novel statcom controller for mitigating ssr and

IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 25, NO. 2, FEBRUARY 2010 429

Novel STATCOM Controller for Mitigating SSR andDamping Power System Oscillations in a Series

Compensated Wind ParkMohamed S. El-Moursi, Birgitte Bak-Jensen, Member, IEEE, and Mansour H. Abdel-Rahman, Member, IEEE

Abstract—This paper addresses implementation issues associ-ated with a novel damping control algorithm for a STATCOM ina series compensated wind park for mitigating SSR and damp-ing power system oscillations. The IEEE first benchmark modelon SSR is adopted with integrating aggregated self-excited induc-tion generator-based wind turbine to perform the studies. Thepotential occurrence and mitigation of the SSR caused by induc-tion generator effects as well as torsional interactions, in a seriescompensated wind park, are investigated. The auxiliary subsyn-chronous damping control loop for the STATCOM based on anovel design procedure of nonlinear optimization is developed tomeet the damping torque in the range of critical torsional fre-quencies. The intelligent shaft monitor (ISM) scheme with synthe-sized special indicator signals is developed and examined in theSTATCOM control structure. The performances of the controllersare tested in steady-state operation and in response to system con-tingencies, taking into account the impact of SCRs. Simulation re-sults are presented to demonstrate the capability of the controllersfor mitigating the SSR, damping the power system oscillation, andenhancing the transient stability margin in response to differentSCRs.

Index Terms—Damping power system oscillations, SSR mitiga-tion, STATCOM, transient stability margin.

NOMENCLATURE

BPF Bandpass filter.FRT Fault ride through.HPF High-pass filter.ISM Intelligent shaft monitor.LPF Low-pass filter.MCCT Maximum critical clearing time.PLL Phase-locked loop.SCR Short circuit ratio.SEIG Self-excited induction generator.SSR Subsynchronous resonance.STATCOM Static synchronous compensator.

Manuscript received January 20, 2009; revised June 16, 2009. Current versionpublished February 12, 2010. Recommended for publication by Associate EditorJ. H. R. Enslin.

M. S. El-Moursi is with the Electrical Engineering Department, Universityof El-Mansoura, 35516 El-Mansoura, Egypt (e-mail: [email protected]).

B. Bak-Jensen is with the Institute of Energy Technology, Aalborg University,9100 Aalborg, Denmark (e-mail: [email protected]).

M. H. Abdel-Rahman was with the Institute of Energy Technology, AalborgUniversity, 9100 Aalborg, Denmark. He is now with the University ofEl-Mansoura, 35516 El-Mansoura, Egypt (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.2009.2026650

VSC Voltage source converter.WTG Wind turbine generator.S Slip.dIq Modulation protection.Idm Measured active current of the STATCOM.Idref Reference active current of the STATCOM.Iqm Measured reactive current of the STATCOM.Iqref Reference reactive current of the STATCOM.Kds Damping power coefficient.KST1 Synchronizing power coefficient of the

STATCOM.Pe1 Active power transfer-based constant reactance

control of static synchronous series compen-sator (SSSC).

Pe2 Active power transfer-based constant injectedvoltage control of SSSC.

Rg Grid resistance.Rr Rotor resistance.T1−2 Mechanical torque between Mass 1 and Mass 2.Te Electromagnetic torque.Vdm Measured quadrature voltage.Vqm Measured quadrature voltage.Vt Terminal voltage of the STATCOM.Xg Grid reactance.Xr Rotor reactance.θ Synchronizing phase angle.∆Vdamp1 Damping voltage signal-based rotor speed

deviation.∆Vdamp2 Damping voltage signal-based active power

deviation.∆ωr Generator rotor speed deviation.

I. INTRODUCTION

IN RECENT years, the large penetration of wind energy isconsidered as an effective means of power generation. Due

to the continued growth in the wind energy, power utilities’interests have shifted from power quality issues caused by windpower to potential stability problems [1]. This shift to windenergy installed in large wind parks requires transmitting thepower generation through transmission systems that can sustainlarge power flows [2]. Series compensation is considered as aneffective mean of increasing the power transfer capability ofthe existing transmission system. However, the series capacitorcompensation can produce a significant adverse effect such as

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430 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 25, NO. 2, FEBRUARY 2010

SSR on the WTGs and thermal turbine generator units connectedto the series compensated power system [3].

