1104 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 23, … · 2008-07-07 · 1104 IEEE TRANSACTIONS...

1104 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 23, NO. 3, MAY 2008

Low Voltage Ride Through of Wind Farms WithCage Generators: STATCOM Versus SVC

Marta Molinas, Member, IEEE, Jon Are Suul, and Tore Undeland, Fellow, IEEE

Abstract—This paper analyzes the extent to which the lowvoltage ride through (LVRT) capability of wind farms usingsquirrel cage generators can be enhanced by the use of aSTATCOM, compared to the thyristor controlled static var com-pensator (SVC). The transient stability margin is proposed as theindicator of LVRT capability. A simplified analytical approachbased on torque-slip characteristics is first proposed to quantifythe effect of the STATCOM and the SVC on the transient stabilitymargin. Results from experiments with a STATCOM and a 7.5 kWinduction machine emulating a wind turbine are used to validatethe suggested analytical approach. Further verifications basedon detailed time-domain simulations are also provided. Calcula-tions, simulations and measurements confirm how the increasedSTATCOM rating can provide an increased transient stabilitymargin and thus enhanced LVRT capability. Compared to theSVC, the STATCOM gives a larger contribution to the transientmargin as indicated by both calculations and simulations. Theinaccuracies introduced by neglecting the flux transients in thesuggested approach are discussed and found reasonable for anestimation method when considering the simplicity compared todetailed time-domain simulation studies. A method for estimatingthe required rating of different compensation devices to ensurestability after a fault is suggested based on the same approach.

Index Terms—Grid code, induction machine transient stabilitylimit, low voltage ride through (LVRT), voltage source static varcompensator (SVC).

I. INTRODUCTION

I N Norway, the potential for large scale generation of windpower is huge, but the impact of the wind generation on the

power system will no longer be negligible if high penetrationlevels are going to be reached. The extent to which wind powercan be integrated into the power system without affecting theoverall stable operation depends on the technology available tomitigate the possible negative impacts such as loss of genera-tion for frequency support, voltage flicker, voltage and powervariation due to the variable speed of the wind and the risk ofinstability due to lower degree of controllability.

Many countries in Europe and other parts of the world are de-veloping or modifying interconnection rules and processes for

Manuscript received February 27, 2007, revised November 12, 2007. Recom-mended for publication by Associate Editor Z. Chen.

M. Molinas and T. Undeland are with the Department of Electric Power Engi-neering, Norwegian University of Science and Technology, Trondheim N-7491,Norway (e-mail: [email protected], [email protected]).

J. A. Suul was with Sintef Energy Research, Trondheim N-7465, Norway andis now with the Norwegian University of Science and Technology, TrondheimN-7465, Norway (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TPEL.2008.921169

Fig. 1. Ride through profile from the Nordel grid code for the Nordic countriesNorway, Denmark, and Sweden.

wind power through a grid code [1], [2]. The grid codes haveidentified many potential adverse impacts of large scale integra-tion of wind resources. The risk of voltage collapse for lack ofreactive power support is one of the critical issues when it comesto contingencies in the power system. Closely linked to this isthe low voltage ride through (LVRT) capability, which is oneof the most demanding requirements that have been included inthe grid codes. The LVRT requirement, although details are dif-fering from country to country, basically demands that the windfarm remains connected to the grid for voltage dips as low as5% retained voltage [3]. The Nordel grid codes have adoptedthe LVRT profile shown in Fig. 1 for recommendation in theNordic region [4].

Significant barriers to interconnection are being perceived al-ready with the requirements of the new grid codes, and thereis a need for a better understanding of the factors affecting thebehavior of the wind farm under severe contingencies such asvoltage sags. Wind farms using squirrel cage induction genera-tors directly connected to the network will most acutely sufferfrom the new demands, since they have no direct electrical con-trol of torque or speed, and would usually disconnect from thepower system when the voltage drops more than 10–20% belowrated value [5]. In general, fulfilment of LVRT by reactive com-pensation will require fast control strategies for reactive powerin wind turbines/farms with cage induction generators.

Different solutions are found to support the transient be-havior of cage induction generators in case of changes in the gridvoltage. Mechanically switched capacitors, SVC, SynchronousCondensers and Voltage Source Static Var Compensator suchas the STATCOM can be used to regulate voltage as shuntcompensator to improve the grid interface of directly connected

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MOLINAS et al.: LOW VOLTAGE RIDE THROUGH OF WIND FARMS 1105

Fig. 2. Schematic configuration of the system under study: directly connected wind generation with controlled reactive compensation at the PCC.

asynchronous wind generators. Thyristor-controlled static varcompensators (SVCs) have been reported in [6], [7] for voltagesupport of critical loads, transient stability improvement andpower oscillation damping in electric power transmission sys-tems. The STATCOM has the same capabilities, as reported in[8], [9], but with a higher control bandwidth and the additionalcapability of providing higher currents at low voltage levels.Studies of transient stability of induction generators related tothe use of a STATCOM have been reported in [10], [11], anda general analysis of the ride through capability of fixed-speedwind farms with a STATCOM is provided in [12], [13].

In this paper, both the STATCOM and the SVC are analyzedfrom the point of view of their potential for increasing the tran-sient margin as reported in [14], [15] to indicate their capabilityas candidate solutions for providing LVRT to wind farms withinduction generators directly connected to the electric grid. Thetransient stability margin is defined as the difference betweenthe speed after a specified fault duration and the critical speed ofthe generator. A torque-slip based analysis of transient stabilitylimit with a STATCOM and SVC is first presented. Estimates forcritical speed and critical clearing time (CCT) are calculated fordifferent compensation levels of STATCOM and compared withthe case of no compensation, ideal compensation (stiff voltage)and compensation with SVC. Measurements under voltage sagcondition that gives 20% remaining voltage for 300 ms on alab set-up of 7.5 kW motor-generator set representing the windgeneration are then compared to the calculated values and eval-uated for LVRT capability assessment. Calculations and mea-surement results compared show a clear increase of transientstability margin with increased rating of the SATCOM. The cal-culations also indicate the better potential of the STATCOM toincrease the LVRT capability compared to the SVC. Compar-ison of critical speeds from the calculation method and detailedsimulation under the same conditions are also provided as a val-idation and to discuss the effect of the neglected flux transientsin the accuracy of the proposed calculation method.

