1096 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 27, NO. 3, JULY 2012

Wide-Area Robust Coordination Approach of HVDCand FACTS Controllers for Damping Multiple

Interarea OscillationsYong Li, Member, IEEE, Christian Rehtanz, Senior Member, IEEE, Sven Rüberg, Longfu Luo, Member, IEEE,

and Yijia Cao, Member, IEEE

Abstract—A robust coordination approach for the controllerdesign of multiple high-voltage direct-current (HVDC) and flex-ible ac transmission systems (FACTS) wide-area controls (WACs)is presented in this paper and has the aim of stabilizing multipleinterarea oscillation modes in large-scale power systems. Thesuitable wide-area control signals, which are given to HVDC andFACTS wide-area controllers, respectively, are chosen from alarge number of candidate items. Then, a sequential robust designapproach is planned for the wide-area controller coordinationof HVDC and FACTS devices. This approach is based on therobust control theory and is formulated as a standard problemof multiobjective mixed �� � output-feedback control withregional pole placement constraints. The linear matrix inequality(LMI) theory is applied to solve such a robust control problem.A case study on the 16-machine 5-area system, which is modifiedwith one HVDC interconnected transmission, one shunt-FACTSdevice (SVC), and one series-FACTS device (TCSC), is performedto validate the robust performance in terms of multiple oscillationsdamping under various operating conditions.

Index Terms—Controller coordination, flexible AC transmissionsystems (FACTS), high-voltage direct current (HVDC), interareaoscillations, linear matrix inequality (LMI), robust control, wide-area control (WAC).

NOMENCLATURE

WAMS Wide-area measurement systems.

WAC Wide-area control.

PMU Phasor measurement unit.

PSS Power system stabilizer.

Manuscript received December 07, 2010; revised March 14, 2011 and May19, 2011; accepted February 27, 2012. Date of publication June 13, 2012; date ofcurrent version June 20, 2012. This paper was supported in part by the NationalNatural Science Foundation of China (NSFC) under Grant 51007020 and in partby the China Scholarship Council (CSC). Paper no. TPWRD-00949-2010.

Y. Li is with the Institute of Energy Systems, Energy Efficiency and En-ergy Economics, TU Dortmund University, Dortmund 44221, Germany, andalso with the College of Electrical and Information Engineering, Hunan Uni-versity, 410082 Changsha, China (e-mail: yong.li@tu-dortmund.de).

C. Rehtanz and S. Rüberg are with the Institute of Energy Systems, EnergyEfficiency and Energy Economics, TU Dortmund University, 44221 Dort-mund, Germany (e-mail: christian.rehtanz@tu-dortmund.de; sven.rueberg@tu-dortmund.de).

L. Luo and Y. Cao are with the College of Electrical and Information Engi-neering, Hunan University, Changsha 410082, China (e-mail: llf@hnu.edu.cn;yjcao@hnu.edu.cn).

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

Digital Object Identifier 10.1109/TPWRD.2012.2190830

HVDC High-voltage direct current.

LMI Linear matrix inequality.

LQG Linear-quadratic Gaussian.

CSG Chinese southern power grid.

NETS New England test system.

NYPS New York power system.

SCADA Supervisory control and data acquisition.

EMS Energy-management system.

SVC Static var compensator.

TCSC Thyristor-controlled series capacitor.

SSSA Small-signal stability assessment.

CI Constant impedance load.

CP Constant active power load.

CC Constant active current load.

I. INTRODUCTION

A S A RELATIVELY new type of stability control strategybased on WAMS, the WAC can utilize PSS, flexible ac

transmission system (FACTS) devices, or other control devicesto damp power oscillations. Currently, various control methods[1]–[4] have been proposed for PSS or FACTS controller de-sign with local and wide-area control structures. However, forthe PSS-WAC, the coordination of different PSSs linked to anample number of generators in a practical large-scale powersystem has to be carefully considered. For the FACTS–WAC,its damping performance is highly dependent on the allocation[5], [6] being suitable. In contrast to these potential limitations,the HVDC–WAC could be a better choice for damping interareaoscillations [7], [8]. Since HVDC transmission is generally usedto interconnect regional grids, it can effectively influence the op-erating characteristics of the electric networks.

