vector controlled vsc based transmission under grid disturbances

IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 28, NO. 2, FEBRUARY 2013 661

Vector-Controlled Voltage-Source-Converter-BasedTransmission Under Grid Disturbances

Babak Parkhideh, Student Member, IEEE, and Subhashish Bhattacharya, Member, IEEE

Abstract—Voltage-source converter (VSC)-based transmissionsystems have attractive potential features in terms of power flowcontrol and stability of the network. Although relatively low switch-ing frequency operation of high-power converters (9–15 times theline frequency) is desirable, it makes them sensitive to power net-work imbalances when they may be needed the most. This paperspecifically proposes a control structure to improve the perfor-mance of high-power vector-controlled back-to-back VSC systemsfor conventional and emerging utility applications. The main im-provement is to suppress the possible dc-link voltage fluctuationsunder power line faults and unbalanced conditions. The proposedcontroller structure is designed based on regulating the convertersystem’s states locally in dq synchronous reference frame withoutsequence components extraction or resonant notch compensator.RTDS results verify the validity of the proposed control architec-ture during normal and unbalanced power system conditions.

Index Terms—High-voltage direct current (HVDC), Lyapunovmethods, power systems faults, pulsewidth modulation (PWM)voltage-source converter (VSC), recovery transformer, RTDS,vector-controlled VSC, wind power.

I. INTRODUCTION

I T IS desirable to have high-power high-voltage converter-based systems available during power system faults when

they may be needed the most. If the protection measures tripthe converter system, it can take several fractions of an hour,depending on the size of the converter, to discharge the dc linkand check the healthiness of the whole system. Hence, sev-eral practical methods have been proposed and implemented tokeep a system operating under power system faults and distur-bances [1], [2]. Today, the most promising market for HVDCtechnology is interconnection of the networks where the centersof the loads are located far from the points of connection. Theproblem of ac systems arises as the phase angle drifts and variesover a wide range with daily load changes [3]. This phenomenonespecially in a weak ac network along with the power line faultsexacerbates the operation of HVDC systems.

A voltage-source converter (VSC) is the main building blockfor flexible ac transmission systems (FACTS) devices and, asof today HVDC technology up to several hundred megawatts.

Manuscript received November 22, 2011; revised April 19, 2012; acceptedMay 24, 2012. Date of current version September 27, 2012. Recommended forpublication by Associate Editor J. H. R. Enslin.

The authors are with the Department of Electrical and Computer Engi-neering, North Carolina State University, Raleigh, NC 27606 USA (e-mail:[email protected]; [email protected]).

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

Digital Object Identifier 10.1109/TPEL.2012.2204071

Fig. 1. Simplified schematic of closed-loop BTB VSC systems.

The increasing emergence of VSC-based transmission is the re-sult of development in semiconductor devices, power electroniccircuits, control, and executive engineering, [4]–[6]. Previously,the lack of these developments had prohibited the VSC-basedtechnology from being the first choice. While each developmentis moving forward individually, the result of each one influencesthe design criteria and application requirements of the overallsystem.

However, generally, less dependence on power semiconductorcharacteristics amounts to having more supplier possibilities forthe VSC-based transmission. The most important limiting fac-tor of power semiconductors is their switching properties sincethey are usually optimized for the conduction intervals. Hence,high-power electronic converters are desired to operate with rel-atively low switching frequencies (maximum 9–15 times the linefrequency, and even lower for multilevel converters). The lowswitching frequency operation of VSC systems imposes controllimitations in case of power system faults and disturbances whenthey may be needed the most. To the best of the authors’ knowl-edge, in the installed operating FACTS and HVDC systems,the ride-through capability is obtained either by proper passiveelement design [7], [8] or a change in the control mode [1].On the other hand, with emerging high-power applications suchas 10-MW wind generation turbines [9] or transportable recov-ery transformers [10], the dynamic operation of the VSC underpower system disturbances must be revisited. This paper pro-poses an alternative control framework to obtain robust dc-linkvoltage with specific attention to design the VSC controller inthe back-to-back (BTB) configuration, as shown in Fig. 1. Theproposed controller is implemented in the dq (rotating) syn-chronous reference frame without sequence extraction.

The rest of this paper is organized as follows. Section IIreviews research and advances to control the VSC under unbal-anced conditions. This section also provides the backgrounds

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662 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 28, NO. 2, FEBRUARY 2013

Fig. 2. Bus voltage variations under normal and single-line-to ground faultin the three-phase abc stationary and the two-phase dq synchronous referenceframes.

and advantages of the proposed methods and their applicabil-ity for high-power high-voltage VSCs. Section III describes themodeling approach for the VSC. In this section, general closed-loop functions and control constraints of the BTB VSC systemswill be discussed briefly. In Section IV, the proposed controlarchitecture and its implementation will be presented. RTDSverification of the proposed control method on the BTB VSCsystem for different applications will be presented in Section V.Finally, Section VI presents the conclusion of the research.