Wind turbines are subjected to different mechanical modes ofvibration related to the mechanical system, such as the blades,the shaft, the drive train, the tower, and so on [4]. For the ra-dial connected wind parks on the end of a series compensatedtransmission line, the SSR due to the induction generator ef-fect is highly expected [5]. The energy exchange and the inter-action between the mechanical and electrical system, coupledthrough the generator, are potentially the cause of resonant con-ditions (SSR) with a resonant-frequency below the fundamentalfrequency.

This paper is focus on a STATCOM based on a new con-troller structure. However, the STATCOM does not change theSSR characteristics of the network significantly [6]. Therefore,additional damping control loops are required for damping tor-sional modes and power system oscillations. The damping con-trol loops should be tuned to reach optimum performance toprovide positive damping in the range of torsional frequencies.This paper investigates the SEIG-based wind turbine SSR andthe monitoring and damping of shaft torsional oscillations. TheIEEE first benchmark model on SSR is adopted for the inte-gration of an aggregated SEIG-based wind turbine. Also themitigative solution for damping SSR oscillation, voltage sta-bilization, damping the transient torques, and enhancing thetransient stability margin will be investigated in response todifferent SCRs.

II. SHAFT TORSIONAL OSCILLATION MONITORING

Transient torques are those that result from system severedisturbances. System disturbances cause sudden changes in thenetwork topology, resulting in sudden change in currents flowsthat will tend to oscillate at the natural frequencies of the acnetwork. In a transmission system without series capacitors,these transients are always almost dc transients, which decay tozero with a time constant that depends on the ratio of inductanceto resistance. For networks that contain series capacitors, thetransient currents will be of a form similar to (1) and will containone or more oscillatory frequencies that depend on the networkseries capacitance as well as the inductance and resistance.

i(t) = k[A sin(ω1 + ψ1) + Be−ξω2 t sin(ω2t + ψ2)] (1)

where all of the parameters in the equation are function of thenetwork elements except ω1 , which is the frequency of the driv-ing voltage source. Note that even ω2 is a function of the networkelements or circuit topology. Current waveforms similar to (1)flow in the stator winding of the generator and hence reflectedinto the generator rotor via a physical process that is describedmathematically by Park’s transformation. This transformationmakes the 50 Hz component of current appear, as viewed fromthe rotor, as a dc zero frequency current in the steady state,but the currents of frequency ω2 are transformed into currentsof frequencies containing both the modulating sum (ω1 + ω2)and difference (ω1 − ω2) of the two frequencies. The differencefrequency is especially important and is called subsynchronousfrequencies. These subsynchronous currents produce their own

shaft torque oscillations on the turbine generator rotor assemblythat cause the rotor to oscillate at subsynchronous frequencies.These SSR or subsynchronous oscillations can build up resultingin shaft twisting torques and damage.

In a simple radial RLC system, there will be only one suchnatural frequency, with exactly the situation described in (1), butin a network with many series capacitors there will be many suchsubsynchronous frequencies. If any of these subsynchronousnetwork frequencies coincide with one of the natural modesof the mechanical system sustained shaft torques that are quitelarge might appear, since these torques are directly proportionalto the magnitude of the oscillating current. Currents due to shortcircuits, therefore, can generate very large shaft torques bothwhen the fault is applied and also when it is cleared. In a realpower system, there may be many different subsynchronousfrequencies involved and the analysis is quite complex.

Traditional direct sensing of any torsional torque oscillationrequires the measurement of the instantaneous rotor speed andshaft torque, which can be both noisy and very difficult to ac-cess. Previous indirect measurement methods only use the sud-den change in the synchronous machine air-gap torque. Thestator current provides complete information about the unstabletorsional mode of oscillation. The novel online ISM scheme isdeveloped to monitor the torsional modes of SSR oscillationsand can be used for damping oscillations (see Fig. 1).

