06169971

IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 27, NO. 3, AUGUST 2012 1441

Impact of DC Line Voltage Drops on Power Flow ofMTDC Using Droop ControlTemesgen M. Haileselassie and Kjetil Uhlen, Member, IEEE

AbstractThis paper discusses the impact of dc transmissionvoltage drops on the distribution of dc grid balancing power whendc voltage droop control is applied. DC line voltage drops in amultiterminal VSC-HVDC (MTDC) system result in nonuniformvariations of dc bus voltages when changes in dc grid power flowoccur. This in turn affects the distribution of instantaneous bal-ancing power in a MTDC that uses dc voltage droop control. Thevalues of dc voltage droop constants determine the degree of im-pact that dc voltage drops will have on the sharing of balancingpower in the dc grid. In this paper, an analytical expression for es-timating the distribution of balancing power which accounts for dcline voltage drops is derived. A five-terminal MTDC was modelledin PSCAD for demonstrating the effects of dc line voltage drops aswell as for validating the proposed analytical expression which es-timates balancing power distribution.

Index TermsDC grid, droop control, multiterminal VSC-HVDC (MTDC), voltage source converter high-voltage dc trans-mission (VSC-HVDC).

NOMENCLATURE

VSC Voltage source converter.

HVDC High voltage dc transmission.

MTDC Multiterminal VSC-HVDC.

I. INTRODUCTION

I N recent years, there have been many research activities ondevelopment of VSC based multiterminal HVDC systems.This has mainly been driven by increasing number of off-

shore wind farms in places such as the North Sea region. Ad-vantages of a multiterminal VSC-HVDC (MTDC), sometimesalso called a dc grid, include lower transmission losses, flexi-bility in control, connection of asynchronous grids, and ease ofincorporating new VSC-HVDC terminals to an already existingMTDC system.Control strategies proposed so far in the literature for MTDC

could be broadly categorized into two groups, namely, constantdc voltage control schemes (sometimes called masterslavecontrol scheme) and dc voltage droop control schemes. The op-erational principle of constant dc voltage control strategy (i.e.,masterslave scheme) has been presented in [1][3]. The main

Manuscript received July 01, 2011; revised July 12, 2011; accepted January30, 2012. Date of publication March 14, 2012; date of current version July 18,2012. Paper no. TPWRS-00613-2011.The authors are with the Department of Electric Power engineering, Nor-

wegian University of Science and technology, Trondheim, N-7491, Norway(e-mail: [email protected], [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.2012.2186988

drawback of this control scheme is that operation of the entiredc grid depends upon the normal operation of the dc voltageregulating terminal (i.e., the master terminal). In the case ofdc voltage droop control, two or more terminals participate indc voltage control, thereby sharing the duty of instantaneous(primary) power balancing among them. The working principleof dc voltage droop control has been presented, among others,in [4][7].In the case of a masterslave scheme, disconnection of the

master terminal will lead to immediate outage of the entire dcgrid. When a disconnection of one of the terminals occurs indc voltage droop control mode, the remaining part of the dcgrid will continue in normal operation. Hence, the latter type ofcontrol scheme is considered to be more reliable than the firstone since power balancing, and consequently the operation ofthe entire MTDC system, should not be dependent on a singleVSC-HVDC terminal.Even though the basic working principle of dc voltage droop

control in MTDC has been explored in the literature, the impactof the dc line voltage drops on the primary dc grid power bal-ancing has not been properly analyzed. This paper has the mainobjective of addressing this issue.The principle behind dc voltage droop control could be ex-

plained as similar to frequency droop control ac grid, but thereare some differences as well due to dc line voltage drops. Fre-quency in ac grids is a universal measurement of the systemloading and hence the means for automatic balancing of powerflow [8]. DC voltage can also play a similar role in dc grids,with themain difference coming from dc line resistances. The dcline resistances, via terminal voltage differences, influence thedc droop controller in two ways, namely in static (steady-state)power control and in dc grid balancing power distribution (afteroccurrence of a deficit/surplus of power in the dc grid).In static power flow control, the main objective is to get a

