1818 ieee transactions on power systems, vol. 27,...

1818 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 27, NO. 4, NOVEMBER 2012

Small-Signal Stability Analysis of Multi-TerminalVSC-Based DC Transmission Systems

Giddani O. Kalcon, Grain P. Adam, Olimpo Anaya-Lara, Member, IEEE, Stephen Lo, andKjetil Uhlen, Member, IEEE

Abstract—A model suitable for small-signal stability analysisand control design of multi-terminal dc networks is presented. Ageneric test network that combines conventional synchronous andoffshore wind generation connected to shore via a dc network isused to illustrate the design of enhanced voltage source converter(VSC) controllers. The impact of VSC control parameters onnetwork stability is discussed and the overall network dynamicperformance assessed in the event of small and large perturba-tions. Time-domain simulations conducted in Matlab/Simulinkare used to validate the operational limits of the VSC controllersobtained from the small-signal stability analysis.

Index Terms—DC transmission, offshore wind generation,small-signal stability, voltage source converter.

NOMENCLATUREHVDC High-voltage direct current transmission.

HVAC High-voltage alternating current transmission.

VSC Voltage source converter.

LCC Line-commutated converter.

MTDC Multi-terminal direct current transmission.

PCC Point of common coupling.

DFIG Doubly-fed induction generator.

FRC-WT Fully-rated converter wind turbine.

SSSA Small-signal stability analysis.

I. INTRODUCTION

H IGH-VOLTAGE dc (HVDC) transmission is emergingas the prospective technology to address the challenges

associated with the integration of future offshore wind power

Manuscript received June 07, 2011; revised October 03, 2011, December 05,2011, and February 09, 2012; accepted February 24, 2012. Date of publicationApril 17, 2012; date of current version October 17, 2012. Paper no. TPWRS-00467-2011.G. O. Kalcon, G. P. Adam, and S. Lo are with the Institute for En-

ergy and Environment, University of Strathclyde, Glasgow G1 1XW, U.K.(e-mail: [email protected]; [email protected]; [email protected]).O. Anaya-Lara is with the Institute for Energy and Environment,

University of Strathclyde, Glasgow G1 1XW, U.K., and also with theFaculty of Engineering Science and Technology, Norwegian Universityof Science and Technology, NTNU, 7491 Trondheim, Norway (e-mail:[email protected]; [email protected]).K. Uhlen is with the Department of Electrical Power Engineering, Norwe-

gian University of Science and Technology, NTNU, 7491 Trondheim, Norway(e-mail: [email protected]).Color versions of one or more of the figures in this paper are available online

at http://ieeexplore.ieee.org.Digital Object Identifier 10.1109/TPWRS.2012.2190531

plants [1], [2]. Small-signal stability analyses (SSSA) have be-come important in the design stage of HVDC controllers to en-hance their resilience to faults, and to improve their ability tocontribute to power network operation [3].Stability studies of hybrid networks comprising HVDC and

HVAC transmission are discussed in [4] and [5]. In [4], theauthors investigate the potential interactions between multi-in-feed LCC-HVDC converters and synchronous generators’ dy-namics using SSSA. However, the LCC-HVDC controllers arenot modeled in detail (only current and extinction angle con-trollers are incorporated). In [5], a detailed linearized model ofa point-to-point LCC-HVDC is presented, and SSSA is con-ducted using a sampled data modeling approach. However, theLCC-HVDC controllers and ac network are not represented indetail.In [6], small-signal stability analysis is used to design the

controls of a point-to-point LCC-HVDC connected in parallelwith an ac line to provide damping of sub-synchronous oscilla-tions. The state-space model is derived in detail including thedynamics of the network, the machine multi-mass shaft sys-tems, and the HVDC system. The authors of [1] also presenteda linearized model for a hybrid system that includes compre-hensive dynamic models for point-to-point LCC-HVDC, ac net-work, and synchronous generators [7]. The paper addresses thepossibility of using small-signal stability analysis to investigatesub-synchronous oscillations damping in hybrid systems.Small-signal stability analysis has also been used in [8] to