However, in practical large-scale interconnected systems,there are usually various interarea oscillation modes with var-ious oscillation shapes that act together and endanger the stableand secure operation of power networks. In such a case, thesimple FACTS or HVDC WAC may not be sufficient to providethe effective damping for the multiple interarea oscillationmodes. Therefore, the multiple wide-area controllers should beconsidered together in order to establish the effective wide-areacontrol network for the overall stability enhancement of thelarge-scale power systems.

0885-8977/$31.00 © 2012 IEEE

LI et al.: WIDE-AREA ROBUST COORDINATION APPROACH OF HVDC AND FACTS CONTROLLERS 1097

Fig. 1. Basic framework of the WAC network using multiple WAMS-basedHVDC and FACTS controllers.

This paper will propose a WAC network by using multipleWAMS-based HVDC and FACTS wide-area stabilizing con-trollers to provide efficient damping against multiple interareaoscillation modes under various operating conditions. The se-quential robust design approach, which is formulated as a stan-dard robust problem of output-feedback control [9],will also be presented as a way of executing the robust design.This design approach can consider the output disturbance rejec-tion problem, reduce the control effort, and ensure robustnessagainst model uncertainties all at once.

The structure of this paper is organized as follows: InSection I, the WAC network using multiple WAMS-basedHVDC and FACTS controllers is briefly described. InSection II, the robust design formulation regarding mixed

output feedback control with regional pole placementin the LMI framework is discussed. In Section III, the generalprocedure on the robust coordinated control design is presented.In Section IV, the control concept and design method is testedon a 16-machine 5-area study system. Section V presents theconclusions.

II. DESCRIPTION OF WAC NETWORK USING MULTIPLE

WAMS-BASED HVDC AND FACTS CONTROLLERS

The WAC network using multiple WAMS-based HVDC andFACTS controllers can be described, as shown in Fig. 1, wherethe five-area system is, in fact, the NETS—NYPS intercon-nected systems modified with one HVDC interconnected linebetween NETS (Area-5) and NYPS (Area-4), one shunt-FACTSdevice (SVC) at one bus of Area-4, and one series FACTS de-vice (TCSC) between NYPS and the neighboring equivalentarea (Area-3). The single-line diagram of the studied systemswill be shown in Section IV.

Fig. 2. Configuration of the multiobjective wide-area robust controllersynthesis.

The presented WAC network mostly consists of the followingaspects.

• Measurement of wide-area information. Through PMUsplaced in optimal locations of each area, various dynamicvariables (e.g., bus voltage, line active power flow, speed ofremote generator, etc.) are monitored and transmitted fromeach area to the WAMS center.

• Processing of wide-area information. The useful informa-tion is selected and preprocessed in the WAMS center, andthen sent to SCADA/EMS.

• Implementation of WAC strategy. The suitable WAC sig-nals are selected for HVDC and FACTS controllers, re-spectively. Then, through the designed centralized con-troller embedded in the WAC center, the control output sig-nals are sent to HVDC and FACTS devices simultaneously.

• Implementation of the local control strategy using wide-area information. As the supplementary control linked tothe local controller, the WAC output can be adopted bythe related HVDC and FACTS local controllers to providestabilizing control for the stable and secure operation ofpower systems.

III. CONTROLLER DESIGN FORMULATION: MIXED

CONTROL APPROACH WITH LMIS SOLUTION

A. Multiobjective Synthesis of Wide-Area Robust Control

In order to achieve the robustness under a wide range ofsystem operating conditions, the robust design technique, thatis, the mixed synthesis with regional pole placement,is employed in this paper to execute the multiobjective syn-thesis design of WAMS-based HVDC and FACTS wide-areadamping controllers.

The configuration of multiobjective wide-area robust con-troller synthesis is shown in Fig. 2, where the output channel

is associated with the performance while the channelis associated with the LQG aspects ( performance). Both

the low-pass and the high-pass filter (i.e., the weight functionsand ) are placed in the performance channel

and ensure the output disturbance rejection and the robustnessagainst model uncertainties, respectively. The high-pass filter orsome small constant is placed in the performance toreduce the control effort.

1098 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 27, NO. 3, JULY 2012

Fig. 3. LMI region for pole placement.

If the weight function ( , 2, 3) goes unconsideredat first, which can be placed later on, the state-space representa-tion of the formulated plant can be given as

(1)

where , , and are the state, input, and output matrix, re-spectively; is the state vector; is the regulator output; is theplant output; is the disturbance input; and is the plant input.