II. BACKGROUNDS ON CONTROLLING THE VSC UNDER

UNBALANCED CONDITIONS

A. Single VSC Control Under Unbalanced Conditions

The VSC is the main building block for FACTS devices andmany other converter-based utility interfaces. Therefore, thestudy on the methods to improve the converter performance as asingle system under network unbalanced conditions is unavoid-able. The theory of instantaneous active and reactive powers forthree-phase switching converter control was proposed by Akagiet al. [11]. It has been shown that the power quality in termsof current harmonics and reactive power can be improved usingthe instantaneous reactive power definition. The work in [12]and [13] showed that network voltage unbalances cause inputcurrent distortions which can be transferred to the dc side dueto the negative-sequence component of the voltage. An exampleof negative-sequence appearance in the positive-sequence dqsynchronous frame is shown in Fig. 2.

Rioual et al. [14] probably proposed the very first controlscheme for the VSC that regulates the instantaneous power gen-erated under network voltage dips. Their work mainly generatedcurrent references in both positive and negative synchronousreferences to regulate the power at the point of common cou-pling (PCC). Since then, researchers have been developing “en-hanced” control schemes mostly to minimize input harmon-ics which are coupled to dc-link voltage ripples. For instance,

Stankovic and Lipo [15] presented a model that can eliminate theharmonics for generalized unbalanced conditions. However, thismethod needs a great deal of computation steps for DSP-basedcontrol. In [16] and [17], the authors consider the instantaneouspower at the converter poles, not the PCC, and consequentlyobtain better harmonic responses. Although these methods aremore effective than the work in [14] and relatively simpler thanthat in [15], the proposed methods suffer from solving nonlinearequations in real time and low bandwidth of the current regu-lator due to the extraction of the current sequence components.Suh and Lipo continued their work [18], which resulted in ahybrid synchronous stationary frame with oscillating referencecurrents. Consequently, the bandwidth-diminishing functionsare avoided. They also proposed a simplified current referencegenerator that can be implemented more easily than that in [16]and [17]. It might be of reader’s interest that in [16]–[18], theinstantaneous reactive power definition is different from the“classical” notion of outer products of vectors presented in [11].Instead, these authors mainly employed the work in [19] inwhich the authors developed the so-called extension PQ theoryto resolve the singularity issues existing in the work of Akagiet al. [11] for the generalized unbalanced condition. Accord-ingly, the instantaneous reactive power is redefined on the basisof a set of voltages that lag the pole voltages by 90◦ and isnot the imaginary part of the complex power. Despite satisfac-tory operation of a three-phase rectifier under unbalanced condi-tions, the proposed scheme in [18] requires several feedback andfeedforward compensators. A simplified controller is proposedin [20] which uses stationary current controller (resonant com-pensator) that considers both positive and negative sequencessimultaneously. Notch filters tuned at 120◦ [21] are nonethelessused to extract the bus voltage sequences for current referencegeneration. In [22], the authors also consider notch filters but toseparate the positive- and negative-sequence current controllers.One potential constraint of these methods is the emergence ofthird harmonic in the input current that is proportional with thevoltage dip, and in [23], the authors analyzed the effects of sev-eral methods to estimate the proper sequence components. Mostrecent work is reported in [24] which implemented the wholecontrol frame in the stationary frame resulting in a new cur-rent reference generator. Fast dynamic performance with smalldc-link voltage ripple in a 20-kVA/10-kHz pulsewidth modu-lation (PWM) prototype converter under a 30% supply voltagedip is reported. A desirable feature of the scheme is that nophase-locked loop (PLL) strategies are needed but constant linefrequency is assumed and sinusoidal compensators as in [18] aredeployed due to the control logic of the oscillating references.