The ISM scheme is developed based on the following depen-dent equations:

α = is ∗ (sin w0t + cos w0t) (2)

β = is ∗ (sin w0t − cos w0t) (3)

δ =β

α(4)

γ—The synthesized special indicator signals for shaft torsionalmodes based on the stator current excursion patterns using (LPF,HPF, BPF) filters.

w0 = 314 − Radians/Second.

There are applications where a particular frequencies needto be filtered from a wider range of mixed signals. The BPF isdesigned to accomplish this task by combining the propertiesof LPF and HPF. Both the low-pass and high-pass sections willalways be blocking signals to some extent, and their combi-nation makes for an attenuated (reduced amplitude) signal atbest, even at the peak of the “passband” frequency range, thusthe weighting factors are adjusted. The selected building blocksparameters of LPF, HPF, and BPF are designed and tuned inresponse to a weak power system performance. These newlyderived or synthesized signals are used to detect the shaft tor-sional modes of oscillations and any unstable patterns based onrelevant phase portrait trajectory recognition. The ISM utilizesthe generator stator current and a novel frequency-based trans-formation as the detection scheme and to construct syntheticdamping signals depicting any torsional patterns in the 2-D and3-D phase portraits. The unified ac system has been simulatedby using the PSCAD/EMTDC software in order to validate the

EL-MOURSI et al.: NOVEL STATCOM CONTROLLER FOR MITIGATING SSR AND DAMPING POWER SYSTEM OSCILLATIONS 431

Fig. 1. ISM scheme with synthesized special indicator signals (α, β, γ, δ).

ISM and novel controllers for STATCOM for SSR damping andtorsional oscillations contour measure.

III. POWER SYSTEM DESCRIPTION

The existing wind parks integrated in the electric grids utilizeseveral WTGs technologies of different ratings and system per-formances. This paper considers wind parks based on SEIGs asthe majority of the wind parks employing SEIGs. Therefore, thegrid codes become a challenge for such type of wind turbines interms of voltage and frequency controls and FRT capabilities.The study system is derived based on the IEEE first benchmarkmodel of SSR studies [7]. The system is adopted with connect-ing a wind park based on SEIGs rated at 100 MW to the electricgrid through a fixed series compensated transmission system

comprising a STATCOM, as shown in Fig. 2 with the systemparameters as shown in the Appendix.

The wind park based on SEIGs requires additional substa-tion equipments in order to meet the grid codes. The studies inthis paper are conducted with installing a STATCOM as centralcompensator complemented with voltage control for enhanc-ing the wind park performance. The STATCOM voltage controlis associated with auxiliary damping control loops for mitigat-ing SSR, subsequent damping power system oscillations andimproving the transient stability margin of the interconnectedpower system [8]–[13].

IV. CONTROLLER DESIGN OF STATCOM

Fig. 2 illustrates the STATCOM compensated radial powersystems. The STATCOM is controlled by a novel voltage


Fig. 2. Wind park comprises STATCOM connected to a series compensated power system.

Fig. 3. Proposed STATCOM voltage control.

control associated with auxiliary damping control loops, asshown in Fig. 3 [14]. The shunt flexible ac transmission sys-tem (FACTS) device STATCOM resembles in many respect asa synchronous compensator, but without the inertia [15]. Eventhough the primary purpose of the STATCOM is to support thebus voltage by injecting or absorbing reactive power, it is alsocapable of improving the power system stability. It has beenproved that the shunt FACTS device gives maximum benefitby their stabilized voltage support especially when sited at themidpoint of the transmission line.

A. Synchronizing Power and Damping Power of STATCOM

The STATCOM compensates the power system at the mid-point of transmission system. The transmitted power is ex-

pressed as the following [16] and [17]:

Pe =VS Vm

XT /2sin

δS

2. (5)

The damping power control loop signal should be includedin phase with the rotor speed deviation ∆ωr and added to (5).Therefore, different control algorithms can be synthesized de-pending on the desired type of friction. There are different pos-sible functions for the friction f(∆ωr ) that fulfill the followinggeneral condition:

f(∆ωr ) :{

>0 if ∆ωr > 0

<0 if ∆ωr < 0

}. (6)


Fig. 4. Damping control loops based on generator speed deviation and active power variation in a specified time interval.