The main task of the robust design is to find an output-feed-back controller that minimizes subject to

, where and are the closed-loop transferfunctions from to and , respectively. In addition, theclosed-loop poles need to be placed in the desired LMI region

. Generally, the design problem can be solved by suitablydefining the objectives in the argument of the function hinfmix,which is available in the LMI Toolbox of Matlab [9], with thespecified pole placement in LMI regions as described in the fol-lowing section.

B. Pole Placement in LMI Regions

The transient response of the closed-loop plant is related tothe location of poles. In order to achieve a good response and,at the same time, to avoid the fast dynamics and high-frequencygain in the controller, all closed-loop poles should be limited inthe expected region of the left-half plane, as shown in Fig. 3.The bound of the desired damping ratio can be defined by set-ting the inter angle and the minimum decay rate for theconic sector region. In this way, the function can construct theconstraint condition of pole placement of the closed-loop plant.The result constitutes the solution of the multiobjective controlproblem concerning mixed synthesis.

IV. DESIGN PROCEDURE OF WIDE-AREA ROBUST

COORDINATED CONTROL

In the WAC network, various HVDC and FACTS controllerscan be used to implement wide-area damping control for en-hancing the overall stability of electric networks. However, the

problem as to how to coordinate these wide-area controllers si-multaneously in order to achieve optimal robust performanceshould be considered carefully. Combined with the aforemen-tioned multiobjective mixed control synthesis, the de-sign procedure, which could be the guideline for the kinds ofwide-area robust coordinated control, is presented, and it mostlyincludes the following steps.

Step 1) System-linearized modeling and SSSA. The lin-earized plant model of the electric networks,including multiple HVDC and FACTS devices,should be obtained first. In this paper, the linearizedplant model is established by a set of differential-al-gebraic equations containing the dynamic modelof the HVDC device, FACTS devices, generators,loads, and other equipment and related controllers.Following this, the SSSA can be performed basedon the established model to obtain the system dy-namic information, including the interarea modes.

Step 2) Choice and assignment of suitable WAC signalsto each HVDC and FACTS controller. Generally,there are several operating variables, such as the busangle, the line current, the active power flow, etc.,which can be selected as the WAC signal. Basically,such a selection should satisfy the index of modalcontrollability/observability. Here, combing theSSSA results in Step 1), and the practical residuemethod is used to choose optimal control inputsfrom abundant operating variables. Further, duringthe process of control signal selection, the suitableHVDC and FACTS devices, which can dominateinterarea oscillation modes, are also assigned. Be-sides, the performance evaluation on the WACsignals, which are sent to each assigned HVDC orFACTS controller, can also be performed to guidesuch selection and assignment.

Step 3) Sequential design with the method of multiobjec-tive mixed controller synthesis. Based onthe plant model obtained in Step 1) and the op-timal control signals obtained in Step 2), the ro-bust controller synthesis introduced in Section IIcan be implemented for the first WAC design. Then,based on the controller and the plant model, theclosed-loop system model can be formed, whichcan be used as the open-loop plant for the secondWAC design. Similarly, once the second wide-areacontroller is obtained, it can be utilized to formthe second closed-loop plant for the third WAC de-sign. In this way, all of the HVDC and FACTSwide-area controllers can be designed sequentially.For each controller design, the multiobjective mixed

controller synthesis is performed for theupdated open-loop plant with the HVDC or FACTSdevice.

Step 4) Robust performance evaluation and nonlinearsimulation validation. The robustness of the de-signed HVDC and FACTS wide-area controllerscan be evaluated with the formed full-order linear

LI et al.: WIDE-AREA ROBUST COORDINATION APPROACH OF HVDC AND FACTS CONTROLLERS 1099

Fig. 4. Modified 16-machine 5-area test system.

closed-loop plant. Moreover, these designed con-trollers should be verified under various operatingconditions and fault scenarios, such as line fault,line outage, load shedding, etc.

V. CASE STUDIES

A. Multimachine Test System

The concept of the wide-area robust coordination approachfor HVDC and FACTS controllers is validated on the 16-ma-chine 5-area test system. As mentioned in Section I, such atest system is, in fact, the NETS-NYPS interconnected system,which is divided into five areas. The machines G1-G9 andG10-G13 belong to Area 5 and 4, respectively, and there arethree other machines (G14-G16), which are equivalent to threeneighboring areas (from Area 1 to 3) that interconnect with Area4 separately. In order to improve the interconnected ability, oneHVDC transmission system is configured between Bus 1 (inArea 4) and 2 (in Area 5), one shunt FACTS device (SVC) isinstalled on Bus 51 (in Area 4), and one series-FACTS device(TCSC) is installed between Bus 46 (in Area 4) and 49 (in Area3). The detailed description of the test system, including thenetwork data and the dynamic data of the generators and theexcitation systems, can be found in [10].