B. BTB VSC Control Under Unbalanced Conditions

The transmission-level multi-VSC option requires a carefulconsideration of system interactions, while switching frequencyis kept relatively low (9–15 times the line frequency). An ex-ample of this theme is investigated for a unified power flowcontroller (UPFC) in [25] where additional compensating termsare added to reduce or remove the interactions of rectifier andinverter. The interaction has been highlighted as one of the

PARKHIDEH AND BHATTACHARYA: VECTOR-CONTROLLED VSC-BASED TRANSMISSION UNDER GRID DISTURBANCES 663

potential issues of BTB VSC system operation with conven-tional controllers applied to single VSCs [26]. This fact ismore critical under power system faults since the controllersintroduced previously should take these interactions into ac-count. Therefore, simply separating sequence controllers maynot achieve the desired performance due to the system coupling,filtering delays, etc. To solve these problems, Xu et al. [26] in-troduced a framework which mainly used the results of [14]and [27]. Xu et al. [26] proposed to nullify the oscillating poweras in [14] by generating a current reference. In addition, Xu etal. [26] considered the improved “cross-coupling control” men-tioned for UPFC in [27]. This control scheme was first proposedfor UPFC applications in [28] where authors showed that thecrossing gain of a transmission line is much larger than its directgain. The cross-coupling controller uses the q-axis voltage vec-tor, to control the d-axis current and the d-axis voltage vectorto control the q-axis current. Numerical results in [26] illus-trate the satisfactory performance under a single-line-to-groundfault but with more than double the rated current. The latter re-sult is important in VSC HVDC transient dynamics. It has beenpointed out in [29] that increase of the current limit significantlyimproves the power quality of the system. Yazdani and Iravanimention in [30] that it is possible to suppress the dc-link voltageoscillations by using the notch filter approach; therefore, thesame issues exist as for a single VSC. For a specific VSC BTBHVDC system, Hagiwara and Akagi [31] proposed a unique dc-link control structure that has the load feedforward term. Withthe proposed structure, a robust dc-link voltage is achieved ifthe fault occurs in the inverter side. It has been shown thatload estimation can improve the converter performance. In fact,Winkelnkemper [32] had shown that adding the load estimationinto the main controller better attunes the dc-link voltage toload power change. Parkhideh et al. [33] also showed how it ispossible to remove the varying load effect from the closed-looplarge mining converter control systems (1.5–24 MW) which arebasically BTB VSC systems.

On the other hand, there are emerging interests to havemedium voltage interfaces for renewable integration such aswind generations currently up to 10 MVA with direct-drive tech-nologies (BTB VSC) [9]. In [34], the authors have presented aunique controller in the stationary frame for direct-drive windgeneration systems that is based on reactive power compen-sation. Applying the proposed method ensures balanced gridcurrents even under power system faults. Nonetheless, due topossible low-speed operation of wind turbines, dc-link dynam-ics have been addressed as one of the key factors which affectthe operation of the turbine [35]. Therefore, more investigationsare essential to determine the proper control strategy: balancedcurrents or a stiff dc-link voltage.

This paper proposes a control structure specifically for thedc-link controller converter in the BTB VSC system which isimplemented in a single synchronous reference frame withoutany sequence component extraction or resonant compensator. Itwill be shown that dc-link dynamics are coupled to the interac-tion imposed by the inverter performance. On the other hand,there is no direct control input that can remove this interactionor disturbance with conventional frequency-oriented controller

Fig. 3. Schematic of a VSC.

design. This study introduces a dq (rotating) synchronous-basedframework to design a more robust controller for relatively lowswitching frequency (9–15 times) PWM or vector-controlledBTB VSC systems.

III. MODELING AND CONTROL OF VSC

A. Modeling of VSC

The modeling of VSC, the building block of the BTB system,is based on the state-space average modeling approach [36].This modeling is based on the principal circuit analysis andvoltage and current equations for storage elements known asstate equations. The general schematic of a three-phase VSCcircuit is shown in Fig. 3, and the state equations of a VSC inthe three-phase stationary coordinates are as follows:

dIabc

dt= −Rs

LsIabc +

Eabc

Ls− Vabc

Ls(1)

dVDC

dt=

IDC

CDC− VDC

RpCDC− Pload

CDCVDC. (2)

In order to benefit from all decoupling and constant prop-erties of a two-phase system instead of a three-phase one, dqtransformation is considered to convert all quantities in the abcstationary coordinate frame to the synchronously rotating refer-ence frame, i.e., de–qe

dId

dt= −Rs

LsId − ωsIq +

Ed

Ls− Vd

Ls(3)

dIq

dt= −Rs

LsIq + ωsId +

Eq

Ls− Vq

Ls. (4)

In (3) and (4), Vd and Vq are the converter output voltagesin the synchronous reference frame. The modulation index canalso be written in this frame as (5) where k depends on themodulation technique. In this study, we use the vector controlmethod or type-I control denoted by Schauder and Mehta [7]

md =Vd

kVDC, mq =

Vq

kVDC. (5)

In many literature works especially for dc/dc converters, themodulation index is used as the control input; therefore, (3) and(4) present the nonlinear system. DC-link dynamics are alsononlinear by introducing the definition for IDC as (6). However,by considering Vd and Vq as the control inputs, (3) and (4) can betreated as linear ones. Also, power balance is used to derive the


Fig. 4. Proposed backstepping control structure for the dc-link voltage controller converter in a BTB VSC system.

