2910 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 59, NO. 7, JULY 2012

Voltage-Sensor-Less Synchronization to UnbalancedGrids by Frequency-Adaptive Virtual Flux Estimation

Jon Are Suul, Member, IEEE, Alvaro Luna, Member, IEEE, Pedro Rodríguez, Senior Member, IEEE, andTore Undeland, Fellow, IEEE

Abstract—This paper proposes a simple method for inher-ently frequency-adaptive virtual flux (VF) estimation intended forvoltage-sensor-less grid synchronization and control of voltagesource converters. The frequency-adaptive characteristics are ob-tained by using a second-order generalized integrator configuredas a quadrature signal generator (SOGI-QSG) with the grid fre-quency as an explicit input variable. It is also shown how theproperties of VF estimation based on SOGI-QSGs can be utilizedto achieve a simple and effective synchronization technique thatintegrates frequency-adaptive bandpass filtering, VF estimation,and symmetrical component sequence separation into one oper-ation. This new method avoids cascaded delays of VF estima-tion and sequence separation and is labeled as dual SOGI-basedVF (DSOGI-VF) estimation since it is based on two parallelSOGI-QSGs. The properties and performance of the DSOGI-VFestimation are analyzed in comparison to conventional configu-rations of VF estimation and sequence separation, demonstratingthat it is a simpler structure with improved dynamic response. Infact, similar response time as for grid synchronization based onvoltage measurements is achieved. The operation and performanceof the proposed DSOGI-VF estimation method have been verifiedby laboratory experiments in a small-scale converter setup.

Index Terms—Grid synchronization, three-phase voltage sourceconverter (VSC), unbalanced grid voltage, virtual flux (VF),voltage-sensor-less control.

I. INTRODUCTION

A S THE USE of power electronic converters is continu-ously increasing, the voltage source converter (VSC) is

emerging as the main topology for modular and standardizedgrid-connected converter units in a wide power range [1]. Alarge variety of strategies and techniques for grid synchroniza-tion and control of VSCs have therefore been proposed andanalyzed in the scientific literature [2]–[4]. Voltage-sensor-lessoperation is among the topics that are gaining increasing inter-est for cost reduction, increased modularity, and, in some cases,even increased reliability of grid-connected VSCs [5], [6].

Manuscript received November 7, 2010; revised March 9, 2011, May 4,2011, and July 1, 2011; accepted August 15, 2011. Date of publicationSeptember 19, 2011; date of current version February 17, 2012. This workwas supported in part by the Spanish Ministry of Science and Innovation underProjects ENE2008-06841-C02-01/ALT and TRA2009-0103.

J. A. Suul and T. Undeland are with the Department of ElectricPower Engineering, Norwegian University of Science and Technology, 7491Trondheim, Norway (e-mail: jon.are.suul@elkraft.ntnu.no; Tore.Undeland@elkraft.ntnu.no).

A. Luna and P. Rodríguez are with the Department of Electrical Engi-neering, Technical University of Catalonia, 08222 Terrassa, Spain (e-mail:luna@ee.upc.edu; prodriguez@ee.upc.edu).

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

Digital Object Identifier 10.1109/TIE.2011.2168793

The estimation methods required for voltage-sensor-less oper-ation also have the potential to improve the converter perfor-mance by estimating grid conditions at remote points that arenot available for real-time measurements [7], [8].

Several different strategies have been suggested for voltage-sensor-less grid synchronization of VSCs [5], [6], [9]–[12]. Oneof the most common and easily applicable methods for suchsensor-less operation is based on the integral of the converteroutput voltage, interpreted as a “flux.” The usefulness of thisvoltage integral for analysis and control of converters and driveshas been known for a long time as documented in [13]–[19].Voltage-sensor-less control of grid-connected converters basedon the voltage integral was, however, not thoroughly analyzeduntil the works of Malinowski et al. [20]–[22], which alsoestablished the term “virtual flux” (VF) in the literature.

Since the estimation of VF based on pure integration willbe sensitive to drift and saturation of the estimated values,many different methods for practical implementation have beenproposed [18]–[20], [23], [24]. The simplest estimation tech-niques are usually based on low-pass or bandpass filters that aretuned to emulate integration for the grid voltage fundamentalfrequency. Such methods can therefore be sensitive to gridfrequency variations.