design the controllers of an LCC-HVDC connecting a windfarm based on fixed-speed induction generators. The results re-ported contain very high-frequency components due to the in-teraction between the HVDC converter controller and the windfarm network.In [9], a modeling platform to analyze conventional electro-

mechanical oscillations and high-frequency interactions inhybrid networks, comprising an LCC-HVDC and the ac grid,using small-signal stability analysis is proposed. The linearizedmodels of the dynamic devices and the network dynamics arecombined together using Kirchhoff’s laws. Then, the resultantnetwork dynamic models are combined with the admittancematrix of the rest of the network, using current injection models.The authors in [10] present the small-signal stability analysisof ac/dc systems with a novel discrete-time representation of atwo-terminal LCC-HVDC based on multi-rate sampling. Thecomplete state-space model of the ac/dc system incorporatessuitable interfaces of the various subsystems involved. Thesynchronous machine and ac network use a common dq-axesreference frame. The ac and dc networks are interfaced usingcurrent injection relationships.

0885-8950/$31.00 © 2012 IEEE

KALCON et al.: SMALL-SIGNAL STABILITY ANALYSIS OF MULTI-TERMINAL VSC-BASED DC TRANSMISSION SYSTEMS 1819

Fig. 1. Test system.

In this paper, the authors present a detailed state-space modelof amore elaborated 4-terminal VSC-MTDC system connectingtwo offshore wind farms to an ac network. Small-signal stabilityanalysis is carried out to define the ranges for the gains of theVSC controllers that ensure dynamic stability, and the resultsare confirmed via time-domain simulations in Matlab/Simulink.Also, a simple example to calculate the converter controllergains using root-locus is provided in the Appendix.The wind turbine generators are modeled as fixed-speed in-

duction generators (FSIGs) to represent the worst-case scenario,in terms of wind turbine controllability. However, the modelpresented can also be used with variable-speed wind turbinessuch as doubly-fed induction generators (DFIGs), or fully-ratedconverter wind turbines (FRC-WTs), at the expense of increasedmodeling complexity due to the power electronic converters(and associated controllers) comprised in these type of windturbines.

II. GENERIC TEST NETWORK

Fig. 1 shows the network used in this research. It consistsof four VSC stations connecting two offshore wind farms tothe onshore grid ( and ). Each wind farm is ratedat 33 kV, 400 MVA. The dc transmission voltage is 300 kVpole-to-pole ( -bipolar). The length of the dc link ca-bles is 150 km, and the length of the auxiliary cables is 5 km.The onshore grid comprises conventional thermal generationaggregated and modeled by a synchronous generator, SG, withratings of 33 kV, 2400 MVA. Due to the asynchronous con-nection, the offshore wind farms and the onshore network aretreated as independent systems in the small-signal and transientstability analyses [3].

III. SMALL-SIGNAL STABILITY MODEL DEVELOPMENT

A. Assessment of Small-Signal Stability

The most direct way to assess small-signal stability is viaeigenvalue analysis of a model of the power system [11]–[14].In this case, the “small-signal” disturbances are considered

sufficiently small to permit the equations representing thesystem to be linearized and expressed in state-space form.Then, by calculating the eigenvalues of the linearized model,the “small-signal” stability characteristics of the system canbe evaluated. The way in which system operating conditionsand controllers’ parameters influence dynamic performancecan be demonstrated by observing the influence on the loci ofthe dominant eigenvalues, i.e., the eigenvalues having the mostsignificant influence on network dynamic performance.The linearized model of the test system in Fig. 1 is expressed

in state-space form as [9], [15]

(1)

where is the state vector, is the input vector, is the statematrix, and is the input or control matrix. The eigenvaluesof the state matrix provide the necessary information aboutthe small-signal stability of the system. The participation factormatrix formed from the left and right eigenvectors of matrixgives information about the relationship between the states andthe modes.