The paper also gives a simple and efficient method for esti-mating the required ratings of STATCOM and SVC in terms ofLVRT capability, based on system sensitive parameters such asduration of voltage sag, generator parameters and network pa-rameters at the point of connection.

II. SYSTEM MODEL

A. System Model

Fig. 2 shows the schematic configuration of the system underconsideration for compensation with a STATCOM or SVC. Forthis study it is assumed that the power system is subjected to athree phase fault at the point of common coupling (PCC). Anytransformer connecting the generator to the PCC is not explic-itly represented in the figure but can be accounted for as seriesconnecting impedance.

The STATCOM is a power electronics device based on thevoltage source converter principle [16]. The technology typ-ically in use is, depending on voltage level and total rating,a two- or three-level voltage source converter, controlled bydigital techniques and connected to the power system in shuntthrough a filter and possibly a coupling transformer [17].

The SVC consists of a thyristor controlled reactor, andthyristor or mechanically switched capacitors. For the purposeof this investigation, the SVC can be considered as a shuntimpedance determined by the parallel connection of the ca-pacitor and the effective inductance of the thyristor controlledreactor [6], [16].

The main advantage of the STATCOM over thyristor typeSVC is that the compensating current does not depend on thevoltage level of the connecting point and thus the compensatingcurrent is not lowered as the voltage drops [18]. This is an impor-tant feature now that the new grid codes will require wind tur-bines to supply reactive power variably depending on networkdemand and actual voltage level. However, regarding the LVRT,the most relevant feature of the STATCOM will be its inherentcapability to increase the transient stability margin by injectinga controllable reactive current independently of the grid voltage.

For the case of the STATCOM, the system model of the com-pensation device is expressed by the equation of the voltage atthe point of compensation. The three phase voltage is expressedas

(1)


Fig. 3. Block diagram of the vector control technique implemented in the STATCOM and the control of the SVC.

where are grid voltages at the PCC, ,are STATCOM currents, and voltages generated

by the STATCOM, and are the per unit resistance andinductance between the converter and the grid, as shown in thedetail to the right of Fig. 2.

B. Control of the STATCOM and the SVC

The control strategy implemented in the STATCOM is basedon the vector control principle.[19], [20]. The main advantageof this is the decoupled control of the dc link voltage and reac-tive current in the same way as decoupled control of torque andflux can be obtained for a motor drive [21]. Equation (1) is trans-formed into a reference frame rotating at the grid frequency

(2)

Aligning the axis of the Park reference frame with the gridvoltage vector we have that . The angular position of thesupply voltage vector is found by a Phase Locked Loop (PLL)[22], [23].

The power balance between the dc link and the converteroutput gives

(3)

where is the dc link voltage and is the dc link current.In (3), is the direct component of the voltage at the PCC andduring the fault is the amplitude of the remaining voltage. The

dc link voltage can be controlled by modulating the converter di-rect axis current component to compensate for theconverter losses. The grid voltage can be controlled by the con-verter quadrature current component modulatingthe flow of reactive power from the STATCOM to the grid. Ablock diagram showing the structure of the vector control tech-nique implemented in the STATCOM is given in Fig. 3(a).

The control of the SVC can be assumed as a PI controllerthat regulates the firing angle of the thyristors of the thyristorcontrolled reactor (TCR). In this case it is assumed that theavailable capacitance and inductance of the SVC has the samerating, and that the inductance can be controlled to zero reactivecurrent. The simple control structure assumed for the SVC fordetermining the firing angle , and by that the resulting shuntimpedance of the SVC is showed in Fig. 3(b).

Both the STATCOM and SVC are controlled so as to obtain1 pu rated grid voltage before and after the fault. During and im-mediately after the fault, the compensating device will be con-trolled to its limits so as to give the maximum reactive compen-sation possible within the specified ratings.

III. TRANSIENT STABILITY LIMIT BY TORQUE-SLIP ANALYSIS

The transient stability of a directly connected induction gen-erator is analysed using a simplified approach based on torque-slip characteristics. The analysis is performed neglecting statorand rotor transients of the induction machine as argued in [24].Although the stator and rotor transients are neglected, the quasi-stationary dynamics of the machine can be used as a relevantsimplification to investigate the dynamic stability limit of thegenerator [25], [26]. This leads to the use of a traditional perphase equivalent circuit representing the induction machine, andstudying only the mechanical acceleration dynamics [27]. This


simplification will not be valid for transient phenomena domi-nated by the dynamics of the stator flux and rotor flux of the ma-chine, but is traditionally considered a suitable detailing levelfor power system studies involving voltage stability and loadrestoration [28]. In general, more simplifications are requiredwhen studying power systems compared to the dynamics of oneindividual device.

A. System Description and Principal Assumptions

With reference to the implemented control systems of theSTATCOM and the SVC, the following premises are stated re-garding analysis of the torque-slip curve before, during and aftera grid fault:

• before the fault, the STATCOM is controlled to keep thevoltage at its connection point constant at 1 pu. Initial op-erating conditions can be calculated from the inductiongenerator equivalent circuit (see Fig. 4) with the terminalvoltage at its nominal value;

• with reference to the assumed control structure, theSTATCOM will give maximum reactive current, and theSVC will be controlled to its maximum capacitive limitimmediately after the fault.

To simplify the analysis of rotor acceleration during the fault,it is also assumed that:

• during a severe three-phase fault reactive compensation bySTATCOM or SVC have negligible influence on the ter-minal voltage of the generator, and thus on the system be-havior;

• the voltage during the fault is close to zero, and the accel-erating torque during a three-phase fault is approximatelyconstant and equal to the initially applied mechanicaltorque.