Even if voltage-sensor-less control of grid-connected VSCsbased on the concept of VF is becoming well established inthe literature, only few studies have, until now, systematicallyaddressed the operation of such systems under unbalanced gridconditions. The first reported approach to unbalanced condi-tions was based on low-pass filtering of the VF vector amplitudeand the use of a slow phase-locked loop (PLL) for extractingthe positive-sequence component of the VF [25]. A method forextraction of the positive-sequence flux component based oncombining notch filters and low-pass filtering in the synchro-nous reference frame has also been recently presented in [26].The use of a combined positive- and negative-sequence (PNS)PLL for the detection of the positive-sequence VF componentunder unbalanced conditions was proposed for the first timein [27], and the same approach has been applied to studies ofVSC-based HVDC transmission in [28]. A similar approach, inthe more general and well-known form of the decoupled doublesynchronous reference frame PLL (DDSRF-PLL) from [29],has also been applied to HVDC systems in [30]. The commonfeature of these studies is that they are first estimating the VFand then applying different techniques for the detection of thepositive (and negative) sequence phase angle. This implies thatthe synchronization strategy is cascaded to the VF estimation,causing cascaded delays influencing the transient response.

0278-0046/$26.00 © 2011 IEEE

SUUL et al.: VOLTAGE-SENSOR-LESS SYNCHRONIZATION TO UNBALANCED GRIDS BY VF ESTIMATION 2911

Fig. 1. Basic system under consideration.

A different approach to VF-based grid synchronization wasproposed by Kulka [24]. In this case, the converter out-put voltage was first separated into PNS components, be-fore the corresponding VF components were estimated sep-arately. In the same way as for the methods in [25]–[28]and [30], this method will suffer from cascaded delays ofsequence separation and VF estimation. Implementation basedon second-order low-pass filters for both sequence separa-tion and VF estimation, as proposed in [24], can also makethe system sensitive to grid frequency variations. In addition,a large number of second-order filters are required for se-quence separation of both the converter output voltage andthe measured currents, and for separate estimation of thePNS-VF components.

Two significant limitations can thus be identified from theexisting literature on VF-based grid synchronization. First, thesimple and commonly applied filter-based methods for VFestimation are sensitive to grid frequency variations. Second,the available techniques for VF-based grid synchronizationunder unbalanced conditions are based on cascaded flux esti-mation and sequence separation. They are therefore resultingin complex structures with high computational requirementsand relatively slow transient response. This paper attempts toaddress both of these issues by proposing a simple methodfor explicitly frequency-adaptive estimation of VF that can beorganized to achieve inherent sequence separation in one singleoperation.

The estimation methods proposed in this paper are basedon the application of second-order generalized integrators(SOGIs), configured as quadrature signal generators (QSGs)[31], [32]. The application of SOGI-QSGs for VF estimationand the presented strategy for frequency-adaptive estimationof PNS-VF components were first proposed by Suul et al.[33]. In this paper, the discussion is expanded to include com-parison with conventional strategies for grid synchronizationbased on voltage measurements or VF estimation. Laboratoryexperiments are presented as verification of the operability andperformance of the proposed method for frequency-adaptiveVF estimation with inherent sequence separation.

II. VOLTAGE-SENSOR-LESS GRID SYNCHRONIZATION

BASED ON VF

The definition of “flux” Ψ, calculated as the integral of thevoltage V , as given in the following equation, is the basicstarting point for the concept of VF:

Ψ =∫

V · dt + Ψ0. (1)

This equation has been used for a long time in electric drivesystems but has also been applied to measured voltages in grid-

connected converters [13]–[19], [34]. For voltage-sensor-lessoperation, the flux integral is based on the output voltage ofthe converter, usually calculated from the switching states andthe dc-link voltage as discussed in [20]–[22], [24], and [35].

A. Ideal VF Estimation for Grid Synchronization

Considering the basic system configuration in Fig. 1, meth-ods for voltage-sensor-less operation based on VF estimationare usually designed to replace voltage measurements at thegrid side of the filter inductor indicated in the figure. Thecorresponding estimation strategy is easily found by combiningthe definition from (1) with the voltage equation for the filterinductor as given by

Vf,αβ = Vc,αβ − R1 · Ic,αβ − L1 ·dIc,αβ

dt. (2)

In this equation, Vf is the voltage at the grid side of thefilter inductor, Vc is the converter output voltage, and Ic is theconverter current, with all three-phase variables represented inthe two-phase stationary αβ reference frame. The parametersL1 and R1 represent the inductance and the internal resistanceof the filter inductor, respectively. In the case of PWM operationof the converter, the VF Ψf,αβ at the grid side of the filterinductor can then be calculated from the reference voltagesvref,αβ’s, the dc-link voltage Vdc, and the measured currentsIc,αβ’s, as given by [20], [24], [36]

Ψf,αβ =∫ (

vref,αβ · 12Vdc − R1 · Ic,αβ

)dt − L1 · Ic,αβ .

(3)

The initial value of the flux integral is needed for initializa-tion of the estimation but will be omitted in the followingdiscussion.

Introducing per unit values, where the base values for voltageand “flux” are given by

Vb = Vphase Vb,dc = 2 · Vb Ψb =Vb

ωb(4)

the VF estimation can be expressed by

ψf,αβ = ωb

∫(vref,αβ · vdc − r1 · ic,αβ)dt − l1 · ic,αβ . (5)

This equation is an expression for ideal VF estimation and isalso shown by a block diagram in Fig. 2. The figure showsclearly how the resistive voltage drop (r1 · ic) is subtractedfrom the effective output voltage of the converter, while theinductive flux drop (l1 · ic) is subtracted from the integratedvoltage, to result in the VF at the grid side of the filter inductor.