B. Grid-Side VSC Converter Model

Fig. 2 shows the equivalent circuit of the grid-side convertersand , which control the dc link voltage and the ac

voltage at buses and , respectively. The dynamic equa-tions of these converters in the dq reference frame are (inverteroperation) [8], [13], [14]

(2a)

(2b)

(3)

where and are the total resistance and inductance betweenthe VSC and the PCC; , are the voltages at the VSC ter-minals and PCC, respectively; is the dc voltage; and isthe dc capacitor.


Fig. 2. One-phase of a VSC converter.

After linearization of (2) and (3), the linearized model of thegrid-side converter is

(4a)

(4b)

(5)

Fig. 3 shows the control system block diagram for both grid-side converters and .From Fig. 3, the reference currents and are obtained

from the dc voltage and ac voltage controllers as

(6)

(7)

where , , , and are the proportional and integralgains of the dc voltage and ac voltage controllers, respectively.The auxiliary variables and are used to represent theintegral parts of these controllers.The voltages at buses , , and (onshore grid), and

their linearized forms are expressed as

(8)

(9)

The linearized forms of (6) and (7) are

(10a)

(10b)

Fig. 3. Control system of the grid-side converters.

From Fig. 3, the VSC terminal voltage obtained from the currentcontrollers, including the feed-forward terms, is expressed in dqcoordinates as

(11a)

(11b)

where and are the active and reactive current com-ponents; and are the proportional and integral gains ofthe current controller; and are auxiliary variables rep-resenting the integral parts of the controllers, where

and .After manipulation of the equations and change of variables,

the final linearized differential equations of and areexpressed as in (12) (the full matrix representation is providedin the Appendix):

(12a)

(12b)


(12c)

where the auxiliary variables to introduced to representthe integral parts of the dc voltage, ac voltage and current con-trollers are

(13a)

(13b)

(13c)

(13d)

C. Wind Farm-Side VSC Converter Model

The linearized model of the wind farm-side convertersand in the dq coordinates are (rectifier operation)

(14a)

(14b)

(14c)

Fig. 4. Control system of the wind farm-side converters.

Fig. 4 shows the control system of the wind farm-sideconverters.Based on Fig. 4, the reference currents, and , ob-

tained from the active power and ac voltage controllers are

(15a)

(15b)

where are the ac voltage controllers’ gains; representsthe integral part of the ac voltage controllers. The final linearrepresentation of each wind farm-side converter is

(16a)

(16b)


Fig. 5. Single-line diagram of the dc offshore network.

(16c)

(16d)

(16e)

(16f)

The matrix form of (16) is given in the Appendix.

D. DC Offshore Network

The dc network in Fig. 1 is represented by a set of quasi-steady-state equations, which are linearized as follow (the dclink voltages and currents are shown in Fig. 5). The converterstations are based on simple two-level converter with commondc link capacitors, which attenuate high-frequency harmonicsthat may result from any transient in a similar manner as dc cableseries inductance do:

(17)

Fig. 6. Single-line diagram of the onshore network.

E. Synchronous Generator

The synchronous generator in the onshore grid, SG, is mod-eled with a seventh-order model, including excitation and tur-bine-governor control [14], [16].

F. Wind Farm Based on Fixed-Speed Induction Generator

The offshore wind farms are assumed fixed-speed with fifth-order model induction generators. A detailed state-space modelincluding the static capacitors is given in the Appendix [17],[18]. Variable-speed wind turbines such as DFIG or FRC-WTcan also be used, but at the expense of increased model com-plexity due to the power converters (and associated controllers),incorporated in these wind turbine generator technologies.

G. Onshore Network

The onshore network in Fig. 6 is modeled using theimpedance matrix (18) based on the matrix partitioning tech-nique (load buses are neglected). The current and voltage ineach bus is referred to a common reference frame as describedin [16], [19]

(18)

where is the reduced impedance matrix. The voltage-currentrelationship is

(19)

The state-space representation of the onshore network is

(20)

where and are the currents and voltages in buses ,, and . R and X are the impedance matrix components.