power flow equal to the scheduled level for each of the VSC-HVDC terminals. This is achieved by eliminating the steady-state dc voltage error in the droop controller. This implies that,in a load flow analysis of the entire dc grid, it is necessary todetermine the appropriate dc voltage references [9].Apart from the static power flow, the dc line voltage drops

also have a more subtle influence on the distribution of bal-ancing power in droop-controlled MTDC. The dc bus voltagesof all terminals change whenever there is a change in power flowin the dc grid. However, the dc bus voltages show unequal vari-ations due to the dc line resistances. This, in turn, due to the dcvoltage droop controllers, causes a deviation in distribution ofdc grid balancing power compared to what would be estimatedby ignoring the effects of dc line losses and voltage drops. This

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1442 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 27, NO. 3, AUGUST 2012

paper focuses on the second mechanism by which dc line resis-tances affect the power flow in a dc grid.DC bus voltage variations are dependent upon the topology

and line conductances of the dc grid. As a result of this, a con-verter terminal will respond differently to the same changes inpower flow occurring at different locations of the dc grid. Thechosen dc voltage droop constants also have influence on theseverity of impact of dc bus voltage variations on distributionof balancing power.In this paper, two mathematical models for dc grid power

balancing has been compared to understand the influence of dcline voltage drops on power flow. In the first approach, the dcline voltage drops are neglected. The second one, which is themain contribution of this paper, takes the dc line voltage dropsinto consideration for describing the system interaction moreaccurately. A five-terminal VSC-HVDC has been simulated inPSCAD, and the results are compared with the estimations bythe two mathematical models. It is demonstrated that the pro-posed model (i.e., the second approach) accurately describes thedroop interactions in the dc grid, and it is a useful tool to under-stand the influence of dc line voltage drops on the power flowof dc grids.This paper is outlined as follows. In Section II, the different

types of VSC-HVDC control are discussed. Section III dis-cusses the distribution of dc grid balancing power in an ideallossless dc grid in the presence of dc voltage droop control. InSection IV, the impact of dc line voltage drops is discussed.Section V discusses proposed analytical expression for esti-mating the distribution of balancing power in dc voltage droopcontrolled dc grid system. In Section VI, simulation studies arepresented and discussed for demonstrating the impacts of dcvoltage line drops and for validating the proposed analyticalestimation method. Conclusions are drawn in Section VII.

II. VSC-HVDC TERMINAL CONTROL

A. Basic VSC Controller

The most commonly used control approach for VSC is thedecoupled-axes (d-q axes) oriented control, where the d-axis ofthe synchronously rotating reference frame is aligned tothe voltage phasor of phase-A measured at the point of commoncoupling (PCC) (point in Fig. 1). This alignment also meansthat the quadrature axis (q-axis) component of the voltage mea-surement becomes zero. The sign convention used here forthe power and current measurements of the converter is in sucha way that power/current measured at a converter terminal ispositive if it is flowing from the ac grid to the dc grid via theconverter station. In other words, positive corresponds torectifier mode of operation and negative corresponds to in-verter mode of operation.The basic structure of the controller consists of an inner cur-

rent control loop enabling effective decoupling of active andreactive power control. A complete schematic diagram of theVSC controller is shown in Fig. 1. The symbols used in Fig. 1are described in Table I.

Fig. 1. Schematic diagram of the VSC controller.

TABLE ILIST OF SYMBOLS IN FIG. 1

The voltagecurrent relation in Fig. 1 is given by

(1)

After the abc/dq transformations, (1) takes the form of

(2)

Proportional-integral control is used for the inner currentloop, and the mathematical relation is given by

(3)

HAILESELASSIE AND UHLEN: IMPACT OF DC LINE VOLTAGE DROPS ON POWER FLOW OF MTDC USING DROOP CONTROL 1443

Fig. 2. DC terminal control configurations and the corresponding dc voltage versus power characteristics. (a). DC bus power controller (b). DC voltage regulator(c). DC voltage droop controller.