The equivalent per phase circuit of the system after a faultis shown in Fig. 4, where , are grid voltage and induc-tion machine terminal voltage phasors, and , , ,

and are line, STATCOM, stator, magnetizing and rotorcurrent phasors. Grid impedance is while , arestator and rotor resistance and , , are stator, magne-tizing and rotor reactance. The STATCOM is represented by acurrent source and the generator is connected to a stiff voltagesource through the Thevenin impedance of the grid. The equiv-alent circuit of Fig. 4 can incorporate an SVC, by replacingthe current source with a capacitor, since during the fault andrestoring phases the SVC will be controlled to its capacitivelimits. Constant capacitor compensation at the machine termi-nals can also be included in the equivalent circuit, and any seriesimpedance between the STATCOM and the generator terminals,accounting for line- and/or transformer-impedance, can be in-cluded between the stator terminals and the shunt connection ofthe STATCOM or SVC.

Provided that a PWM converter is considered, the responseof the current and dc-link voltage controllers of the STATCOMcan be made very fast compared to the change of rotor speed,which will make the assumption of instantaneous current con-trol represented in the circuit of Fig. 4 to be relevant. Since sta-bility is determined shortly after reclosing, the representation of

Fig. 4. Quasi stationary equivalent circuit for the system under study, con-sisting of the traditional induction machine equivalent, STATCOM modelled asa current source or SVC modelled as a fixed capacitance, and a grid equivalent.

the STATCOM as a constant current source equal to its ratingwill be reasonable. Assuming that the SVC control system isfast enough to control the SVC to its capacitive limit during thefault, the representation of the SVC as a constant capacitor isalso reasonable. For investigations of stability, the dynamics ofthe control system during the recovery process of the voltagecan be disregarded for both the SATCOM and the SVC, sinceonly the reactive compensation immediately after the fault willbe of importance.

B. System Equations

From the presented assumptions, the SVC can be treated as aconstant impedance in the situations of interest for determiningstability of the system. Currents and voltage in the equivalentcircuit can be found from phasor calculation, and suitable equa-tions for such investigations are already presented, for instancein [24]. However, the equations for investigations of the systembehavior with the STATCOM need to be developed. With thecurrent directions indicated in Fig. 4, the relation between perphase grid voltage and STATCOM voltage will be given as

(4)

The current will depend on the voltage and the slip, andcan be expressed by (5), where and are defined bythe slip dependent impedance of the parallel connection of therotor branch and the magnetizing reactance in Fig. 4

(5)

Neglecting losses, the STATCOM current will be purely re-active, and always leading the voltage by 90 . The STACOMcurrent phasor can therefore be expressed by

(6)

Combining (5) and (6) with (4) gives

(7)

In this equation, the grid voltage , is the constant referencevoltage, and for a given STATCOM current and a given slip,this equation can, as shown in Appendix I, be solved to find thevoltage . The corresponding stator current is given by (5),


Fig. 5. (a) Torque-speed curves for uncompensated system and for compensation with 0.5 pu STATCOM with corresponding speed-time plots for a three-phasefault of 300 ms duration, used for defining relevant terms. (b) Torque-speed curves for uncompensated system, for different STATCOM and SVC current ratings,and for constant terminal voltage.

TABLE IPARAMETERS USED FOR CALCULATION EXAMPLE

and the per unit rotor current and electromagnetic torqueare given as

(8)

(9)

From these equations a torque-slip curve after the fault, fora given rating of maximum STATCOM current, can be estab-lished, and a critical clearing slip or speed can be found as theintersection of the torque-slip curve with the mechanical torque.This is similar to what is previously reported for induction gen-erators with only passive capacitor compensation [24], and tothe way the SVC is treated in this paper. The critical clearingspeed will in general not depend much on the type of distur-bance, since the stability of the induction machine depends onlyon the magnitudes of mechanical torque and reapplied electro-magnetic torque after the disturbance [24].

The mechanical equation is given by

(10)

where is the inertia constant, is the speed, , aremechanical torque and electromagnetic torque. Assuming zeroelectromagnetic torque during a three-phase short circuit, andconstant accelerating torque equal to mechanical torque, thecritical clearing time (CCT) can be calculated directly from thecritical speed and the initial speed, or the corresponding slipvalues, as

(11)

C. Torque-Slip Calculation Example

The given equations are used for an example calculation withparameters given in Table I. The parameters are given in per uniton base of machine kVA rating and chosen to correspond to thepu parameters of the laboratory setup.

Fig. 5(a) shows the torque-speed curves of the system fromTable I without any reactive compensation, and for compensa-tion with a STATCOM rated 0.5 pu, combined with speed-timeplots from a corresponding simulation of a 300 ms three-phaseshort circuit imposed to the same system. This figure is usedto define the concepts of critical clearing time (CCT), initialspeed , reclosing speed , and critical speed

that will be used throughout the paper in relation withcalculation and simulations.

For the system to be stable after a fault, the speed at faultclearing must be lower than the critical speed whichis given by the intersection between the torque-speed curve forthe specified system and the mechanical torque [25], [26]. Fora stable situation, the torque as function of speed will approxi-mately follow the corresponding quasi-stationary torque-speedcurve until the speed is reduced enough for the STATCOM tobring the terminal voltage back to its nominal value. Thereafter


TABLE IICRITICAL CLEARING SLIP AND SPEED FOR DIFFERENT RATINGS OF

STATCOM AND SVC WITH CORRESPONDING CRITICAL

CLEARING TIME FOR A THREE-PHASE FAULT

the torque-slip curve will be given by the constant voltage curve,which is the same as used to find the initial conditions. Close tothe stability limit, where the calculated torque of the generatorequals the mechanical torque on the curves of Fig. 5., the fluxtransients that are not accounted for in this approach will deter-mine whether the system is able to maintain stability or not.

It is clear from Fig. 5(a) that the uncompensated system inthis case is unstable, since the reclosing speed is larger thanthe critical speed, while the compensated system is stable sincethere is a small margin from the reclosing speed to the criticalspeed. A small difference in initial speed, caused by machineterminal voltage below 1 pu in the case of the uncompensatedsystem can also be seen in the figure. The speed-time plots ofFig. 5(a) also shows that the short circuit current when the faultoccurs, gives a small reduction of speed before the almost linearincrease starts, increasing the critical clearing time compared towhat would be expected from the use of (11). The influence ofthe flux transients of the machine at reclosing on the accuracyof the calculation method is discussed in Section VI.

