoctoral Research Fellow. His research interests include nonlinear modeling and control of dynamic systems, with particular interest in simulation and control of wind turbines and their integration into electrical networks.

Mark O’Malley (S ’86–M’87–SM’96) received the B.E. and Ph.D. degrees from University College Dublin, Dublin, Ireland, in 1983 and 1987, respectively. He is currently a Professor in University College Dublin and the Director of the Electricity Research Centre,with research interestsin power systems,control theory, and biomedical engineering.