The apparent power and real power measured at PCC are ex-pressed as

(4)

where and are apparent power and real power of theconverter. and refer to direct-axis (d-axis) voltage anddirect-axis current of the converter measured at PCC. Reactivepower/ac voltage control is not the focus of this paper and willnot be discussed here. Depending on the mode of operation, theactive current reference is used to control active power ordc bus voltage of the VSC.

B. DC Voltage and Power Control Modes

A VSC-HVDC terminal, hereafter simply referred as dc ter-minal, may have one of the three control modes, namely: con-stant power mode, constant voltage mode or droop mode ofcontrol. The dc voltage versus power characteristic curve ofconstant powermode dc terminal is shown in the top of Fig. 2(a).is the power axis and is dc bus voltage.Constant dc voltage control is represented by Fig. 2(b)

(bottom), where and refer to dc voltage reference and ac-tual dc bus voltage, respectively. A dc terminal which regulatesdc voltage will have a dc voltage versus power characteristiccurve shown in Fig. 2(b) (top).DC voltage droop control can be seen as a combination of

the two first types of VSC-HVDC control. It tries to controlpower to its reference level while at the same time contributingsome balancing power. Since these two actions are somewhatcontradicting (i.e., power control and dc voltage control) oneaction happens at the cost of steady state deviations for the other.DC voltage droop control is shown in Fig. 2(c) (bottom) and thecorresponding versus characteristic is shown in Fig. 2(c)(top).

In Fig. 2(c) (bottom), the symbol refers to the dc voltageresponse (analogous to the frequency response of synchronousgenerators in ac grids) and has the unit of MW/kV. The slope isoften given in terms of the dc droop constant , which is theratio of change in dc bus voltage to the corresponding changein converter power both in per-units. It could also be defined asthe change in dc voltage in per-unit that results in 100% changein converter power flow. The dc voltage droop constantand the dc voltage response are related to each other by

(5)

where and refer to rated power and rated dcvoltage of the dc terminal, respectively.From the dc voltage droop controller in Fig. 2(c) (bottom),

the error signal is given by

(6)

At steady state, the relation between dc voltage and converterpower then becomes

(7)

It could be noted that the steady-state characteristics in con-stant power control mode and constant dc voltage control modecould be represented by dc voltage droop controllers with(i.e ) and (i.e., ), respectively. Foranalytical purposes, a large (but finite) value of could suf-ficiently represent steady-state behavior in constant dc voltagecontrol mode.In the absence of dc voltage error signal, the converter power

will be same as the power reference without any steady-statedeviations. Hence, for precise control of power, the dc voltagereference in Fig. 2(c) (bottom) should be assigned according toresults from load flow analysis conducted for the entire dc grid.


For further details about dc grid load flow analysis the reader isreferred to [9].Now let us consider an initial steady-state operating point of

the controller in Fig. 2(c) (bottom) with input and output vari-ables represented by the superscript , i.e., , , ,and . The input/output variables at another steady-state pointcould be expressed in terms of the initial steady-state conditionsexpressed by

(8)

Furthermore, we assume that during initial steady-state con-ditions all error signals are zero, as in

(9)

From (6), (8), and (9), the change in output of the droop con-troller due to changes in inputs becomes

(10)

From (10), it could be observed that the power flow of the dcterminal can be controlled either by changing the power refer-ence or by changing the dc voltage reference . Nowlet us focus on the impact of change in power reference (i.e.,

). Assuming that the dc voltage reference remains fixed(i.e., ), the relation given by (10) could be simplifiedas in

(11)

Equation (11) is the small-signal equivalent of the versuscharacteristic shown by Fig. 2(c) (top).