Some of them are:1) Linear friction: f(∆ωr ) = Kd∆ωr

2) Colombian friction: f(∆ωr ) = Kdsign(∆ωr )3) High-order polynomial friction: f(∆ωr ) =

∑i Kd1∆ωi,

with i = 3, 5, 7. . . .4) Combination of the above.5) Similar structure to case (1)–(4), but with parameters, K

adaptable in accordance with the evolution of the systemvariables.

Once the injected friction function f(∆ω) is selected, theexpression of the control law is designed using (7) based on thecontrol mode. The STATCOM is controlling the bus terminalvoltage Vt , thus the control law is ∆Vt = Kd∆ωr .

By linearizing (7)

∆Pe =(

12

VS Vt

XT /2cos

δs

2

)∆δS +

(VS Kd

XT /2sin

δS

2

)∆ωr

= KST1∆δS + Kd∆ωr . (7)

The damping loops utilize the integral time absolute errorof the rotor speed and the active power. They are set by thefollowing objective functions:

J1 =∫ t=ts im

t=0(|∆ωr |) tdt (8)

J2 =∫ t=ts im

t=0(|∆P |) tdt (9)

where∆ωr rotor speed deviation;∆P active power deviation in a specified time interval.The target is to minimize the objective functions in order

to improve the system response. Therefore, adopting the pa-rameters of the control loops should be tuned to achieve anappreciated system response.

B. STATCOM Voltage Control Structure

The STATCOM is operated based on the voltage control toregulate the terminal bus voltage Vm to follow the assigned

reference voltage, Fig. 3. The voltage and current measurementsat the 0.69 kV bus are frequently undertaken and sampled. Thesampled voltage measurement is sent to the voltage control,which is compared to the reference voltage assigned for theterminal bus. The voltage error drives the voltage regulators(PI controller) considering the regulation slope K. The voltagecontrol determines the reference reactive current and sends itdirectly to the inner current control of the STATCOM for fastvoltage response.

1) Auxiliary Damping Control Loops: Introducing theSTATCOM controllers at an appreciate location, by itself doesnot provide adequate damping, as the primary task of the con-troller is to control voltage. Hence, in order to increase thesystem damping, it is necessary to add additional control blockswith an adequate input signals.

There are two damping control loops specified based on therotor speed deviation and the variation of active power in aspecified time interval. The two damping control loops are struc-tured using the analytical approach for synchronizing power anddamping power, as described in Section IV. The lead-lag controlstructure is chosen for the two control loops, as shown in Fig. 4.

The damping control loops consists of: a gain block, a signalwashout block, and a two-stage phase compensation blocks. Itis preferably that the additional control signal is local to avoidthe impact of communication time delay. The damping signalis fed through a washout control block to avoid affecting thesteady-state operation, and an additional lead-lag control blockis used to improve the dynamic system response. The washoutblock performs as a HPF, which allows signals associated withoscillations to pass unchanged.

2) Detailed and Average Model of STATCOM: The detailedmodel of the 6-pulse VSC STATCOM comprises a forced-commutated converter that converts ac voltage into dc voltage orvice versa. The VSC topology that has been used is a two levelVSC. The VSC comprises six power semiconductor-switchingdevices with antiparallel-connected diodes together with heatsinks and auxiliary equipment for gating, monitoring, and grad-ing. The dc link is represented by a charged capacitor; the con-verter produces a set of controllable three-phase output voltages


Fig. 5. Global control scheme of the STATCOM.

at the fundamental frequency of the ac system voltage using apulsewidth modulation (PWM) switching technique. The PWMinject third order of harmonics to the fundamental for enhancingthe modulation index. The STATCOM can be operated in eithercapacitive or inductive mode of operation.

The average model of the STATCOM is much convenient forthe following studies in this paper, as it will speed up the simula-tion time by factor of 20. The detailed model of the STATCOMis modified by replacing the switching converter by a control-lable voltage source, as shown in Fig. 2. The three-phase outputvoltages from the park transformation (dq-abc) are used di-rectly as input signal of the controllable voltage source, Fig. 5.Thus, the PWM, VSC, and third harmonics injection are re-moved with respect to the detailed model. The dc link voltagecontrol is replaced with the STATCOM active power controlloop.