B. Choice of Suitable WAC Signals

Fig. 5 shows the mode shapes of the critical interarea oscil-lation modes between different areas. From this, it is clear thatthere are four typical interarea oscillation modes with the lowdamping ratios, that is, the oscillation between Area 4, 5 and

Fig. 5. Mode shapes of interarea oscillations. (a) For mode 1, 0.4278 Hz.(b) For mode 2, 0.5734 Hz. (c) For mode 3, 0.6723 Hz. (d) For mode 4,0.8215 Hz.

Area 1, 2, 3, between Area 3 and Area 1, 5, between Area 4 andArea 5, and between Area 2 and Area 1, 3. Table I further rep-resents the participation generators, oscillation frequencies ,damping ratios , etc.

1100 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 27, NO. 3, JULY 2012

TABLE IINTERAREA OSCILLATION MODES OF THE TEST SYSTEM

Fig. 6. Damping contribution of different HVDC and FACTS devices using theavailable line current as the control input for interarea oscillation modes. (a) Formode 1. (b) For mode 2. (c) For mode 3. (d) For mode 4.

The WAC network mainly concerns these interarea modes.For the controller design, the first task is to assign the suit-able controller and choose the suitable control input. Here, theresidue method is employed to select the suitable HVDC andFACTS devices that can be used to introduce the supplementarywide-area damping control strategy.

Fig. 6 shows the damping contribution of the optionalHVDC and FACTS devices, which use different line current

Fig. 7. Frequency response of the full- and the reduced-order system. (a) ForSVC WAC design. (b) For HVDC WAC design.

as the control input for each concerned interarea mode. FromFig. 6(a) and (c), it can be found that when the HVDC wide-areacontroller selects the specified WAC signals, it can achievebetter damping performance for mode 1 and 3 than the SVCand the TCSC. Thus, the current in Line 82 (Line 37–65) isselected for the HVDC wide-area controller to damp mode 1and 3. Similarly, from Fig. 6(b) and (d), it can be found thatthe SVC WAC, which selects the specified WAC signals, canachieve better damping performance for mode 2 and 4 thanthe HVDC and the TCSC. Thus, the current in Line 85 (Line52–68) is selected as the WAC input of the SVC wide-areacontroller to damp modes 2 and 4.

It is worth noting that although the TCSC is the candidate forthe WAC network, from Fig. 6, it can be found that comparedto the HVDC and the SVC, the TCSC cannot provide the ef-fective damping for the concerned interarea modes. In addition,from the aforementioned analysis, it can be seen that the HVDCand the SVC are sufficient to damp these four interarea modes.Therefore, the HVDC and the shunt FACTS are finally selectedfor the WAC network.

C. Robust Design of HVDC and FACTS WACs

The multiobjective mixed synthesis introduced inSection II is implemented for the sequential robust design ofHVDC and FACTS WACs. In order to perform the robust de-sign in the LMI framework, the full-order system should bereduced to an acceptable order. Here, the balanced truncation

LI et al.: WIDE-AREA ROBUST COORDINATION APPROACH OF HVDC AND FACTS CONTROLLERS 1101

Fig. 8. Frequency response of the full- and reduced-order controller. (a) ForSVC wide-area control. (b) For HVDC wide-area control.

method is used for the model reduction. For the SVC WAC de-sign, the open-loop system is reduced from 201 to 11 order.For the HVDC WAC design, the open-loop system, which isreconstructed with the SVC WAC, is reduced from 211 to 11order. Fig. 7 shows the comparison between the full- and re-duced-order system. It can be seen that the frequency responseof the reduced-order system is close to that of the full-ordersystem.