IV. FORMULATION OF THE OVERALL LINEARIZED SYSTEM

The complete state-space representation of the test systemin Fig. 1 is formulated by combining the individual state-spacemodels of the wind farms, offshore and onshore converters, dcnetwork, onshore ac network, and synchronous generator, as


shown by the block diagram in the Appendix. The dc currentsand voltages in (17) are used to link the grid-side converters tothe offshore converters. The synchronous generator and windfarms are linked to the converters using nodal theory. The com-plete state-space matrix has a dimension of 56 56.

V. SMALL-SIGNAL STABILITY ANALYSIS

The small-signal stability of the test network is assessed usingeigenvalue analysis. A base-case scenario is considered in orderto provide a yardstick against which the influence of VSC con-trollers and network loading can be judged. The power flowresults for the base-case scenario are shown in Fig. 1, and theeigenvalues associated with this case are given in Table I.As seen in Table I, all eigenvalues have negative real parts

indicating a stable operating condition for the base-case sce-nario. The eigenvalues that dominate the transient response ofthe system are and . The participation factor matrixindicates that the synchronous generator states have a dominanteffect on the complex pair (with time constant of 26.3 s,frequency of oscillation of 1.65 Hz, and 0.004 damping ratio).Therefore, any attempt to improve network damping must takethese states into account. The participation factor matrix alsoindicates that the VSC states influence greatly the eigenvaluesassociated with super-synchronous oscillation modes to. Therefore, proper tuning of the VSC control parameters

may result in fast damping of these oscillation modes. Inaddition, Table I shows that the complex pairs and(corresponding to fast transients, with frequencies of 3169 Hz,time constant of 3.18 ms, and 0.016 damping ratio) are dampedout at a much faster rate. These modes are often caused bysuper-synchronous oscillations due to the interaction betweenadjacent converters, as reported in [20].For example, modes and are associated with oscil-

lations of the dc voltage of the two grid-side convertersand and their effect on the direct-axis currents. Modes

and are associated with the interaction betweenconverters and , and and through theirdc voltage and active current components. It is observed thatmodes and represent the interaction between theoffshore converters and wind farms through their voltage con-trol loops and reactive current components.

VI. IMPACT OF VSC CONTROLS ON SMALL-SIGNAL STABILITY

The transient behavior of interconnected ac/dc systems ishighly dependent on the characteristics of both synchronousgenerators and VSC converters and their controllers. Largesynchronous generators have slow response during abnormalconditions due to their relatively large inertia, while VSCconverters are fast-acting devices, which can respond withintens of milliseconds and influence the transient behavior sig-nificantly. Hence, during a disturbance, the transient behaviorof the interconnected ac/dc system will mainly depend on theability of the VSC converter controllers to damp out networkoscillations, and to provide the necessary reactive powerduring the fault, allowing sufficient time for the synchronousmachines to adjust their controllers to provide further support.This section investigates the suitable range for different VSCcontrollers’ gains that ensures network stability (time-domain

TABLE IEIGENVALUES OF TEST SYSTEM FOR THE BASE-CASE SCENARIO

simulations are also used to validate the results). To this aim,a line-to-ground fault with fault resistance isapplied at bus at with 0.05 s duration.

A. Grid-Side VSC—Current Controller Effect

The effect of the proportional gain of the grid-side VSCs cur-rent controllers on system stability is investigated in this section.


TABLE IIEFFECT OF OF THE GRID-SIDE VSC CURRENT CONTROLLER

TABLE IIIEFFECT OF OF THE GRID-SIDE VSC CURRENT CONTROLLER

Fig. 7. Active power output of for different values of and .