The decoupled current control consists of two control loops,which are controlling the direct, and quadrature components ofthe STATCOM current. The direct component of the STATCOMcurrent Idref is responsible for controlling active power of theSTATCOM while the STATCOM is operating in capacitive orinductive mode of operation.

The quadrature component of the STATCOM current Iqrefcontrols the reactive power exchange between the converter andac system. The reference direct and quadrature STATCOM cur-rents are compared with the measured values of Id and Iq , andthe errors drive the current regulators. The output of the currentregulators is the controlling voltage signals Vd and Vq , whichare added to the feedforward signals of the direct and quadra-ture components of the three-phase terminal voltage. For higherperformance, the voltage drop across converter inductors is alsoadded to the controlling voltage signals. The determined direct-

and quadrature-controlling voltages are transformed from dqframe to three-phase voltages, which are used directly to con-trol the controllable voltage sources.

V. SSR MITIGATION IN A SERIES COMPENSATED WIND PARK

The series compensated wind park is tested in response tothe variation of series compensation by increasing the levelof series capacitive compensation from 0.18 to 0.33 pu. Thisis done in the simulation at time t = 20 s. The analysis ofSSR with STATCOM associated with damping control loopsis conducted based on damping torque analysis and transientsimulation. The damping torque analysis is considered in thedesign of the damping control loops. The concept of the controldesign is to secure a net positive damping torque at any of thetorsional mode frequencies. Therefore, at any given oscillationfrequency of the generator rotor, the electrical torque should bein phase with rotor speed, acting as damping torque.

The damping torque analysis is an approach to design the aux-iliary control loops for FACTS devices. It enables the developerto provide a robust control design upon a countermeasure for themitigation of the determined effects of SSR. It helps to securethe torsional mode stability with adopted tuning parameters ofthe control loops.

The proposed system observes the SSR resonance due totorsional modes, which tends to instability, as shown in Fig. 6(a)for the generator speed. The system comprising the STATCOMshows superior performance for mitigating SSR, subsequentdamping power system oscillations. The STATCOM associatedwith auxiliary damping control loops improves the dampingof torsional modes. The controller minimizes the peaks of thenegative torques and secures the system stability Fig. 6(b)–(d).


Fig. 6. [(a)–(f)] SSR due to the variation of the capacitive series compensation of the series compensated wind park and mitigation, using STATCOM associatedwith auxiliary damping loops.

A. Dynamic Performance of STATCOM Control

Increasing the level of capacitive series compensation booststhe voltage at the terminal of the STATCOM. Therefore, theSTATCOM operates in inductive mode of operation to regulatethe terminal bus voltage to 1 pu, as shown in Fig. 7.

The following system measurements are undertaken for awind turbine, comprising a STATCOM rated at 0.7 MVAR andthe wind turbine rated at 1 MW. Then, the whole system is ag-gregated to deliver 100 MW at full load capacity. The aggrega-tion is carried out using unique amplification technique, whichhas been developed to provide the same system identity for the


Fig. 7. Reference and measured voltage at the terminal bus of the connectedSTATCOM.

Fig. 8. Measured active and reactive power of the single unit of the STATCOM.

electrical connection with identical transient performance scaledup to the desired connected grid with definable SCR. The anal-ysis is carried out based on the following operating conditions:

1) The wind park is adopted to deliver 80 MW to the trans-mission system.

2) The electric grid is scaled up for SCR = 2 and X/R = 5.3) The capacitive series compensation of the transmission

system is increased from 0.18 to 0.33 pu at instant t =20 s.

4) The STATCOM voltage control is associated with the dualdamping control loops, as described in Section IV (A.1).

5) The STATCOM is installed at the terminal of the SEIGwith fixed shunt capacitor banks and operated based onvoltage control mode to regulate the terminal bus voltageto 1 pu.

The sudden increase of the capacitive series compensationdrives the STATCOM to operate in inductive mode of operationdue to the increase of the terminal voltage compared to the ref-erence terminal voltage. Therefore, reactive power is absorbedfrom the network to regulate the terminal bus voltage to 1 pu,as shown in Fig 7. The total reactive power drawn from thesystem is 15 MVAR, taking into consideration the aggregationwith respect to 100 units; each draws 0.15 MVAR, as shown inFig. 8.