Regarding the multiobjective mixed synthesis foreach WAC design, the suitable weight function ( ,2, 3) should be configured for the output channels andin order to simultaneously consider the output disturbance re-jection, ensure the robustness against model uncertainties, andreduce the control effort [11], [12]. Here, considering that allof the concerned interarea oscillation modes are below the fre-quency 10 rad/s, the and configured in theperformance channel are determined so that they intersect ataround 10 rad/s. Besides, a small constant is also selected forthe configured in the performance channel. The se-lected weight functions for HVDC and FACTS WAC design aregiven as follows:

(2)

Combined with the robust design method mentioned inSection II and the presented design procedure mentioned inSection III, the WAC of HVDC and FACTS devices can beobtained sequentially. However, the order of the obtainedcontrollers is relatively high, which could be impossible for

TABLE IIDAMPING RATIOS AND FREQUENCIES OF THE CRITICAL INTERAREA MODES

WITH OR WITHOUT WIDE-AREA CONTROLLERS

practical application. Thus, the model reduction is performedagain to reduce the number of controller orders. Fig. 8 showsthe frequency response of the full- and the reduced-ordercontroller. It can be seen that the reduced-order controller has asimilar control characteristic to the full-order controller. More-over, the final reduced-order models of the HVDC and FACTSWAC are represented in the Appendix (see Section VIII).

D. Evaluation of Robust Performance

The small-signal stability analysis is performed in this sec-tion to evaluate the robust performance of the designed WACs.Table II shows the influence of the designed HVDC and FACTSWACs on the damping ratios and the oscillation frequencies ofthe critical interarea modes. It can be clearly seen that when thesystem is installed with the designed controllers, all of the inter-area modes can be damped effectively with the relative higherdamping ratios. It can also be seen that when the system is onlyinstalled with a FACTS WAC, the damping ratios of modes 2and 4 can be increased greatly, while when the system is onlyinstalled with an HVDC WAC, the damping ratios of modes 1and 3 can be increased greatly. These results coincide with thedesign intention mentioned in Section V-B.

Furthermore, in order to evaluate the robustness of thedesigned WACs to withstand various operating conditions,the various load types and the outages of backbone-intercon-nected lines are considered. Table III shows the influence ofdifferent-type loads on the critical interarea modes. From thistable, it can be seen that the designed multiple WACs can al-ways provide effective damping regardless of the type of load.Moreover, Table IV shows the results concerning the influenceof different tie-line outages on the critical interarea modes. Itcan also be seen from this how good the damping is that thedesigned WACs can provide for these critical interarea modes.

E. Validation of Nonlinear Simulation

In order to further examine the robustness of the designedHVDC and FACTS WACs on the damping of multiple interareamodes excited by different operating conditions, three kinds ofcases, that is: 1) the line fault; 2) the line outage; and 3) the loadshedding, are simulated on the test system.

1) Case-1: Line Fault: In this case, the line-to-ground faultnear Bus 51 of Line 45–51 (see Fig. 4) is simulated to ex-amine the presented wide-area robust coordination concept andthe designed WACs. Fig. 9 shows the dynamic responses of the

1102 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 27, NO. 3, JULY 2012

TABLE IIIDAMPING RATIOS AND FREQUENCIES OF THE CRITICAL INTERAREA MODES

FOR DIFFERENT LOAD CHARACTERISTICS

TABLE IVDAMPING RATIOS AND FREQUENCIES OF THE CRITICAL INTERAREA MODES

FOR DIFFERENT TIE-LINE OUTAGES

Fig. 9. Dynamic responses of the relative angle between different generatorswhen there is a line-to-ground fault near bus 51 of Line 45–51: (a) between G14and G16 and (b) between G15 and G16.

relative angle between different generators located in differentareas. From this, it can be clearly seen that regarding the testsystem without the HVDC and SVC WAC, the occurrence ofthe line-to-ground fault excites obvious interarea oscillations.However, when it implements the WAC, such oscillations aredamped effectively.

Furthermore, Fig. 10 shows the dynamic responses of theHVDC and the SVC WACs. Looking at this, it can be seen thatthe HVDC and the SVC WACs can respond to the power oscilla-tions that occur in the test system and provide the WAC signalsto stabilize these oscillations. Such wide-area stabilizing can befinished in approximately 15 s, which indicates the good con-trol performance that the designed HVDC and SVC WACs canachieve. Moreover, Fig. 11 shows the results concerning the dy-namic responses of the power flow in different tie lines. It canalso be seen from this that the power oscillations in the tie lines

Fig. 10. Dynamic responses of the HVDC and the SVC WAC when there is aline-to-ground fault at bus 51 of Line 45–51. (a) Output of the HVDC wide-areacontroller. (b) Output susceptance of the SVC WAC.