It has been found that the range of that ensures system sta-bility over the entire operating range is between (0.6–35) withbest responses obtained with . In Table II, three dif-ferent gains for the proportional gain ( , 1, and 10)are investigated. In this case, the pair has an oscilla-tion frequency of 211.3 Hz with damping time of 0.002 s and0.345 damping ratio when compared to 224 Hz withdamping time of 0.025 s and 0.028 damping ratio when .The system is unstable when .Table III shows the effect of the current controller integral

gains on system stability. The small-signal stability analysis in-dicates that the system remains stable for any value ,with best responses obtained with . For example, thepair has an oscillation frequency of 3192 Hz with dampingtime of 0.02 s and 0.0025 damping ratio when ,compared to 5048 Hz with damping time of 0.02 s and 0.0015damping ratio when . The system is unstable if isless than 10.The time-domain simulation in Fig. 7 validates the results ob-

tained from the small-signal stability analysis when the line-to-


TABLE IVEFFECT OF VARYING OF THE DC LINK VOLTAGE CONTROLLER

TABLE VEFFECT OF VARYING OF THE DC LINK VOLTAGE CONTROLLER

ground fault is applied at bus . From the participation factormatrix, it was found that the variations of influence the statesassociated with the active power control loops, while variationsin affect those associated with the reactive power controlloops, in both converters.

B. DC Link Voltage Controller Effect

It is found that the dc voltage controller integral gains thatensure stable operation lay in the range .Table IV shows the oscillation frequency and dampingtime for selected eigenvalues for different values of

. The best time-domain response isachieved with the integral gain , where lower os-cillation frequencies and fast damping time are observed (seeFig. 8).Table V shows the effect of the dc voltage controller propor-

tional gain on system stability. It is established that largedecreases the damping time. For example, when , thedamping time for the super frequency oscillations modesis 0.025 s with 0.028 damping ratio, while the damping time is0.01 s with 0.011 damping ratio for and 0.063 s with



TABLE VIEFFECT OF CHANGING OF GRID-SIDE CURRENT CONTROLLER

TABLE VIIEFFECT OF VARYING OF THE AC VOLTAGE CONTROLLER

0.009 damping ratio with . These results are also con-firmed by time-domain responses shown in Fig. 8.

C. AC Voltage Controller Effect

The small-signal stability analysis shows that the ac voltagecontroller proportional gain has a wide operational rangethat ensures stable system as shown in Table VI. The best re-sponse is obtained with . It is noticeable that the pair

has an oscillation frequency of 224 Hz, 0.079 s dampingtime, and 0.009 damping ratio when compared to220 Hz, 0.038 s, and 0.019 damping ratio for . Fig. 9shows the time-domain simulation that validates the results ob-tained via small-signal stability analysis.Similarly, the best guess for the ac voltage controller

integral gain, , for stable operation ranges between. The best damping response is achieved

with . With this gain, the pair oscillationfrequency is 227 Hz, 0.02 s damping time, and 0.35 dampingratio compared to 225 Hz and the 0.025 s damping time and0.028 damping ratio with . The system becomesunstable with values of as shown in Table VII.The ac voltage controller integral gain corresponding to the

Fig. 10. Active power at and during three-phase fault at . (a) Activepower at . (B) Active power at .

system breakpoint (the transition from stable to unstable) laysbetween 640 and 650. The shaded cells of Table VII indicateeigenvalues and have positive real parts (instability).For further validation of the VSC gain limits obtained based

on small-signal stability analysis, and to investigate the VSCsresponse during three-phase faults, a solid three-phase fault isapplied at bus , at time with a fault duration of 5 cy-cles (for 50 Hz). This scenario allows the robustness of VSCscontrollers designs based on small-signal stability analysis tobe assessed. Fig. 10 shows the power waveform at and .It can be seen that the system remains stable and returns tothe pre-fault operating condition after the fault is cleared. Thisdemonstrates the validity of the analysis presented in this paper.