Figs. 9 and 10 show the inner current control signals, wherethe measured active and reactive currents of the decoupled cur-rent control follow their references and demonstrate the dynamicperformance in response to the system stimulation. The reac-tive current is responsible for the reactive power exchange from

Fig. 9. Reference and measured reactive current of the single unit of theSTATCOM controller.

Fig. 10. Reference and measured active current of the single unit of the STAT-COM controller.

the STATCOM and the connected power system subjected tothe inductive or capacitive mode of operation. Consequently,the active current of the STATCOM is used to control the activepower that compensates the coupling transformer and switchingconverter losses.

The STATCOM associated with auxiliary damping controlloops demonstrates superior performance for mitigating the SSRand reducing the peak negative damping at the critical torsionalmode frequency, as shown in Fig. 11, for the generator measure-ment signals.

VI. DYNAMIC PERFORMANCE OF DAMPING CONTROLLERS

The damping performance of the STATCOM control algo-rithm is evaluated in response to system disturbances such asTorque excursion and three-phase-to-ground faults at the ter-minal of the wind park, which is interconnected at level ofSCR = 2.

A. Torque Excursion

In this case, the damping performances of the STATCOM aretested in response to a mechanical torque reduction of 0.5 pufor a period of 1 s. The damping of the STATCOM in mitigatingtorsional interaction is investigated, and the following signalsare examined:

1) Generator rotor speed (ωr);2) Mechanical torque between Mass 1 and Mass 2 (T1−2);3) Delta mechanical speed;4) Electrical torque (Te).


Fig. 11. SEIG measurement signals while employing the STATCOM with auxiliary damping control loops.

Fig. 12. Mechanical torque between Mass 1 and Mass 2.

The examined signals are plotted for the system without anyFACTS device and with the STATCOM. The STATCOM-basedvoltage control associated with damping control loops improvesthe damping of the mechanical torque between Mass 1 andMass 2, as shown in Figs. 12–14.

B. Performance Following Disturbances

The system of Fig. 2 is now subjected to a 3Φ fault at theterminal of the wind park at instant t = 20 s for a durationof 150 ms. The STATCOM is adjusted to regulate the terminalbus voltage to 1 pu. The simulation results are compared withthe results obtained from the base case without installing the

Fig. 13. Delta mechanical speed for the system without dynamic compensa-tion and STATCOM.

dynamic shunt compensation. The transient responses of thecontrol algorithms associated with damping control loops areevaluated and tested in response to short circuits at SCR = 2.

The simulation results illustrate the superior performance ofthe STATCOM for damping the power system oscillations, andmuch faster voltage recovery compared without the STATCOMas shown in Figs. 15 and 16, respectively. The SEIG mea-surement signals demonstrate the effectiveness for dampinggenerator speed in response to the short circuits and signifi-cantly reduce the sharp negative torque, as shown in Fig. 17(b).


Fig. 14. Electrical torque for the single unit of SEIG-based wind turbine.

Fig. 15. Active power generation of the wind park for the system withoutdynamic compensation and with STATCOM associated with damping controlloops.

Fig. 16. Voltage at the PCC.

Fig. 17. [(a) and (b)] SEIG measurement signal for the generator speed andtorque in Mass 1–Mass 2.

Therefore, the transient stability margin is significantly im-proved for the system installing a STATCOM.

VII. TRANSIENT STABILITY MARGIN ENHANCEMENT

The torque-slip analysis is used to investigate the transientstability margin of the wind park based on the self-excited in-duction generators. Therefore, a simplified representation of theSEIG is used in the analysis, neglecting the stator and rotortransients of the induction machine as demonstrated in [18].The quasi-stationary dynamics of the machine is used as arguedin [19] to evaluate the transient stability margin of the generator.The per phase equivalent circuit representing the SEIG is onlyused to study the mechanical acceleration dynamics. However,this simplification is not valid for the transient phenomena stud-ies due to the stator flux and rotor flux of the machine. Fig. 18shows the equivalent per phase circuit of the system after a fault.The STATCOM is represented by a current source, and the gen-erator is connected as a stiff voltage source behind a theveninimpedance of the grid.


Fig. 18. Per phase equivalent of the SEIG with connecting STATCOM as current source.