The resulting torque-slip characteristics for three differentSTATCOM current ratings and two different capacitive ratingsof the SVC are given as torque-speed curves in Fig. 5(b).The curves are plotted together with torque-speed curvesfor no compensation and for constant terminal voltage (idealcompensation). Critical slip and corresponding speed for the un-compensated system, and for the different ratings of STATCOMand SVC, are given in Table II. This table also gives criticalclearing time, assuming constant applied mechanical torqueand zero electromagnetic torque during a three-phase shortcircuit as given by (11).

In general, the reactive compensation allows the inductionmachine to accelerate more before loosing stability than withoutany compensation. The critical clearing speed increases with therating of the compensation device, resulting in a correspondingincrease of critical clearing time during a three phase fault.

Critical clearing time is calculated by (11) with the cor-responding values of critical speeds. It is observed that theSTATCOM gives the most significant contribution to increasethe critical speed, and thereby the stability limit of the inductiongenerator. For a specified fault this can be interpreted as anincreased transient stability margin compared to the SVC.

The critical clearing time will differ from the calculated valuesfor unbalanced faults and for different depths of the voltage sag,but the critical speed will be almost the same, independently ofthe type of fault. The case studied here corresponds to the worstcase of balanced fault with 0 remaining voltage.

D. Mechanical Considerations

Following the suggested approach, neglecting electrical tran-sients, the quasi-stationary torque during voltage recovery is afunction of slip, rating of the compensation device and electricalparameters of the grid and the machine. When a fault is cleared,the decelerating torque for a stable case can be approximatedby the difference between applied mechanical torque and elec-tromagnetic torque from the corresponding torque-speed curve.Subsequently, the electromagnetic torque will approximatelyfollow the torque-speed curve for the given rating of reactivecompensation, until the speed is reduced to the level where thestator voltage reaches its nominal value. In Fig. 5, this corre-sponds to the intersection of the torque-slip curve of the partic-ular compensation and the curve of constant terminal voltage.Keeping maximum available compensation until the voltage isrestored will therefore result in a significant transient in mechan-ical torque. To limit the mechanical strain during recovery, thelowest possible rating of the compensation device that ensuresstability would therefore be favourable. If the compensation cur-rent could be reduced before the nominal voltage is regained, butafter stability is ensured, the mechanical stress during speed re-covery would be reduced. This would require fast controllableresponse of the compensation device, and could be possible toobtain with a STATCOM. An implementation of such controlstrategy of a STATCOM could be described as an indirect torquecontrol of the induction machine by controlling the availablevoltage by flow of reactive current.

In order to be able to compare results and validate them, pa-rameters for the calculation example were purposely selected tocoincide with those of the experimental devices. The availablelaboratory setup used for validation of the approach is basedon a machine with high losses and low inertia compared to areal wind generator system. The high rotor resistance causes themaximum torque to occur at a relatively large deviation from thesynchronous speed, and results in a high torque also for speedsabove the speed at maximum torque. The high stator resistancealso causes a significant asymmetry between the torque as func-tion of speed for motor operation and generator operation, witha considerably higher maximum torque for generator operation.The stator leakage reactance of the machine is also smaller thanusual for large induction generators, allowing for higher per unittorque at high speeds [27], [29]. The combination of these ef-fects results in a higher critical speed than what will be the casewith an induction generator for wind power applications in theMW range. At the same time, the mechanical time constant ofa real wind turbine would be in the range of several seconds,which is much higher than for the laboratory setup, giving amuch slower acceleration during a disturbance.

For a real wind turbine with induction generator, there wouldalso be a gear with quite high speed ratio (in the range of 1:100for 2 MW turbines). This makes it necessary to account for the


Fig. 6. Experimental setup of the wind generation connected to a weak gridand compensated with STATCOM at the PCC.

effects of shaft stiffness, and corresponding stored potential en-ergy because of mechanical torsion, when estimating criticalclearing time [30].

IV. TRANSIENT STABILITY LIMIT BY EXPERIMENTAL STUDY

An experimental study was performed to emulate the systemin Fig. 2 with the purpose of evaluating the transient stabilitylimit achievable with STATCOM compensation. For that pur-pose, the set-up was built using machines and devices availableat the Renewable Energy Laboratory of NTNU and SINTEF En-ergy Research at the time of the experiment.

A. Experimental Conditions

The experimental setup is described in Fig. 6. Ratings andcharacteristics of all system components are summarized inTable III. In all measurements, the pu system is based on the VArating of the machine used to emulate the wind generator, whichis a 7.5 kW wound rotor induction machine with short-circuitedrotor terminals. The wind turbine is emulated by a torque con-trolled dc motor. A constant torque is used to model the powerfrom the wind, because the analyzed transient phenomenon isassumed to be much faster than wind variations.

A local load, having induction motor characteristics isplaced at the point of common coupling as shown in Fig. 6, inorder to force the power system towards its stability limit. TheSTATCOM is an IGBT-based inverter bridge with a controlstrategy based on vector control technique. The vector controltechnique is implemented in a host computer and downloadedinto the processor of a DSP based control system.

A balanced three phase short circuit condition is provoked for300 ms by operating the short circuit device in Fig. 6. The firstexperiment performed is without the control of the STATCOMand it shows to be unstable. Three other experiments are per-formed; with the control of the STATCOM for different currentratings, of 0.5, 1.0, and 1.8 pu, respectively. Results are dis-cussed in Section IV-B.

B. Measurement Results

A sudden severe drop in voltage is caused at the point ofcommon coupling (PCC) by simultaneously triggering all

TABLE IIIRATINGS OF DEVICES USED IN EXPERIMENTS

Fig. 7. Measurement results of a 300ms, 80% voltage drop at PCC under sev-eral control conditions.

thyristors in the short circuit device (SCD) in Fig. 6. The depthof the voltage drop can be modified by properly adjusting theinductance in series with the SCD.