Fig. 5. Implemented proposed control structure in the synchronous frame to generate the reference vectors for the dc-link voltage controller converter.

equation for the dc-link voltage neglecting the interface lossesas in (7) [22], [37], [38]. Ea (the PCC phase A voltage) is alignedwith the d-axis in the synchronously rotating reference frame.The result of dc-link dynamics shown in (7) is linear as long asEd and Eq are constant. Consequently, no linearization aroundspecific operating points is needed and the small-signal VSCmodel looks similar to the large-signal model. The state-spacerepresentation of the VSC can be obtained from (3), (4), and(7). State variable vector x(t) is the state variable vector, u(t)is the input vector, and e(t) is considered as the disturbancevector, (8):1

IDC =32(mdId + mqIq ) (6)

dV 2DC

dt=

3EdId

CDC+

3EqIq

CDC− 2V 2

DC

RpCDC− 2Pload

CDC(7)

x(t) =

⎛⎜⎝

Id

Iq

V 2DC

⎞⎟⎠ , u(t) =

(Vd

Vq

), e(t) =

⎛⎜⎝

Ed

Eq

Pload

⎞⎟⎠ .

(8)

1Notation remark: No linearization has been made for the state-space rep-resentation of the converter system under normal and unbalanced conditions.Hence, the time dependence notation of the variables in (8) has been eliminatedfor the sake of ease of presentation.

Although there is a possibility of using the so-called in-stantaneous PLL presented in [39] to discard the effect of theq-component of the voltage vector even under unbalanced con-ditions (at least in the model), this study considers common PLLstructures in order to unify the problem.

B. Closed Loop of BTB VSC Systems

In the vector-controlled BTB VSC systems regardless of thetopology, one converter typically controls the dc-link voltageand supports its reactive power. This converter can be operatedas rectifier in HVDC applications or as an inverter in direct-driven wind turbines. The other converter is operated in PQ orV/f (voltage/frequency) mode controlling the active and reactivepowers. A simplified schematic of the BTB VSC system withits control functions is depicted in Fig. 1.

To design a closed-loop system, the eigenstructure assign-ment or any linear feedback design method can be used to placethe poles at the desired locations. Eigenstructure assignment isexplained for STATCOM in [40] and we use it to develop thegeneral controller and as the baseline for the VSC in the BTBconfiguration as presented in [38].

According to the system equations, the mode associated withthe q-component of the current (typically for reactive power con-trol) can be adjusted based on the ac-side interface parameters


TABLE IVSC BTB SYSTEM PARAMETERS

and required response time. On the other hand, dc-link voltageclosed-loop dynamics consist of the modes associated with twoeigenvalues. One of the system poles affects the charging anddischarging of the capacitor which is called λc . This eigenvalueshould be placed near to the origin to avoid either high chargingor discharging current. The other pole can be placed at the samelocation the reactive current control mode is, which we call itλi . It should be noted that the poles associated with the currentmode can be placed as far as the inherent delay of the convertermodeling allows; current regulators often present a fast first-order behavior. To achieve a nonoscillatory output response, itis sufficient to place the poles at the real axis. Consequently,the dc-link voltage regulator can be designed based on the sys-tem specifications and requirements. The performance of theBTB system under balanced conditions through the proposedmodeling and control has already been presented in [38].

It has been shown that conventional control methods are notable to regulate the dc bus voltage of VSC-based “transmission”systems under power system disturbances. This failure is mainlydue to the low switching frequency operation of these devicesand limited bandwidth of the converter. Therefore, two struc-tures are constructed without sequence decomposition based onlocal control of the converter states known as back-steppingcontrol (BSC) and integral factor control, which mitigate thedc-link voltage oscillations [41]. The issue in [41] is stated, andfollowed the work of Hagiwara et al. [42], as a possible overvolt-age in the dc link when the fault is incurred in the inverter sideof the BTB VSC system in HVDC applications. However, withincreasing applications of multimegawatt converters in differentapplications, more transient capability is needed, i.e., the unbal-anced condition can be in either converter in the BTB system. Inthis paper, we propose a control architecture that improves thetransient performance of the VSC BTB system in the currentand emerging applications, denoted as HVDC, drive, and hybridpower systems. The proposed controller will be explained in thefollowing section specifically for the dc-link voltage controllerconverter in the BTB system.