Fig. 11. Dynamic responses of the power flow in the tie lines when there is aline-to-ground fault near bus 51 of Line 45–51, (a) Line 52–68, and (b) Line1–47.

can also be damped very well, which further verifies the pre-sented WAC concept using multiple HVDC and FACTS WACs.

2) Case 2: Line Outage: In this case study, the tie line 1–47,which is one of the backbone-interconnected lines betweenAreas 1 and 5, has an outage at 1.0 s to examine the test systemwithout and with the designed WACs, respectively. Fig. 12shows the dynamic responses of the relative angle betweendifferent generators in different areas. It can be clearly seenfrom this that when there is a tie-line outage, the test systemwith the WACs can still maintain the good stable operatingperformance on the generation side. Furthermore, looking atthe dynamic responses of the power flow in the tie lines, asshown in Fig. 13, it can also be seen that the power oscillationsin the tie lines can also be damped very well for implementingthe multiple HVDC and shunt-type FACTS (SVC) wide-areacoordination control strategy.

3) Case 3: Load Shedding: In this third case, the sheddingof the load on bus 46 is carried out at 1.0 s to further verifythe robustness of the designed WACs. Figs. 14 and 15 representthe results regarding the dynamic responses of the relative anglebetween different generators in different areas and the powerflow in the tie lines, respectively. Looking at these results, itcan be clearly seen that the implementation of the HVDC and

LI et al.: WIDE-AREA ROBUST COORDINATION APPROACH OF HVDC AND FACTS CONTROLLERS 1103

Fig. 12. Dynamic responses of the relative angle between different generatorswhen Line 1–47 is outage, (a) between G14 and G16, (b) between G15 and G16,and (c) between G1 and G16.

Fig. 13. Dynamic response of the power flow in the tie lines when Line 1–47is outage. (a) Line 52–68. (b) Line 41–66.

Fig. 14. Dynamic responses of the relative angle between different generatorswhen shedding the load on bus 46. (a) Between G14 and G16. (b) Between G15and G16. (c) Between G1 and G16.

the shunt-type FACTS WAC can effectively damp the interareaoscillations, which also verifies the control concept and the de-signed WACs.

Fig. 15. Dynamic responses of the power flow in the tie lines when sheddingthe load on bus 46. (a) Line 52–68. (b) Line 41–66.

VI. CONCLUSION

This paper presents a wide-area robust coordination approachfor HVDC and FACTS WACs to stabilize multiple interareaoscillation modes. It can efficiently utilize the supplementarycontrol functions of HVDC and FACTS devices. Through in-troducing the suitable WAC signals, the WAC network can beconstructed with the advanced control ability for enhancing theoverall stability of large-scale interconnected systems.

The framework of the WAC network is briefly described, andthe multiobjective mixed control synthesis is used todeal with the robust design problem of the HVDC and FACTSWACs. The design procedure, which could be regarded as theguideline for multiple WACs design, is also presented. Besides,the practical selection method is discussed further in order to se-lect the suitable WAC inputs and configure multiple WACs fromthe available HVDC and FACTS devices distributed in the in-terconnected systems. The robustness of the 16-machine 5-areatest system, which is installed with the designed WACs, is evalu-ated under various operating conditions. Furthermore, the non-linear simulation is performed to verify the presented controlconcept and the designed WACs under various operating con-ditions. All of the research results indicate that the proposedwide-area robust coordination approach can play an effectivepart in damping multiple interarea oscillations and representgood robustness under various operating conditions.

APPENDIX

The reduced-order HVDC and shunt FACTS wide-area sta-bilizing controllers can be represented as the following transferfunction form:

(A1)

1104 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 27, NO. 3, JULY 2012

where

(A2)

where

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Yong Li (S’09–M’12) was born in Henan, China,in 1982. He received the B.Sc. and Ph.D. degrees inelectrical engineering from the College of Electricaland Information Engineering, Hunan University,Changsha, China, in 2004 and 2011, respectively,and is currently pursuing the Ph.D. degree in elec-trical engineering at the Institute of Energy Systems,Energy Efficiency and Energy Economics ��� �, TUDortmund University, Dortmund, Germany.

Currently, he is a Lecturer of Electrical Engi-neering. His current research interests include power

system stability analysis and control, ac/dc energy conversion systems andequipment, analysis and control of power quality, as well as high-voltagedirect-current and flexible ac transmission systems technologies.