TABLE IMCCT OF THE APPLIED FAULT FOR THE POWER PLANT

A. System Equations With STATCOM

The system equations with connecting a current source as arepresentation of the STATCOM are developed based on thedirection of the currents, as indicated in Fig. 18. The systemequations are expressed as the following:

vg = v1 + (Rg + jXg )(i1 + iSTATCOM) (10)

i1 =v1

RS + Req,r + j(XS + Xeq,r ). (11)

Where Req,r and Xeq,r are defined by slip-dependantimpedance of the parallel connection of the rotor branch andmagnetizing reactance, as shown in Fig. 18. The STATCOMcurrent will be pure inductive in case of neglecting the losses.Therefore, the STATCOM can be expressed by

iSTATCOM = jv1

|v1 ||iSTATCOM | . (12)

By substituting (12) and (13) in (11)

vg =(

1 +Rg + jXg

RS + Req,r + j(XS + Xeq,r )

+ jRg + jXg

|v1 ||iSTATCOM |

)v1 . (13)

Equation (12) can be solved to get v1 for a selected STATCOMcurrent and a given slip [9]. The corresponding STATCOMcurrent i1 is expressed in (12), and the per unit rotor current i2and Tem are given as

i2 =jXm

Rr/S + j(X2 + Xm )i1 (14)

Tem =Rr

S|i2 |2 . (15)

It should be noted that critical clearing speed will not de-pend much on the type of disturbance, since the stability ofthe induction machine depends only on the magnitudes of me-chanical torque and reapplied electromagnetic torque after thedisturbance. The mechanical equation is given by

Hdω

dt= Tm − Tem(ω) (16)

where H: the inertia constant.Assuming Tem = 0 during the fault and constant accelerating

torque equal to Tm , the critical clearing time (CCT) can becalculated directly from the critical speed and initial speed as

CCT3−phase ≈ Hωcritical − ωinitial

Tm. (17)

B. Digital Simulation Results

The digital simulation is carried out in order to demonstratethe capability of the STATCOM to improve the transient stabilitymargin of the proposed power system. Therefore, the 3Φ faultis simulated on the power system and is applied at the terminalof wind park for the system shown in Fig. 2. The transientresponse is evaluated with and without the STATCOM. It isessential to observe and compare the most relevant variablesof the transient stability, such as phase angle of the machine,rotor speed, terminal voltage, and the reactive power. A verycommon indicator of the transient stability of SEIG is the CCTof fault, which is defined as the maximum duration of the fault,which will not lead to lose the synchronism of the inductiongenerator. The transient analysis is performed for a weak powersystem connection of SCR = 2. The three-phase-to-ground faultis applied at the terminal of wind park at instant t = 20 s withvarying the duration time to investigate the effectiveness of the


TABLE IIPOWER SYSTEM PARAMETERS

STATCOM for improving the transient stability margin. Thesimulation results are concluded in Table I.

The STATCOM demonstrates much higher CCT of fault andcritical speed. The STATCOM is adopted to operate in volt-age control mode associated with the damping control loops.Hence, it improves the transient stability margin for the systemwith STATCOM. This study provides a new approach of usingSTATCOM with damping control loops for large series com-pensated wind parks and the possibility to improve the transientstability margin especially for a weak interconnected electricgrid.

VIII. CONCLUSION

A novel damping control scheme for the STATCOM and(SSSC) has been proposed, designed, analyzed, and investi-gated in this paper. The use of STATCOM for SSR mitigationand damping power system oscillation has been treated. Thesimulation results demonstrate superior performance of the con-trollers for mitigating SSR due to the increase of the capacitiveseries compensation of the series compensated wind park. Thedamping torque analysis is used in the design of the dampingcontrol loops for the STATCOM. Hence, it provides a net posi-tive damping torque for torsional mode frequencies. Therefore,at any given oscillation frequency of the generator rotor, theelectrical torque is in phase with rotor speed acting as dampingtorque. The STATCOM demonstrated superior performance formitigating SSR and damping the torsional torque and powersystem oscillations. The damping control scheme reduces thepeak of the negative torque and secure higher stability margin

in terms of the values of the maximum clearing time of thefault and critical rotor speed of the wind park induction gener-ators. The simulation results provide a new approach of usingSTATCOM for large series compensated wind parks, which sig-nificantly improves the transient stability margin. The proposeddamping controller of the STATCOM mitigates the SSR addedan additional advantages of installing STATCOM that drives tooptimal cost solution of the problem of SSR.