In the measurement results shown in Fig. 7, a voltage dropof about 80% is produced, and the fault is cleared after 300 ms.Before the fault, the wind generator is delivering about 1.3 pu ofactive power, of which 0.75 pu is absorbed by the local load, andthe rest is sent to the weak grid. Fig. 7(a)–(c) show the systemresponses for different conditions.

During the fault, the wind generator accelerates, since it is nolonger able to generate enough electromagnetic torque to bal-ance the mechanical torque coming from the wind, which is ob-viously unaffected by the grid fault. When the fault is cleared,the generator speed is about 1.6 pu and, without fast reactivesupport; the generator is not able to produce enough brakingtorque to bring the speed back to its pre-fault value. Without anyreactive current injection by the STATCOM, the voltage at thePCC does not recover its nominal value and remains very low


(0.4 pu). In the experiments, the speed of the unstable gener-ator does not continue to increase much after the fault since theavailable voltage for the dc-machine emulating the wind turbineis limiting the torque capability at higher speeds. In this partic-ular system, the speed rises to the high value of 1.6 pu because ofthe specific parameters of the lab setup, as thoroughly explainedin Section III-D.

For a real wind turbine, the mechanical torque from the windwould continue to accelerate the generator in the case of insta-bility, and the speed of the turbine would have to be controlled bymechanical brakes or possibly by pitch control before it reachestoo high mechanical speed [31]. A pseudo-stable post-fault op-erating condition (voltage collapse) at a high speed as obtainedin the experiments would not be a sustainable one neither for themechanical nor the electrical system, and the excessive currentsunder this condition will also cause protections to trip.

With a STATCOM connected at the PCC, injecting reactivecurrent in a controlled manner, the system responses to the samefault condition, starting from the same initial operating point,are shown for different ratings of the STATCOM current (0.5,1, and 1.8 pu.).

When the maximum current the STATCOM can deliver isfixed to 0.5pu of wind generator rated current, the system be-haves exactly like the one with no compensation during thefault, except for a small contribution of the STATCOM to theshort circuit current. The voltage at the PCC and the generatorspeed are not affected by the STATCOM to any significant de-gree, during the fault time. However, it is clear that even withthe relatively small rating of 0.5 pu, the STATCOM is able tostabilize the power system when the fault is cleared; bringingthe PCC voltage, grid current and generator speed back to theirpre-fault values. Complete voltage recovery process takes about0.9 s from the instant of the fault clearance.

With an increased rating for the STATCOM current (1.0 puand 1.8 pu, respectively), things do not change significantlyduring the fault, but the voltage recovery process is considerablyshortened as the STATCOM rating is increased. This means thatthe stability margin for this particular fault case is increased. Inparticular, and as expected from the torque-speed curves, thewind generator is able to generate much more torque at the faultclearance, due to the increased reactive support at its terminals.This is shown in Fig. 8, in which the accelerating torque forall the experimental conditions is calculated based on estimatedspeed .

The influence of the local load after the fault clearing canbe identified as the second response of the voltage curves ofFig. 7, and because of this delayed voltage recovery, the localload causes the STATCOM to output its maximum current fora longer time. This seems to have only minor influence on thespeed recovery of the generator, and by that on the torque tran-sient during recovery. Therefore, it is assumed reasonable tocompare the experimental results with the calculations based onthe torque-slip characteristics. The average estimated acceler-ating torque during the fault is also around 1 pu.

V. COMPARISON OF CALCULATION AND MEASUREMENTS

It is clear, from both calculation and measurements, that thehigher the STATCOM current rating, the larger the decelerating

Fig. 8. Induction generator torque during and after the short circuit under dif-ferent control conditions.

TABLE IVCLEARING TIME MARGIN COMPARED FOR DIFFERENT CONDITIONS

torque, and thus the transient margin. This behavior shows anincreased transient stability margin with increased rating of theSTATCOM. A system with a higher rated STATCOM will there-fore be able to withstand longer short circuits and /or it will beable to withstand voltage drops while delivering higher amountof power. However, the higher rating of the STATCOM givesalso higher torque during voltage recovery, which can repre-sent a problem of mechanical stresses for the wind turbine. Asnoted in Section III-D the lowest possible STATCOM currentthat would keep the system stable is therefore favorable for themechanical system.

In order to give an indication of the transient margin,Table IV presents a clearing time margin for different levelsof compensation with STATCOM and SVC, defined as thetime corresponding to the difference between critical speed andspeed at re-closing, obtained by replacing in (11) the respec-tive speeds calculated for the experimental parameters. Thecalculated speed at fault clearing is a bit higher than the valueobserved in the experimental results. One of the reasons for thisis the remaining voltage during the fault in the experiments,but also the initial transient when the fault occurs and possiblemechanical friction will contribute to this tendency. Because ofthis, Table IV shows a small negative clearing time margin forthe case with 0.5 pu STATCOM even though the experimentalsetup is stable under similar conditions. However, it can be ob-served in Fig. 8 that the system is close to the limit of stability.Considering that electric transients are neglected, there is aquite good accordance between measurements and calculations.There is also a considerable parametric uncertainty for the lab-oratory setup due to saturation effects and the type of machineused with short circuited slip rings and a speed excursion that


TABLE VCRITICAL SPEED AND CRITICAL CLEARING TIME COMPARED FOR CALCULATIONS AND SIMULATIONS

is high enough to affect the value of the parameters by skineffects. For 1.8 pu STATCOM and 2 pu SVC we observe thatin the first case we have a positive margin of 104 ms and in thesecond case a margin of 52 ms. This indicates that for about thesame rating, the STATCOM in this specific case provides withtwice the clearing time margin of an SVC.

Worth remarking here is that the choice of minimum ratingfor the STATCOM should not be done without making a moreconservative assumption when there are many sources of un-certainties. The proposed method could be used efficiently toidentify cases that will need to be more thoroughly analyzed bydetailed simulations for determining if the choice done by thetheoretical approach could fulfill all conditions.