III. DISTRIBUTION OF BALANCING POWER IN AN IDEALLOSSLESS DC GRID

In a lossless dc grid, the total sum of terminal power is zero(i.e., , , -number of dc terminals), whichalso implies the relation given by

(12)

Substituting (11) into (12), the following expression isobtained:

(13)

Moreover, in an ideal lossless dc grid, all dc bus voltages willbe equal (i.e., , ). This implies the relationgiven by

(14)

Substituting (14) into (13) yields the relation

(15)

where is the dc voltage response of the dc grid (analogous tofrequency response of ac grids), i.e., shows the total amountof change in dc grid power flow in MW as a result of a 1-kVchange in dc bus voltage.From (11), steady-state power deviation at terminal is given

by

(16)

Substituting (15) into (16), we obtain

(17)

In matrix form, (17) could be rewritten as

...

...

.... . .

.... . .

...

.... . .

.... . .

...

...

...

(18)Equation (17) indicates that the power flow of terminal

could be affected both by a change in power reference of thesame terminal and/or by change in power reference ofanother terminal , but with differing sign and magnitudeof proportionality constants for the two cases.Moreover, it could be observed from (17) that, in the absence

of line voltage drops, distribution of balancing power will ex-clusively be dependent on the dc voltage response of theindividual dc terminal and the total dc voltage response ofthe entire dc grid system, regardless of the location in the dc gridwhere the change in power reference has occurred.

IV. IMPACT OF DC LINE VOLTAGE DROPS ON BALANCINGPOWER AND PROPOSED ANALYTICAL MODEL

By applying the same approach as in state space modeling,vector and matrix notations will be used in the following dis-cussions for analyzing the dc grid as a single system. In orderto differentiate the vector and matrix quantities as opposed tothe scalar variables, the vectors and matrices will be written inboldface letters. Hence, the vectors , , and are defined as

...

...

...

...

...

...

(19)


Other vectors such as , , , and are also definedin a similar manner. The vector , which refers to power flowinto the dc grid via the dc terminals, is given by

(20)

where refers to the admittance matrix of the HVDC grid andthe symbol is entry-wise (point-to-point) matrix multiplica-tion operator, also called Hadamard product operator. Differen-tiation of the power flow equations of individual terminals withrespect to the nodal voltage vector results in the Jacobian ma-trix of the dc grid [9]. This is mathematically given by

(21)

If the HVDC grid has an initial state given by , thelinearization of power flow equation around the initial steadystate point is given by

(22)

Hence, the relationship between the vectors representingsmall dc voltage variations and small nodal powervariations is given by

(23)

If the vector is known, the voltage vector couldbe found by

(24)

Care should be taken while computing to avoid the sin-gularity condition during the inverse matrix calculation. The in-verse matrix gets closer to singularity if computed close to flatdc voltage profile (i.e., when all dc bus voltages are very closeto each other and dc grid power flow approaches zero). Oncecomputed at a suitable operating point, the Jacobianmatrixcould be applied for a wide range of operations with negligibleerrors.Equation (11) is rewritten in vector form as

(25)

where diag refers to a mathematical operator which transformsa vector into a diagonal matrix.Substituting (24) into (25), we obtain

(26)

Equation (26) could further be simplified as

(27)

where refers to identity matrix and the matrix , termedhere as the steady-state sensitivity matrix, is a dimensionlessquantity. Matrix describes the quantitative relation between

changes in power references of the dc terminals with the re-sulting steady state changes in injected powers at each of theterminals.From (24) and (27), the dc voltage change becomes as

(28)

Comparing (18) and (27), the differences in the two equationsresult from the differences between the constant matrices and. As discussed in Section III, the matrix is independent of

dc grid topology since a lossless grid was assumed to establishthe mathematical relation. In contrast, in the proposed analyticalmethod, the constant matrix is dependent upon dc line resis-tances and hence upon dc grid topology. This is reflected by thepresence of the dc Jacobian matrix in (27). Due to theline voltage drop considerations, the proposed method gives anaccurate mathematical model of the interaction between powercontrol reference changes and the resulting observed power flowpattern in the dc grid.