Fig. 6. BTB VSC system for HVDC applications.

IV. MODIFIED BSC FOR BTB VSC SYSTEMS

In this section, the proposed controller based on the localcontrol of the converter states will be explained, first for reac-tive power control to clarify the method. The reactive powercontrolled by the q-component of the current has a direct inputVq as shown in (4). This controller is desired to have decoupledand disturbance rejection characteristics while achieving the re-quired response time. This criterion is met if its input Vq hasthe form of (9). The first term in this equation is responsible forthe response time of the state and the remaining terms are fordecoupling, disturbance rejection, and command following inorder. The result of first-order system is shown in (10), which isalso available in the literature such as [7].

The direct input for the d-component of the current, Vd , is firstdesigned to have decoupling and disturbance rejection terms asin (11). The additional term Ψ1 is used as the control input toregulate the dc-link voltage and active power through a back-stepping control method.

Vq = −fq Iq + LsωsId + Eq + tq Iqref (9)

Iq =(

Rs + fq

Ls

)Iq −

tqLs

Iqref (10)

Vd = −LsωIq + Ed + Ψ1 (11)

Id = −Rs

LsId − 1

LsΨ1 (12)

In control theory, backstepping is a technique for designingcontrols for nonlinear systems developed around 1990 [43]. Itis a recursive technique in which one designs feedback con-trols and finds Lyapunov functions for a set of n increasinglycomplex systems, the last system being the one of interest. Anexample of using this method on a three-phase PWM rectifiercan be found in [44]. The fundamental idea can be interpretedas the local control of the states that do not access to the in-put. In other words, some states are used as a pseudocontrol tostabilize others by introducing some virtual state variables rep-resenting the difference between the actual and virtual control.Accordingly, β defined below is used to control dc-link volt-age which does not have direct control input, as shown in (13)and (14). The change of the coordinates here to z indicates thatβ should take whatever value is required to make the error z1null corresponding to achieving the reference z3 (stable dc-linkvoltage)

z3 = V 2DC (13)

z1 = β − α(z3 , Eq , Pload) (14)


Fig. 7. Start-up dynamic performance of the BTB VSC system as in HVDCapplications and unity power factor operation of 1 p.u. power under balancedconditions. (RTDS results.)

where

β =3EdId

CDC.

This method is valid only at the level of the Lyapunov func-tion. The selected candidate functions are based on the energyconcept of the dc-link capacitor and the interface inductor. If thedefined state for the dc-link voltage is considered to be V 2

DC , itis sufficient to propose the candidate functions as (15) and (16)which are positive-definite functions

V3 =12z2

3 (15)

V1 = V3 +12z2

1 . (16)

It is remarkable that it is not the key of choosing the virtualand actual controls but choosing the correct Lyapunov functionsand generating their derivatives negative to ensure the stabilityof the whole system. The virtual control input is chosen as (17)

Fig. 8. Dynamic performance of the BTB VSC system as in HVDC appli-cations, changing power flow direction, no change in reactive power referenceunder balanced conditions. (RTDS results.)

to meet these requirements

α(z3 , Eq , Pload) = −fV DCz3 −3

CDCEqIq +

2CDC

Pload

+ tV DCV 2DCref . (17)

The derivative of the proposed Lyapunov functions combin-ing (7) and (13)–(17) results in

V3 = z3 z3 = z3

(z1 + α +

3EqIq

CDC− 2V 2

DC

RP CDC− 2Pload

CDC

)

(18)

V1 = V3 + z1 z1

= V3 + z1

(β

(Ed

Ed+

−Rs

Ls

)+

−3Ed

LsCDCΨ1 − α

). (19)

Choosing the input signal Ψ1(t) as (20), in which we definethe controller gain as fd and replaced β from (14), leads tohaving V1 and V3 in the form of (21) and (22) which ensuresthe stability of the virtual controllers z1 and consequently thesystem. In other words, the derivative functions become negative


Fig. 9. Dynamic performance of the BTB VSC system as in HVDC applica-tions under an unbalanced condition of 50% single-line voltage sag in the powerflow controller side. (RTDS results.)

definite, assuring the stability of the system

Ψ1 =−LsCDC

3Ed

(−fdz1 − z3 − (z1 + α)

(Ed

Ed− Rs

Ls

)+ α

)

(20)

V3 = −fV DCz23 + z3z1 (21)

V1 = −fV DCz23 − fdz

21 . (22)

The proposed backstepping control structure for the dc-linkvoltage controller converter is shown in Fig. 4. From the toplevel view, a feedforward power measurement is added to thecontroller. The required input to ensure the stability of the dclink, Ψ1(t), is generated through the manipulation of the virtualcontrol input z1 , the PCC voltage, and the converter current. Thedetails of how the implemented controller generates the refer-ence vectors are presented in Fig. 5. As can be seen, the structureis fairly straightforward, compared to [18], and has been im-plemented in commonly used synchronously rotating referenceframe (de–qe ) without sequence components extraction blockor resonant compensator, as compared to [24] and [26].