VII. CONCLUSION

A detailed mathematical model for small-signal stabilityanalysis of VSC-based multi-terminal dc transmission systemshas been presented. The approach taken was to divide thesystem into smaller subsystems representing each of them by astate-space model. The individual state-space models were thenintegrated into a single model to give the overall representationof the network. The mathematical model developed was usedto investigate the small-signal stability performance of thehybrid network utilizing the eigenvalues and the participatingfactors matrix. The limits for the VSC controllers’ gains wereestablished and validated using time-domain simulations undersmall perturbations. It was observed that using the small-signalstability model, it was possible to design improved controllersfor the VSCs of the multi-terminal dc network, which ensurestable network operation and enhanced dynamic performance.


Fig. 11. Methodology used to obtain the complete state-space model of the test system.

The modeling approach and analysis presented can be extendedto larger systems with an arbitrary number of converters, syn-chronous machines, and wind farms.

APPENDIX

The complete state-space representation of the test systemin Fig. 1 is obtained by combining the individual state-spacemodels as shown in Fig. 11. The dc currents and voltages in(17) are used to link the grid-side converters to the offshore-sideconverters, while the synchronous generator and wind farms arelinked to the converters using current injection theory. The lin-earized models of individual subsystems are expressed in theform in the following subsections.

A. Grid-Side Converters State-Space Model

See the equation at the bottom of the next page.represents vector

matrix of state variables; is the matrixthat contains the interfacing variables that relate the onshore acnetwork and the dc network.

B. Offshore Wind Farm-Side Converters State-Space Model

See the first equation at the bottom of page 1828.is the matrix

that contains the offshore converter state variables;represents the vector matrix of

interfacing variables that relate the converter to the offshore acnetwork and the dc network.

C. Fixed-Speed Induction Generator [17], [18]

See the second equation at the bottom of page 1828.is a vector

matrix of the state variable of the fixed-speed induction gen-erator; and are interfacing variables between thefixed speed induction generator and the offshore wind farm acnetwork; and is also an interfacing variable that relatesgenerator mechanical input torque to mechanical output of the

turbine. In this paper, is considered constant to reducesystem complexity.

D. Synchronous Machine State-Space Model [14]

See the equation at the bottom of page 1829.is the matrix that

contains state variables; and are interfacing variablesthat relate the synchronous generator to the onshore ac network;and and also represent interfacing variables relatedto the synchronous machine controllers, mainly turbine andexcitation systems.

E. Converter Control System Design and Gains Selection

The converter controller’s gains limits are first definedusing eigenvalues analysis, and then gains which providethe best network dynamic performance are selected withinthese limits. The proposed approach uses the overall systemlinearized model (which involves 56 eigenvalues), makingthe use of root-locus for control design very complex(if possible at all). However, for demonstration purposes,in this Appendix, the control system of each converterstation (using only the converter linearized model and itsassociated controllers) is designed using root-locus based onequations and transfer functions obtained from the linearizedmodel of the converter (assuming a two-level voltage sourceconverter):Current controller:Based on Fig. 2, the linearized model of the converter ac side

is

(E1.1)


(E1.2)

where and.

and are obtained from the proportional and inte-gral (PI) controllers as , and

, whereand . After substitution in

(E1.1) and (E1.2), and algebraic manipulations the followingequations are obtained:

(E2.1)

(E2.2)

(E2.3)

(E2.4)

After Laplace manipulation of the state-space equations(E2.1)–(E2.4), the following transfer function is obtained:

(E3)

With the parameters used in the paper: and, the gains obtained from the root-locus analysis are

, , , and maximumovershoot of 2.6% (these gains put the system closed-loop polesat and a zero at ). These gains do notprovide a satisfactory performance over all operating conditionswhen the converters are connected to the system under investi-gation. The final gains obtained based on eigenvalue analysis ofthe overall system, when all possible interactions are taken intoaccount, are , .dc voltage controller:From Fig. 2 and assuming a lossless converter, the converter

dc-side dynamics can be expresses as

(E4)