APPENDIX

The parameters of the voltage control of the STATCOM wereselected using the offline-guided least square J0 minimizationmethod. The power system parameters are given in Table II.

ACKNOWLEDGMENT

The first author would like to thank Dr. S. El Farahaty for hisfull support in this study and dedicates this contribution to him.The study was made possible by the EU UPWIND project.

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Mohamed S. El-Moursi was born in El-Mansoura,Egypt, on July 5, 1975. He received the B.Sc.and M.Sc degrees in electrical engineering fromEl-Mansoura University, El-Mansoura, Egypt, in1997 and 2002, respectively, and the Ph.D. degreein electrical engineering from the University of NewBrunswick (UNB), Fredericton, Canada, in 2005.

From 1997 to 1998, he was with the Siemens Com-pany, as a Designer Engineer for photovoltaic system.From 1998 to 2002, he was with El-Mansoura Uni-versity, as a Research and Teaching Assistant in the

Electrical Engineering Department, where he was involved in consultant ac-tivities with external companies. From 2002 to 2005, he was a Research andTeaching Assistant in the Department of Electrical and Computer Engineering,UNB, Canada. From 2005 to 2006, he was with the McGill University, as aPostdoctoral Fellow with the Power Electronics Group. From 2006 to 2009, hewas with Vestas as a Research and Development Engineer in the TechnologyR&D, where he was involved in the Wind Power Plant Analysis Group, Arhus,Denmark. He is currently an Assistant Professor in the Electrical Engineer-ing Department, El-Mansoura University. His current research interests includeelectrical power system modeling, power electronics, flexible ac transmissionsystem (FACTS) technologies, system control, wind turbine modeling, and windenergy integration and interconnections.

Dr. El-Moursi was awarded the Expert and Key Employee benefits inDenmark after the assessment from Danish Innovation Counsel and recom-mendation from Vestas Wind Systems A/S.

Birgitte Bak-Jensen (M’88) received the M.Sc. de-gree in electrical engineering, in 1986, and the Ph.D.degree in high-voltage components in 1992, bothdegrees from the Institute of Energy Technology,Aalborg University, Aalborg, Denmark.

From 1986 to 1988, she was with the ElectroluxElmotor A/S, Aalborg, Denmark, as an Electrical De-sign Engineer. She is currently an Associate Professorin the Institute of Energy Technology, Aalborg Uni-versity, where she has been working since August1988. Her current research interests include model-

ing and diagnosis of electrical components, power quality, and stability in powersystems.

Mansour H. Abdel-Rahman (M’79) was born inEgypt in 1947. He received the B.Sc. and M.Sc. de-grees in electrical engineering from Cairo University,Giza, Ezypt, in 1970 and 1975, respectively, and thePh.D. degree in electrical engineering from the Uni-versity of Manchester Institute of Science and Tech-nology (UMIST), Manchester, U.K., in 1979.

Since 1987, he has been a Full Professor at theUniversity of El-Mansoura, El-Mansoura, Egypt. Hewas involved in visiting assignments, teaching andresearching, at the University of Toronto, Canada,

the University of Windsor, Canada, the University of Cambridge, U.K., wherehe was a Fellow of Churchill College, the University of Western Australia,Australia, Doshisha University, Japan, Helsinki University of Technology,Finland, the University of Iceland, the University of Aalborg, Denmark,Jordan University, Jordan, and Kuwait University, Kuwait. His current researchinterests include electromagnetic transients in power system networks and ma-chines, steady-state and dynamic analysis of power systems, and the applicationof artificial intelligence in power systems.

Prof. Abdel-Rahman received the John Madsen Medal for the best papersubmitted to the Institute of Engineers, Australia, in 1989, the IEEE IndustryApplication Society First Prize Paper in 1988, and the IEEE Industrial andCommittee Prize Paper in 1987.

novel statcom controller for mitigating ssr and

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