The control parameters for this type of controller are calcu-lated as in (23) based on the desirable response of the asso-ciated modes: λi and λc for the current and dc-link voltage,

Fig. 10. Dynamic performance of the BTB VSC system as in HVDC appli-cations under an unbalanced condition of 50% single-line voltage sag in thedc-link voltage controller side. (RTDS results.)

respectively

para =

⎧⎪⎪⎨⎪⎪⎩

fd = λi ; fq = Rs + Lsλi

fV DC = λc

tq = −Rs + fq ; tV DC = fV DC +2

RpCDC.

(23)

V. DYNAMIC PERFORMANCE OF BTB VSC SYSTEMS WITH

THE PROPOSED CONTROL ARCHITECTURE

This section presents and evaluates the dynamic performanceof BTB VSC systems in different applications. Applications arecategorized as HVDC, drive (wind), and hybrid power systemapplications. The proposed controller has been implemented inRTDS and compiled on a GPC processor card with a controllersampling time of 50 μs and key circuit parameters as tabulated inTable I. For reference, the performance comparison of the BTBVSC system (based on the average model) with the proposedcontrol scheme and commonly used controller structures hasbeen presented in the Appendix.

In order to analyze the performance of the system, the fol-lowing assumptions have been made.

1) The system references are controlled based on the currentsfor the case studies under faults.


Fig. 11. Dynamic performance of the BTB VSC system in HVDC applicationsunder an unbalanced condition of 50% single-line voltage sag in the dc-linkvoltage controller side operated as inverter. (RTDS results.)

2) There is no change in control mode of the system pre-,during, and post-fault. Under unbalanced grid voltages,reactive power demand can dominate the available con-verter capacity. This demand imposes some limitations inregulating the dc-link voltage.

3) Power systems have same short-circuit capacity.

A. BTB VSC System for HVDC Applications

BTB VSC systems in HVDC applications, represented inFig. 6, are used for power flow control. One converter operatesin PQ mode and the other one is responsible for compensat-ing for the losses and ensuring a stable operation of the dcbus voltage, while it supports its reactive power demands. Invector-controlled VSC systems, reactive power is regulated in-dependent of active power.

The first group of results is presented in Fig. 7 where systemstart-up dynamic performance is shown when 1 p.u. of poweris supplied to network #2. The converter system is chargednaturally in some cycles and it reaches the reference voltageafterward. In this set of results, a unity power factor operationof converters has been verified and presented.

Fig. 8 shows the dynamic performance of the VSC BTB sys-tem in response to a change power flow direction under balancedconditions. The system supplies 0.8 p.u. power, and the VSC#1(dc-link voltage controller) provides 0.2 p.u. capacitive and

Fig. 12. Dynamic performance of the BTB VSC system in HVDC applicationsunder unbalanced condition of 50% in phase B and 90% in phase C voltage sagin the power flow controller side operated as the rectifier. (RTDS results.)

Fig. 13. Simplified BTB VSC system in drive (wind) applications.

VSC#2 (power flow controller) 0.6 p.u. inductive reactive power.As can be observed, the proposed controller for the BTB system,as well as the common control structures, operates satisfactorily.These values are considered in the following case studies to haveconsistency in the obtained result for unbalanced conditions.

The dynamic performance of the VSC BTB system under anunbalanced condition in the inverter side (power flow controllerconverter) is presented in Fig. 9. The unbalanced system isrepresented by a 50% voltage drop in phase A of the inverter-side PCC voltages Vabc 2 which can be considered as a fault nearthe inverter station. The fault remains for six cycles. As canbe observed, the dc-link voltage remains practically stiff, and aharmonic measurement of the dc-link voltage for the second andfourth harmonics shows a satisfactory level of compensation.This mode of operation is mainly of interest in the literature[26], [41], [42].

Fig. 10 presents the dynamic performance of the BTB systemwhen a 50% voltage drop occurs in phase A of the rectifier side


Fig. 14. Dynamic performance of the BTB VSC system in drive (wind) ap-plications under an unbalanced condition of 50% single-line voltage sag in thedc-link voltage controller side and drive side operating at 30 Hz. (RTDS results.)