Using Taylor series with the higher-order terms neglected, thelinearized form of (E4) is obtained as

(E5)

Let and


and the variable be obtained from the dc voltage controlleras and ,then the linearized form of the differential equations that de-scribed the dc side, including dc voltage controller are

(E6.1)

(E6.2)

After Laplace manipulation of equations (E6.1) and (E6.2), thetransfer function for the dc voltage controller is

(E7)

Selection of the dc voltage controller gains can be accomplishedin a similar way as that for the current controller using root-locusor frequency-domain techniques. Normally, the converter loadangle (the angle of the converter terminal voltage relative to thevoltage at the point of common coupling) is sufficiently smallas the total impedance between the converter terminals and thepoint of common coupling must be kept small in order not to

compromise the available dc voltage for reactive power com-pensation, and similarly

.Therefore the reference current is obtained:

, where and arenormalized by .In the control system design, the authors rely on feed-forward

terms of the current controller, which are introduced during thedecoupling of from to improve system disturbance re-jection. However, the controllers’ gains obtained from such de-signs are always subject to change when the converter is oper-ated in a complex power system. For this reason, the gains ob-tained from the control design are used only as a starting point;and the final values of the gains are selected as those that mayproduce the best performance taking into account all the systeminteractions. Gain fine-tuning is also employed in an attemptto establish the influence of voltage source converter gains andcontrollers on the overall network performance.

ACKNOWLEDGMENT

The authors would like to thank NOWITECH for facilitatingthe interaction between the researchers and institutions involvedin the preparation of this research paper. Dr. O. Anaya-Lara


would like to thank Det Norske Veritas (DNV) for the sponsor-ship provided for his Visiting Professorship at NTNU, Trond-heim, Norway.

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Giddani O. Kalcon received the B.Eng degree (with honors) in power systemandmachines from Sudan University of Science and Technology (SUST), Khar-toum, Sudan, in 2001, and the M.Sc degree in electrical power system fromSUST. He is currently pursuing the Ph.D. degree at the University of Strath-clyde, Glasgow, U.K.His research interest include wind power integration and HVDC system.

Grain P. Adam received the first-class B.Sc. and M.Sc. degrees in electricalmachines and power systems from Sudan University of Science and Tech-nology, Khartoum, Sudan, in 1998 and 2002, respectively, and the Ph.D. degreein power electronics from Strathclyde University, Glasgow, U.K., in 2007.He is currently with the Department of Electronic and Electrical Engineering,

Strathclyde University, and his research interests are multilevel inverters, elec-trical machines, and power systems control and stability.

Olimpo Anaya-Lara (M’98) received the B.Eng. and M.Sc. degrees from In-stituto Tecnológico de Morelia, Morelia, México, and the Ph.D. degree fromUniversity of Glasgow, Glasgow, U.K., in 1990, 1998 and 2003, respectively.His industrial experience includes periods with Nissan Mexicana, Toluca,

Mexico, and CSG Consultants, Coatzacoalcos, México. Currently, he is a Se-nior Lecturer at the University of Strathclyde in Glasgow. His research interestsinclude wind generation, power electronics, and stability of mixed generationpower systems.

Stephen Lo received the M.Sc. and Ph.D. degrees from the University of Man-chester Institute of Science and Technology, Manchester, U.K.He is a Professor at Strathclyde University, Glasgow, U.K. His research in-

terests include power systems analysis, planning, operation, monitoring, andcontrol, including application of expert systems and artificial neural networks,transmission and distribution management systems, and privatization issues.

Kjetil Uhlen (M’95) received the M.Sc. degree and the Ph.D. degree in controlengineering from the Norwegian Institute of Science and Technology (NTNU),Trondheim, Norway, in 1986 and 1994, respectively.He is currently a Professor of Electrical Engineering at NTNU and leads the

NOWITECH work package on wind power integration. His main technical in-terests are operation and control of electric power systems.

1818 ieee transactions on power systems, vol. 27,...

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