VI. VALIDATION OF CALCULATION

METHOD WITH SIMULATIONS

Given that the results of the previous section show some dif-ference between the calculation method and measured data, anddue to the high level of uncertainties introduced by the lab ma-chine parameters, it is relevant to give some additional discus-sion regarding the difference observed in the results, and to val-idate them against simulations. This is also done in order to dis-cuss the neglected transients and the direction of influence thesewill have on the accuracy of the results.

Results from detailed time-domain simulations of the investi-gated cases by use of the PSCAD/EMTDC simulation software,are given in Table V in the form of critical speed and criticalclearing time. This allows removing the parameter uncertain-ties while the influence of flux transients of the machine can beinvestigated. In Table V, the values of critical speed, taken asspeed at the moment of fault clearing, and the values of criticalclearing time from the simulations are compared directly withthe values obtained with the calculation method.

From Table V, it can be observed that for this particular setof parameters, the error of critical speed referred to the calcu-lated slip is in the range below 5%, and that the calculated crit-ical speed is larger than the values obtained from the detailedsimulations. This error is caused by the transients at the time ofreclosing, since some time is needed to re-magnetize the induc-tion generator before it is able to give a torque corresponding tothe actual speed in the quasi-stationary torque-speed curve. Thegenerator will at the same time continue to accelerate, as long

as the applied mechanical torque is larger than the electromag-netic torque. The size of this error will depend on the leakageinductances of the machine and on the grid. This effect is morethoroughly explained in [32], and will contribute to reducing thecritical clearing time below the value that can be estimated bythe proposed theoretical approach.

As explained in Section III, there is also an effect of the ne-glected flux transients at the moment the fault occurs, giving abreaking torque caused by the transient short circuit currents.As shown in Fig. 5(a), this causes a reduction of speed beforethe almost linear increase during the fault. In the particular caseof a machine with high losses and low inertia, the effect of thisbreaking torque is significant and can be seen as increased crit-ical clearing time from the simulations, even though the criticalspeed at fault clearing is slightly overestimated by the simplifiedcalculations. With these effects taken into account, the accuracyof the critical clearing time for the proposed calculations is stillwithin 10–15%, with the highest deviations for the SVC.

From this information it can be concluded that the criticalspeed from the proposed method will always be slightly over-estimated. This inaccuracy will mainly be caused by the fluxtransient at reclosing, and will not be much influenced by anyremaining torque during the fault or the flux transient at the mo-ment the fault occurs. However, the accuracy of estimated crit-ical clearing time will depend on more factors. In addition tothe initial and reclosing flux transients, any remaining torqueduring the fault, and any mechanical friction will influence theaccuracy.

In the investigated cases, the CCT is found to be underesti-mated by the calculation method. For a real wind generator witha high total inertia, it can be expected that the flux transient atreclosing are of much more importance than the transients atthe moment the fault occurs, and that the calculated CCT willbe higher than what can be obtained from detailed investiga-tions [32]. To improve the accuracy of the calculation methoda possible future work could be to include the flux transientsat reclosing in a simplified way, by using a correction factoraccounting for the time needed to magnetize the machine as afunction of the system parameters.

VII. CONSIDERATION OF THE STATCOM AND SVC RATINGS

On basis of the presented investigations on stability limitsand LVRT capability, an attempt is made to provide a screening


Fig. 9. Minimum required STATCOM and SVC ratings to maintain stability. (a) STATCOM and SVC current rating as function of speed at clearing for variousstator reactances, (b) STATCOM and SVC current rating as function of speed at clearing for various rotor reactances, (c) STATCOM and SVC current rating asfunction of speed at clearing for various grid reactances, and (d) STATCOM and SVC current rating as function of grid reactances for various critical speeds.

method for evaluating the required ratings of STATCOM andSVC to achieve LVRT. This method follows the same simpli-fied approach as already presented, and takes into considerationsystem sensitive parameters such as speed at fault clearing, pos-sibly estimated from the duration of the fault, generator param-eters and grid parameters at the point of connection.

For the system to be stable at the specified speed, the brakingtorque of the machine must be larger than the applied mechan-ical torque, and this will be the criteria for specifying the torquerequirement at a certain speed. From the required torque at acertain slip, corresponding rotor current of the machine can befound from (9). For generator operation, with negative slip, thenegative value of the rotor current referred to the reference di-rections indicated in Fig. 4 is the one of interest. In addition tothe rotor current calculated from the required torque, the mag-nitude of the voltage source of the grid equivalent is assumed

to be known. From this starting point, the circuit of Fig. 4 canbe solved to find the necessary STATCOM current or the cor-responding impedance of SVC. Assigning a positive magnitudeof the STATCOM current to capacitive operation, the requiredcurrent can be found by a second order equation as given in (12).The coefficients of this equation are defined in Appendix II

(12)

Solving this equation, the minimum solution gives the re-quired capacitive STATCOM current rating to maintain stabilityfor a specified speed/slip at fault clearing. From this currentrating and the voltage required at the connection point to achievethe specified torque, also per unit capacitance of a SVC can becalculated.

Fig. 9(a)–(c) show calculated STATCOM and SVC ratings atthe stability limit for the per unit speed range from 1 to 2, using


the above formulas, with the parameters of Table I as a startingpoint. Fig. 9(a) and (b) show the STATCOM and SVC ratings forvarious values of stator and rotor reactances. The first intersec-tion point of the curves for the rating of the two types of reactivecompensation occurs at zero, when the system with the speci-fied parameters is on the stability limit without any compensa-tion. The second intersection point is when required terminalvoltage to ensure stability is 1pu. For the speed range betweenthese two intersections of the curves for different reactances, therequired rating of SVC to ensure stability is higher than the re-quired STATCOM for the same case. For speeds at fault clearingthat are above the speed at the second intersection point of thetwo curves, the required STATCOM rating is higher than the re-quired SVC. This is because the needed voltage at the point ofcompensation is above 1 pu, and then the passive capacitor ofthe SVC, increasing the reactive power production by the squareof the voltage, will perform better than the STATCOM limitedto its rated current. In both figures, it is clear that by increasingstator and rotor reactances, the generator becomes less stable,and the intersection point corresponding to 1 pu voltage at theconnection point will appear at a lower speed at clearing.