V. EFFECT OF INCREASING/DECREASING DCVOLTAGE DROOP CONSTANT

From (5), it could be seen that the dc droop constant in phys-ical unit (i.e., , the dc voltage response in MW/kV of a singleterminal) could be changed by changing either the rated power

, rated dc voltage or the dc droop constant(i.e., ). Since and are fixed parameters foran already existing dc grid, is the only means for changingthe value of . By following the same practice as in frequencydroop control of synchronous generators, it may be reasonableto assign all dc terminals participating in dc voltage control thesame value of .Now consider an initial value of the dc voltage response

vector , such that a new dc voltage responsevector is given by

(29)

where refers to a scaling factor by which we want to varythe droop constants of the entire dc grid. Then the initial totaldc voltage response will be given by . Substituting(29) into the definition of in (15), we obtain

(30)

Substituting (30) into the definition of , we obtain

.... . .

.... . .

...

.... . .

.... . .

...

(31)Hence, in the ideal lossless model, increasing/decreasing the

size of the dc droop constant in all HVDC terminals bya scalar constant will not have any impact on the steady-statepower flow of the HVDC grid.


Fig. 3. Five-terminal HVDC model used in the simulation study.

By following similar procedure for the matrix , we get therelationships given by

(32)

This indicates that, with increasing values of the scalar multi-plier , the power flow pattern is affected more strongly by thedc grid line resistances (and hence by its topology). As a result,with larger values of , the balancing power distribution showslarger deviation from the one predicted by the lossless analyt-ical model. Since and are inversely proportional, largervalues of correspond to smaller values of and vice versa[see (15)].Hence, we can conclude that, for smaller dc droop constants

applied to the HVDC terminals, the dc line voltage dropscause larger deviation of dc grid balancing power distributionfrom the estimation approach which ignores dc line resistanceeffects.

VI. SIMULATION STUDIES

A five-terminal VSC-HVDC network (shown in Fig. 3) wassimulated using a PSCAD simulation software package. Thesimulation results are needed for checking the validity of theproposed analytical model, which estimates distribution of bal-ancing power among different terminals, and for demonstratingthe impact of dc line voltage drops in comparison to the ideallossless analytical model.Since much of the focus in this paper is on the MTDC aspect,

the ac grids are represented only by aggregated models. Sym-bols used in Fig. 3 are listed here.

TABLE IIPARAMETERS OF HVDC TERMINALS USED IN THE SIMULATION

TABLE IIIDESIRED DC GRID POWER FLOW PATTERN

TABLE IVNUMERICAL SOLUTION FROM THE DC LOAD FLOW ANALYSIS

Rated pole to pole dc grid voltage (in kV).

DC voltage droop constant of the th dcterminal (in per-unit).

Maximum (rated) power capacity of th dcterminal (in MW).

DC transmission distance between terminalsand .

The parameters of the converter terminals used in the simu-lation are shown in Table II.The set of values given in Table III was chosen arbitrarily to

represent an initial steady-state condition for theMTDC system.In practice, this data should come from the power dispatcher(scheduler).In order to get the desired power flow pattern, the unknown

power at terminal 2 should be computed and used as the powerreference for terminal 2.Similarly unknown dc bus voltages at terminals 1, 4, and 5

should be found and used as dc voltage references in the dcdroop controllers of these terminals.Terminal 3 is a constant power terminal of known reference

value and hence does not need any more data. A short MATLABcode was written for solving the given dc load flow problem.DC load flow analysis of the given dc grid (i.e., Fig. 3) togetherwith the desired power flow pattern (i.e., Table III) gives the setof numerical solution shown in Table IV.The values in Table IV were used as power and dc voltage

references in the respective dc terminals. Steady-state powersand dc bus voltages observed from the PSCAD simulation areshown in Table V.The simulation results in Table V indicate that precise power

flow control is established by correctly assigning the power anddc voltage references of all of the dc terminals. This is the initialsteady state from which a change in power flow will be studied.Now, the power reference of terminal 3 is changed from750 to 800MW. This corresponds to 50 MW.