(dc-link voltage controller). Due to the voltage drop, the rectifiercarries higher currents to maintain the load power and regulatethe dc bus voltage. It can be seen that the dc-link voltage hasa minor change of about 1% p.u. and the effect of negative-sequence power is reduced to 1.5% p.u. presented in the dc-linkvoltage. It can also be observed that the inverter current is hardlyaffected by the dynamics of the dc link under the unbalancedcondition.

The dynamic performance of the VSC BTB system in HVDCapplications while the dc-link controller is operated as an in-verter and the power flow controller as rectifier is presented inFigs. 11 and 12. This mode of operation may not be practicalin HVDC power transactions and it is presented to combine theproblem and address the dynamics. In Fig. 11, the unbalancedsystem is represented by a 50% voltage drop in phase A of thePCC voltages Vabc1 . The fault remains for six cycles. As can beobserved the dc-link voltage remains practically stiff, and har-monic measurement of the dc-link voltage for the second andfourth harmonics shows a satisfactory level of compensation.The inverter currents change (increase in phase A) to compen-sate for the unbalanced power flowing into the system; however,it remains within the safe operating area of the switches. InFig. 12, the system performance under more severe imbalancesis shown represented by a 50% and 90% voltage drop in phasesB and C of the power flow controller side, respectively.

Fig. 15. Dynamic performance of the BTB VSC system in drive (wind) ap-plications under an unbalanced condition of 50% in phase B and 30% in phaseC voltage sag in the dc-link controller side (grid) and drive side operating at30 Hz. (RTDS results.)

Fig. 16. BTB VSC system in hybrid power system as transmission trans-former (partial) back-up for life extension of the transmission transformer orcontingencies.

Based on the results obtained in different case studies, theeffectiveness of the proposed controller is shown for HVDCapplications under normal and unbalanced conditions. In otherwords, the deficiency of the high-power VSCs in terms of con-trol bandwidth is improved through a high-bandwidth controlarchitecture that does not require any sequence extraction or anydiminishing bandwidth factors.

B. BTB VSC System for Drive (Wind) Applications

This section is provided to address emerging large capacitywind turbines (>10 MW). These turbines are expected to usedirect-drive technologies shown in Fig. 13 and the BTB VSCsystem as the enabling interface. A robust dc-link voltage is


Fig. 17. Dynamic performance of the BTB VSC system as in hybrid systemsfor transmission transformer (partial) back-up under unbalanced condition of90% in phase A sag. (RTDS results.)

considered to be one of the key factors that affect the turbineoperation. In the following case studies, it is assumed that theturbine-side converter (VSC#2) operates at 30 Hz and supplies0.8 p.u. active power and absorbs 0.6 p.u. inductive reactivepower, while the grid-side converter (VSC#1) regulates the dc-link voltage and provides 0.2 p.u. capacitive reactive power.The dynamic performance of the VSC BTB system in the driveapplication under unbalanced conditions in the inverter side orgrid side (dc-link voltage controller converter) is presented inFigs. 14 and 15. In Fig. 14, the unbalance system is representedby 50% voltage drop in phase B of the inverter-side PCC. InFig. 15, a more severe fault occurs which is represented bya 50% voltage sag in phase B in addition to a 30% voltagedrop in phase C of the grid. From the results obtained, it canbe concluded that the proposed control scheme is effective inmaintaining a robust dc-link voltage even under unbalanced gridconditions. In other words, the drive side in this case of high-power wind generators with a BTB VSC interface can operateindependently from the grid disturbances translating to higheravailability of the renewable resources.

C. BTB VSC System for Transmission Transformer(Partial) Bypass

With increasing demands of power electronics in the network,it is expected to have hybrid systems. One example of a hybrid

Fig. 18. Performance comparison of the BTB VSC system with the proposedcontroller and commonly used control schemes for HVDC applications (averagemodel).

system approach is known as the modular transformer converter(MTC) in which a single or a group of BTB VSC system(s)is connected across transmission-level transformers. An MTCas the transmission controller provides the flexibility of full orpartial utilization for the transmission lines and power trans-formers. This flexibility effectively increases the system’s sparecapacity and operating margins, and also provides back-up incase of substation transformer failure or forced reduced ratingoperation scenarios by continuous power flow control [10], [45].

A simplified schematic of the MTC as the transmission con-troller connected in parallel to a transmission transformer isdepicted in Fig. 16. Introducing the MTC, as shown in Fig. 16,brings remarkable effects on the dynamics of the system. Inparticular, any imbalance in the power system is seen by bothconverters, which has been little appreciated in conventionalapplications of BTB VSC systems.