Fig. 9(c), shows the STATCOM and SVC ratings for variousvalues of grid reactance. For all values of grid reactances weobserve that required STATCOM rating is always lower than re-quired SVC rating with the machine parameters of Table I. Thestronger the grid becomes, the lower the required STATCOMand SVC rating to ensure stability at a specified speed, since thegrid is more able to supply large amounts of reactive power tothe induction generator.

Fig. 9(d), shows required STATCOM and SVC ratings asfunction of grid reactance for three different speeds at faultclearing. For low grid impedance, the system will be stable withlittle STATCOM current rating and a bit higher SVC currentrating. The higher the critical speed, the higher the STATCOMand SVC ratings. For increased grid impedance, there is an in-creased need of reactive current injection for ensuring stability,and needed SVC rating will be higher than needed STATCOMrating for ensuring stability in all cases, as long as the neededvoltage at the point of compensation is below 1 pu.

As can be seen from the presented investigations, the neededcompensation rating to give a significant contribution to in-creased LVRT capability can be quite large. This will especiallybe a challenge regarding cost of a possible SATCOM or SVCsolution. The SVC is traditionally considered as a simpler solu-tion with lower costs compared to the STATCOM, although thismay not be the situation in all cases if the comparison is madebased on the required performance and not only cost per kVA.The cost of a specific STATCOM will usually be higher than foran SVC with the same rating, as illustrated by a cost in the rangeof 45–50 US$/kVAr for the SVC, and in the range of 50–55US$/kVAr for the STATCOM as reported in [33], [34] for largecompensation units. For a 200 MVAr unit the investment costis given as 55 US$/kVAr for an SVC and 71.2 US$/KVAR fora STATCOM in [35]. These figures indicate a general trend ofabout 20%–30% higher cost for a STATCOM solution in thehigher power range. For smaller units intended for individualcompensation of a single generator at lower voltage levels, thesituation can be more in favour of the STATCOM because of

possibilities for modular solutions and correspondingly lowerprices due to series production of a large number of units.

Other issues such as losses, footprint, harmonics, etc must beexamined for each scenario for an optimum investment. BothSVCs and STATCOMs generates harmonics, but generation ofharmonics from a STATCOM and the corresponding need forfiltering will decay with increasing switching frequency. In gen-eral the footprint issues will favour the STATCOM especially atlower voltage levels. As STATCOMs provides improved per-formance compared to the SVC, it will be the choice for thecases in which the cost is justified by specific requirements tothe functionality, such as flicker compensation, need for highcompensation levels at low per unit voltage or for combinationwith active power transfer [13], [18].

To fully utilize the benefits of using a voltage source con-verter as compensation device and at the same time makingSTATCOM a competitive solution regarding cost, further re-search on special converter design adapted for STATCOM appli-cations will be relevant. The standard design of industrial con-verters may not fulfill the requirements of the new grid codesfor LVRT within a reasonable stationary rating and within areasonable cost. The necessary rating for reactive compensa-tion, voltage regulation and voltage quality improvement maybe much smaller than the needed rating to provide LVRT capa-bility and compliance with the grid code requirements for induc-tion generators. Therefore a converter design that could allowfor a very high transient current rating in the time range of a fewseconds, compared to the continuous rating, would allow for areasonable sizing of the STATCOM. This would also give anadditional advantage to the STATCOM over the thyristor con-trolled SVC, that will be a passive impedance when it is con-trolled to its limits.

An expanded over current rating of the voltage source con-verter can be one main factor for obtaining LVRT capability witha STATCOM of reasonable stationary ratings. This over currentrating is determined by the thermal design of the converter, andespecially by the thermal limits of the semiconductor devices.Possibilities for expanding the transient over current rating lieson achieving a larger temperature gap (from temperature at ratedoperation) that will allow an increased over current rating be-fore the thermal limit is reached. Better heat dissipation in allthe components and well coordinated utilization of thermal timeconstants could be one way of achieving this. A converter designthat allows for a transient rating of more than 200%–300% ofthe stationary current limits could lead to a STATCOM solutioncapable of performing stationary voltage regulation and voltagequality improvement within a reasonably low rating, and at thesame time give a larger contribution to LVRT capability than aSVC with much higher rating. Therefore, design of STATCOMconverter systems intended for LVRT purposes needs to be morecarefully approached taking into consideration the design fac-tors that will affect the LVRT capability and that will at the sametime enable an economical solution.

VIII. CONCLUSION

The influence of reactive compensation by STATCOM or SVConthetransientstability limitandLVRTcapabilityofaninductiongenerator is investigated with a simplified theoretical approach


based on quasi-stationary torque-slip characteristics. A methodfor estimating the critical speed and critical clearing time for dif-ferent ratings of a STATCOM or an SVC is proposed.

Laboratory experiments and simulation studies are providedto validate the proposed method, and to discuss the accuracy ofthe approach in light of the simplifications introduced to derivethe method. Although the results indicate that the assumptionsof the simplified theoretical calculations are quite reasonable,the neglected transients will in general have an influence on theaccuracy of estimated critical speed and critical clearing time.Simulation results show that in the investigated cases, the influ-ence of the flux transients on the critical speed at fault clearingis within the range of 5% for a wide range of reactive compen-sation. For the critical clearing time, the difference between thevalues obtained from the proposed calculations and from de-tailed time-domain simulations is larger; although still below10%–15%. The deviations are discussed, and in this particularcase they are identified to originate mainly from the initial fluxtransients, resulting in underestimation of CCT. It is remarkedthat the effect of the initial flux transients will be lesser for agenerator with lower losses and higher inertia, and that for sucha system the CCT will more likely be overestimated by the pro-posed method because of the flux transients at reclosing. How-ever, these results indicate that the accuracy of the approachis within an acceptable level for an estimation method, and inproportion to the introduced simplifications. Investigation abouta correction factor based on the quantification of the transientat reclosing from machine and grid parameters is suggested asa possible way to improve the accuracy of the theoretical ap-proach to make it more general.