Christian Rehtanz (M’96–SM’06) was born inGermany in 1968. He received the Ph.D. degreein electrical engineering from the TU DortmundUniversity, Dortmund, Germany, in 1997, and thevenia legendi in electrical power systems from theSwiss Federal Institute of Technology (ETHZ),Zurich, Switzerland, in 2003.

From 2000 onward, he worked at ABB CorporateResearch, Zurich, Switzerland. He became Headof Technology for the global ABB business area ofpower systems in 2003 and director of ABB Corpo-

rate Research, Beijing, China, in 2005. Since 2007, he has been Head of theInstitute of Energy Systems, Energy Efficiency and Energy Economics ��� �,TU Dortmund University. In addition, he has been Scientific Advisor of theef.Ruhr GmbH, a joint research company of the three universities of Bochum,Dortmund, and Duisburg-Essen (University Alliance Metropolis Ruhr), since2007. He is Adjunct Professor at the Hunan University, Changsha, China. Hisresearch activities are in the field of electrical power systems and power eco-nomics, including technologies for network enhancement and congestion reliefsuch as stability assessment, wide-area monitoring, protection, and coordinatednetwork control as well as integration and control of distributed generation andstorages. He is the author of more than 150 scientific publications, three books,and 17 patents and patent applications.

Dr. Rehtanz holds the MIT World Top 100 Young Innovators Award 2003.

Sven Rüberg was born in Hamm, Germany, in 1979.He received the Diploma degree in electrical engi-neering from the RWTH Aachen University, Aachen,Germany, in 2009. He is currently pursuing the Ph.D.degree in HVDC transmission and its impact on theoperation, stability, and dynamics of electrical powergrid at the Institute of Energy Systems, Energy Effi-ciency, and Energy Economics��� �, TU DortmundUniversity, Dortmund, Germany.

From 2005 to 2006, he was with ABB (China) Ltd.,Beijing, China, where he completed an internship in

the field of real-time simulation of power grids with flexible ac transmission de-vices. He is also involved as a contributor in the REALISEGRID project withinthe Seventh Framework Programme (FP7) of the European Union, which dealswith the efficient development of pan-European power grid infrastructures tosupport the achievement of a reliable, competitive, and sustainable electricitysupply. His main research interests are innovative power transmission technolo-gies, power system stability and dynamics, bulk power transmission, and coor-dinated power-flow control.

Mr. Rüberg is a member of the Power Engineering Society (ETG) withinthe Association for Electrical, Electronic and Information Technologies (VDE)in Germany, the Convention of National Societies of Electrical Engineers ofEurope (EUREL) in Belgium, and the International Council on Large ElectricSystems (CIGRE) in France.

LI et al.: WIDE-AREA ROBUST COORDINATION APPROACH OF HVDC AND FACTS CONTROLLERS 1105

Longfu Luo (M’09) was born in Hunan, China, in1962. He received the B.Sc., M.Sc., and Ph.D. de-grees in electrical engineering from the College ofElectrical and Information Engineering, Hunan Uni-versity, Changsha, China, in 1983, 1991, and 2001,respectively.

From 2001 to 2002, he was a Senior VisitingScholar at the University of Regina, Regina, SK,Canada. In 2002, he became a Full Professor ofElectrical Engineering at Hunan University.

His main research interests include the design andoptimization of modern electrical equipment, the development of new ac/dc en-ergy conversion systems and equipment, power system control and stability, aswell as high-voltage direct-current and flexible ac transmission technologies.

Yijia Cao (M’98) was born in Hunan, China, in1969. He received the M.Sc. and Ph.D. degrees inelectrical engineering from Huazhong University ofScience and Technology (HUST), Wuhan, China, in1991 and 1994, respectively.

From 1994 to 2000, he was a Visiting ResearchFellow and Research Fellow at Loughborough Uni-versity, Loughborough, Leicestershire, U.K.; Liver-pool University, Liverpool, U.K.; and the Universityof the West of England, Bristol, U.K. From 2000 to2001, he was a Full Professor at HUST, and from

2001 to 2008, he was a Full Professor at Zhejiang University, Hangzhou, China.He was appointed Deputy Dean of the College of Electrical Engineering, Zhe-jiang University, in 2005. Currently, he is a Full Professor and Vice Presidentof Hunan University, Changsha, China. His research interests are power systemstability control and the application of intelligent systems in power systems.