TABLE VPSCAD SIMULATION RESULTS WITH DC VOLTAGE AND DC POWER

REFERENCES COMING FROM TABLE IV

TABLE VIPSCAD SIMULATION RESULTS FOR 50 MW

The resulting steady-state power flow pattern after applyingis shown in Table VI.

A. Comparison of Simulation Results With Estimation by IdealLossless ModelThe total dc voltage response of the HVDC grid is given

by

MWkV

(33)

Substituting relevant values of from Table II and the valueof from (33) into the expression of in (18), we get

(34)Decreasing power reference of terminal 3 by 50 MW (i.e.,

50 MW) corresponds to the vectorMW. Substituting this value of and the value of

from (34) into (18), we find the estimated changes in nodalpower flow shown in Table VII. The changes in dc bus voltagesare estimated by (15).From Table VII, it is evident that the ideal lossless model re-

sults in large errors in estimating the changes in dc bus volt-ages and nodal powers. It is also noticeable that, for terminalswith droop control (i.e., 1, 2, 4, and 5), the estimation errors forchange in power are nearly equal to the corresponding estima-tion error for change in dc bus voltage, suggesting that the dc

TABLE VIICOMPARISON OF ESTIMATED STEADY-STATE CHANGES (BY LOSSLESS MODEL)

WITH PSCAD SIMULATION RESULTS

bus voltage variations should be accounted for in order to accu-rately estimate the distribution of dc grid balancing power afterthe occurrence of power flow change at one terminal.

B. Estimation of Power Sharing by Proposed AnalyticalExpressionNow we try to estimate the power flow after change in power

reference of terminal 3 50 MW , but this time usingthe proposed analytical method which considers dc line voltagedrops. In order to do so, we first have to compute the matrix .For the initial steady state given by Table V, the resulting Jaco-bian matrix is given by (35), shown at the bottom of thepage. This is computed by derivating the power flow equationof each node with respect to the dc bus voltage vector .By substituting for MW kV

(from Table II) and from (35) into (32), the matrixbecomes

(36)Multiplying by MW,we can find the

resulting power distribution . The dc bus voltage vectorcould be computed by (28). The estimated steady-state

changes in dc bus voltages and powers from the analytical ex-pressions are shown in Table VIII. The corresponding changesfrom the PSCAD simulation of system are also included forcomparison.It is interesting to check the possibility that errors do not

arise from the droop controllers not working properly. FromTable VIII, it could be shown for all terminals that

, both in the analytical and simulation

MWkV

(35)


TABLE VIIICOMPARISON OF ESTIMATED STEADY-STATE CHANGES (BY PROPOSED MODEL)

WITH PSCAD SIMULATION RESULTS, MW

TABLE IXINFLUENCE OF SIZE OF DC DROOP CONSTANT ON BALANCING POWER

DISTRIBUTION FOR MW

results (the values of are given in Table II). Hence, any esti-mation errors are attributed to the linearized power flow modelsin the analytical expression.The small estimation errors in Table VIII show that the de-

rived analytical expression can indeed accurately estimate thesteady-state changes of terminal powers and terminal voltages.

C. Impact of Size of DC Voltage Droop ConstantTo observe the impact of size of dc voltage droop constant on

load sharing, three droop constants (for terminals 1, 2, 4, and 5)were tested for the same step change in power of terminal 3 (i.e.,from 0 to 250 MW). Simulation results are shown in Table IX.The sizes of the converters were kept same as in Fig. 3.It is shown in Table IX that, as the droop constant decreases,

the balancing power distribution deviates more and more fromthe one predicted by the ideal lossless model.