Calculations, experiments, and simulations show that in-creased rating of the compensation device will extend thetransient stability margin of the system by providing higherdecelerating torque, but will at the same time increase themaximum mechanical stress during recovery. The results fromthe experiments and the simulations also indicate that a fastcontrollable source of reactive power like the STATCOM,can allow for more advanced control strategies to reduce themechanical stress on the drive train of a wind turbine duringrecovery after a fault.

A method for calculating the required current rating ofa STATCOM, and for comparison with other compensationdevices like the SVC, is also suggested. The influence of thesystem parameters on the required rating of the compensa-tion device has been investigated and it is shown that theSTATCOM performs better than the SVC in terms of LVRTcapability if the same rating is assumed for the devices. For thesame contingency, the required SVC rating is generally largerthan required STATCOM rating. Even if the SVC is usuallyconsidered a cheaper and simpler solution, the difference inrequired rating can result in the STATCOM as the economicalsolution for specific cases. For instance, if a 50% larger SVCthan STATCOM would be required for a particular applicationand the STATCOM has 30% higher costs per kVA than the SVCas indicated in the previous section, the net cost of STATCOMwould be about 85% of the cost of SVC, or SVC would be15% more expensive than STATCOM for the same case. If ahigh transient current rating of the voltage source converter is

available for LVRT purposes, these figures could be even morefavourable for the STATCOM, and the STATCOM could be theeconomical solution in more situations. On this basis, furtherinvestigations into converter design for high short term overloadcapacity will be of interest, and this can give additional benefitto the STATCOM compared to the SVC, which has no capacityof providing transient overload rating in capacitive operation.In this setting, it will also be relevant to investigate and utilizethe advantages regarding controllability of a voltage sourceconverter as a STATCOM, in addition to providing LVRT toinduction generators within a reasonable stationary rating at areasonable cost.

APPENDIX I

The equivalent impedance of the rotor circuit in parallel withthe magnetizing reactance, as used in (5), is given by

(13)

From (7), also the following equivalent impedances can bedefined:

(14)

In a simplified form, (7) can then be written with complexcoefficients

(15)

Decomposed in real and imaginary parts, this results in theset of equations given in

(16)

with corresponding constants defined from (15). This set ofequations can be solved to find the real and imaginary part ofthe voltage as a function of slip. The solution is given in

(17)

where the coefficient is the solution of the second order equa-tion

(18)


(19)

(24)

The positive solution to this second order equation is the one ofinterest, and the value of , is therefore given by (19), shown atthe top of the page.

The voltage phasor that is found from these equations canbe introduced into (5), (8), and (9) to calculate the post-faulttorque-slip characteristics of an induction generator with a givenSTATCOM current rating.

APPENDIX II

Starting from a required torque at a specified slip, the rotorcurrent can be found from (9), and the corresponding voltageat the machine terminals can be calculated from the equivalentcircuit of Fig. 4. The direction of the STATCOM current phasoris given by (6) and can then be expressed as

(20)

where the coefficients are dependent on the slip of the machineand given by

(21)

Expressing both stator current and stator voltage by therotor current , (4) can be changed into (22), using the slipdependent coefficients defined in (23)

(22)

(23)

Since the magnitude of the grid voltage is assumed to beknown, this can be solved for the compensation current neededto obtain the required rotor current and by that, required torqueat the specified slip. The resulting second order equation is given

by (24), shown at the top of the page. This is equivalent to (12),and can be used to estimate the needed compensation currentto obtain a specified torque. This could be used to calculate theneeded rating of a compensation device for a specified fault andpossibly to calculate needed reactive current to reduce the tran-sient torque during recovery after fault.

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[32] M. Molinas, J. A. Suul, and T. Undeland, “A simple method for analyt-ical evaluation of LVRT in wind energy for induction generators withSTATCOM or SVC,” in Proc. 12th Eur. Conf. Power Electron. Appl.(EPE’07), Sep. 2007, pp. 1–10.

[33] B. Kirby and E. Hirst, “Ancillary Service Details: Voltage Control,”Oak Ridge National Laboratory, U.S. Department of Energy , Tech.Rep. ORNL/CON-453 (DE-AC05-96OR22464), 1997.

[34] D. Eromon, J. Kueck, and T. Rizy, Distributed Energy Resource (DER)Using Facts, Statcom, SVC and Synchronous Condensers for DynamicControl of Var. St. Louis, MO: National Association of IndustrialTechnology Convention (NAIT), 2005, p. 6.

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Marta Molinas (M’00) received the Diploma inelectro-mechanical engineering from the NationalUniversity of Asuncion, Paraguay, in 1992, the M.Sc.degree from Ryukyu University, Okinawa, Japan, in1997, and the Doctor of Engineering from the TokyoInstitute of Technology, Tokyo, Japan, in 2000.

From 2004 to 2007, she was a Post Doctoral Re-searcher with the Norwegian University of Scienceand Technology, Trondheim. She is now Professorwith the Norwegian University of Science and Tech-nology engaged in the research of wind energy sys-

tems. Her interests include power electronics and electrical machines in powersystems.

Jon Are Suul received the M.Sc. degree from theNorwegian University of Science and Technology,Trondheim, in 2006 where he is currently pursuingthe Ph.D. degree.

He joined Sintef Energy Research, Trondheim,in 2006. His interests include control of powerelectronics converters in power systems and windpower generation systems.

Tore Undeland (F’00) is with the NorwegianUniversity of Science and Technology, Trondheim,as a Full Professor since 1984. He has also beenan Adjunct Professor at Chalmers University ofTechnology, Goteborg, Sweden, since 2000, andScientific Advisor to Sintef Energy Research,Trondheim. His interests are in power electronicsand wind energy systems. He is the co-author of thewell known book Power Electronics, Converters,Applications and Design (New York: Wiley, 2006).

Dr. Undeland has been President of the EuropeanPower Electronics Society and is a member of the Norwegian Academy of Tech-nological Sciences.

1104 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 23, … · 2008-07-07 · 1104 IEEE TRANSACTIONS...

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Transcript of 1104 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 23, … · 2008-07-07 · 1104 IEEE TRANSACTIONS...