Fig. 19. Performance comparison of the BTB VSC system with the proposedcontroller and commonly used control schemes for the drive application operatedat 30 Hz (average model).

Fig. 20. Performance comparison of the BTB VSC system with the pro-posed controller and commonly used control schemes for hybrid power systemapplications—example of transmission transformer back-up (average model).

The dynamic performance of the VSC BTB system with theproposed control structure for hybrid power system applica-tions under balanced and unbalanced conditions is presented inFig. 17. The power flow in the BTB system remains as stated inthe previous case studies except that the two networks have a 5◦

phase difference for the natural power flow of the grid. The un-balanced system is represented by a 90% voltage drop in phase Aof the PCC voltages. As can be observed, the dc-link voltage re-mains practically stiff, and harmonic measurement of the dc-linkvoltage for the second and fourth harmonics shows a satisfactorylevel of compensation under this severe fault case. Therefore, anMTC with the proposed control structure can be utilized evenunder unbalanced conditions when it is needed the most.

VI. CONCLUSION

This paper has addressed the dc-link voltage control issuesfor vector-controlled VSC-based transmission systems underpower system disturbances. Having analyzed the currentstate-of-the-art methods of mitigating the dc-link voltage fluc-tuations under grid faults and disturbances, we have proposeda control structure in the commonly used dq synchronous

reference frame. The proposed structure obviates the need forthe sequence extraction blocks or the resonant compensators.Therefore, there is no diminishing bandwidth factor. Thescheme, however, utilizes the interaction of the converters, theload, bus voltage, and their derivatives to compensate for thephase delay in the current regulator. The proposed scheme wasexplained through a backstepping control method in which itsLyapunov-based structure ensures the stability of the system.The RTDS verification of the controller attained less than1% dc-link voltage deviation under most common faults anddisturbances, demonstrating the applicability and effectivenessof the proposed scheme for different transmission applicationsdenoted as HVDC, drive, and hybrid power systems.

APPENDIX

The controller is initially designed and tested with an av-eraged model approach implemented in PLECS package inMATLAB environment. In this appendix, the performance of theBTB VSC system in the aforementioned applications (HVDC,drive, and hybrid power systems) with the proposed controllerand a “commonly” used controller is presented (see Fig. 18–Fig. 20). The common control structure and its design can befound in the literature such as [26], [38], and [42]. Each resultcorresponds to the case presented in this paper.

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Babak Parkhideh (S’07) received the B.Sc. (Hons.)degree from the University of Tehran, Tehran, Iran,in 2003, the M.Sc. degree from the Institute of PowerElectronics and Electrical Drives, RWTH AachenUniversity, Aachen, Germany, in 2006, and the Ph.D.degree from the North Carolina State University,Raleigh, in 2012, all in electrical engineering.

Since 2007, he has been with North Carolina StateUniversity where he is currently a Research Associateat the NSF Engineering Research Center for FutureRenewable Electric Energy Delivery and Manage-

ment Systems. During his Ph.D. study, he worked for Siemens mining indus-tries as a graduate intern and ABB Corporate Research Center as a VisitingResearcher. His research interests include utility and industrial applications ofpower electronics including flexible ac transmission system, high-voltage directcurrent, integration of energy storage systems, and mining equipment.

Subhashish Bhattacharya (M’85) received the B.E.(Hons.) degree from the Indian Institute of Tech-nology Roorkee (formerly University of Roorkee),Roorkee, India, in 1986, the M.E. degree from theIndian Institute of Science, Bangalore, India, in1988, and the Ph.D. degree from the University ofWisconsin-Madison, Madison, in 2003, all in electri-cal engineering.

He has worked in the Flexible AC TransmissionSystems (FACTS) and Power Quality Group at West-inghouse R&D Center in Pittsburgh, PA, which was

later part of Siemens Power Transmission & Distribution, from 1998 to 2005. Hejoined the Department of Electrical and Computer Engineering, North CarolinaState University (NCSU) as an Assistant Professor in August 2005, where he hasbeen the ABB Term Associate Professor since August 2011 and also a FacultyMember of the NSF Engineering Research Center for Future Renewable Elec-tric Energy Delivery and Management Systems Center (www.freedm.ncsu.edu)and Advanced Transportation Energy Center (www.atec.ncsu.edu) at NCSU.His research interests include FACTS, utility applications of power electronicsand power quality issues, solid-state transformer, high-frequency magnetics, ac-tive filters, high-power converters, converter control techniques, integration ofenergy storage to the grid, and application of new power semiconductor devicessuch as SiC for converter topologies.

vector controlled vsc based transmission under grid disturbances

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