D. Impact of DC Transmission-Line DistanceDue to the dc line resistance, terminals which are located fur-

ther from the point where a change in power injection occurs(i.e., terminal 3 in the test case) observe smaller voltage drop attheir dc bus. This describes why the changes in dc bus voltageat terminal 5 have been lowest in all previous cases. To furtherelaborate on this phenomenon, a similar change of reference(i.e., MW) was tested for various lengthsof the dc transmission line between terminals 4 and 5. The droopconstant of terminals 1, 2, 4, and 5 was kept as . Theresults from the simulations are shown in Table X.FromTableX, it could be observed that the contribution of ter-

minal 5 to dc grid power balancing decreases while the dc trans-

TABLE XINFLUENCE OF DC LINE TRANSMISSION LENGTH. SIMULATION RESULTS FOR

MW AND

mission distance between terminals 4 and 5 increases (comparethe numbers in boldface letters). From this, it could observed thatHVDC terminals respond more strongly to power balancing de-mands occurring at closer distances than at further locations.

VII. CONCLUSIONIn this paper, the impact of dc line voltage drops on distri-

bution of balancing power is studied. It was demonstrated thatthe response of each dc terminal to the instantaneous balancingpower demand is influenced by:1) the dc grid topology and line resistances;2) the location where the power deficit/surplus has occurred;3) the value of the dc voltage droop constant applied in the dcgrid.

Due to these factors, power flow pattern after occurrence of achange in injected power at a dc terminal shows large deviationsfrom the one predicted by a lossless dc grid model.An analytical expression for accurate estimation of terminal

power has been proposed in this paper. The validity of thederived analytical expression was demonstrated by the goodagreement between results from using the proposed methodand the corresponding dynamic simulation results applied to afive-terminal MTDC test model.

REFERENCES[1] T. Nakajima and S. Irowaka, A control system for HVDC trans-

mission by voltage sourced converters, in Proc. IEEE PES SummerMeeting, Jul. 1999, pp. 11131119.

[2] W. Lu and B.-T. Ooi, Optimal acquisition and aggregation of offshorewind power by multiterminal voltage-source HVDC, IEEE Trans.Power Del., vol. 18, no. 1, pp. 201206, Jan. 2003.

[3] W. Lu and B. T. Ooi, Premium quality power park based on multi-terminal HVDC, IEEE Trans. Power Del., vol. 20, no. 2, pp. 978983,Apr. 2005.

[4] R.L.Hendriks,G.C.Paap, andW.L.Kling, Control of amulti-terminalVSC transmission scheme for interconnecting offshore wind farms, inProc. Eur. Wind Energy Conf. Exhibition, May 2007, pp. 18.

[5] L. Xu, B. W. Williams, and L. Yao, Multi-terminal DC transmissionsystems for connecting large offshore wind farms, in Proc. IEEE PESGeneral MeetingConversion andDelivery of Electrical Energy in the21st Century, Jul. 2008, pp. 17.

[6] R. da Silva, R. Teodorescu, and P. Rodriguez, Power delivery inMTDC transmission system for offshore wind power applications, inProc. IEEE PES ISGT Europe, Oct. 2010, pp. 18.

[7] W. Lu and B.-T. Ooi, Multi-terminal HVDC as enabling technologyof premium quality power park, in Proc. IEEE PES Winter Meeting,Jan. 2002, pp. 719724.

[8] P. Kundur, Power System Stability and Control. New York: Mc-Graw-Hill, 1994, p. 589.

[9] J. Beerten, S. Cole, and R. Belmans, A sequential AC/DC power flowalgorithm for networks containing multi-terminal VSC HVDC sys-tems, in Proc. PES General Meeting, Jul. 2010, pp. 17.


Temesgen M. Haileselassie received the M.Sc. de-gree in electric power engineering from NorwegianUniversity of Science and Technology (NTNU),Trondheim, Norway, in 2008, where he is currentlyworking toward the Ph.D. degree.His research interests include multiterminal

HVDC, grid integration of wind farms, and controland dynamics of power systems.

Kjetil Uhlen (M98) received the M.S. degree andPh.D. degree in control engineering from the Norwe-gian University of Science and Technology, Trond-heim, Norway, in 1986 and 1994, respectively.He is currently a Professor of power systems

with the Norwegian University of Science andTechnology, Trondheim, Norway. His main interestsare control and operation of power systems, powersystem dynamics, and wind power integration.

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06169971