Since the VF corresponds to the integral of the voltage, itsinstantaneous phase angle γ lags the voltage phase angle by

2912 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 59, NO. 7, JULY 2012

Fig. 2. Basic concept of ideal VF estimation.

90◦ for fundamental frequency signals. Therefore, the voltagephase angle θf can be easily estimated as given by

γf = arctan(

ψf,β

ψf,α

)θf = γf + 90◦. (6)

Since the integration required for VF estimation implies a fil-tering effect, the instantaneous phase angle for synchronizationcan usually be calculated directly from (6), but it can also betracked by a PLL [37].

B. Filter-Based Implementation of VF Estimation

The simplest and most common approach for estimation ofVF is to use a first-order low-pass filter with a crossover fre-quency that is usually about one decade below the fundamentalgrid frequency of the power system. This filter will behavealmost like an integrator for fundamental frequency signals,but there will be significant amplitude attenuation and a smallphase error [23], [24]. Approaches based on bandpass filtersgive more freedom to shape the frequency response, but therewill still be small errors in the amplitude or phase angle of theestimated VF [18], [19], [23].

Another simple method for VF estimation is given by[24], [38]

ψ(s) = vc(s)2 · ω2

0

(s + ωo)2. (7)

This method is based on two cascaded low-pass filters withcrossover frequency equal to the fundamental angular fre-quency ω0 of the grid. With this strategy, a relatively fasttransient response is achieved, and the amplitude and phasecharacteristics are analytically corresponding to unity gain and90◦ phase shift at the fundamental frequency.

These filter-based methods, and several other varieties, canbe used for VF estimation with good results in strong grids.The accuracy of the estimated phase angle, flux amplitude, orboth phase angle and amplitude will, however, be influencedby deviations from the nominal grid frequency unless specialmeasures are taken to make the implementation frequencyadaptive.

Adaptive integration techniques based on low-pass-filtershave been extensively investigated and applied for flux estima-tion of machines in electric drive systems where large frequencyvariations are expected [23], [39]–[42]. However, most of thesemethods are based on the correction of flux estimate by usingfeedback from the flux vector amplitude or by consideringthe centricity of the flux vector trajectory. Although achieving

Fig. 3. Explicitly frequency-adaptive second-order bandpass filter and QSGbased on a SOGI, with the in-quadrature output signal qv′ representing thescaled VF χ.

good performance for flux estimation of balanced three-phasesystems, such methods will therefore not be directly applicableto single-phase systems or unbalanced operation of three-phasesystems.

C. New Method for Explicitly Frequency-adaptiveVF Estimation

The VF estimation method proposed for the first time in[33] is based on a SOGI from [31] and [32]. A SOGI oper-ates as an explicitly frequency-adaptive amplitude integratorfor sinusoidal signals and can be configured as a frequency-adaptive bandpass filter and QSG by using a feedback from theoutput signal. The resulting structure is shown in Fig. 3 for ageneric voltage v, where it is clearly seen that an estimate ω′

of the fundamental angular frequency is an explicit input to thefilter structure. The transfer function of the filter from the inputvariable v to the filtered variable v′ is given by

v′(s)v(s)

=k · ω′ · s

s2 + k · ω′ · s + ω′2 (8)

and it can be seen that the frequency response can be shapedby selecting the gain k. According to the denominator of (8),a value of k equal to

√2 corresponds to a critically damped

second-order system. As discussed in [31], this will be a goodcompromise between overshoot and stabilization time and willtherefore be considered as the default value in the followingdiscussions.

Considering the block diagram in Fig. 3, it is clearly seen thatthe in-quadrature output signal labeled as qv′ is the integral ofthe filtered output v′ multiplied with the resonance frequencyω′, as given by

qv′ = ω′∫

v′dt = ω′p.u. · ωb

∫v′dt = ω′

p.u. · ψ = χ. (9)

With reference to the expression for per-unit VF in (5), thissignal can be considered to represent the VF scaled with theper-unit value of the fundamental frequency. This quantity islabeled as χ as further explained in [33] and shown in Fig. 3.Applying this definition, the estimation of the scaled VF can beexpressed by

χf = ω′∫

[vc − r1 · ic]′dt − ω′p.u. · l1 · ic. (10)

SUUL et al.: VOLTAGE-SENSOR-LESS SYNCHRONIZATION TO UNBALANCED GRIDS BY VF ESTIMATION 2913

By considering (8) and (9) or Fig. 3, it is seen that the transferfunction of the SOGI-based integration is given by

χ(s) = qv′(s) =k · ω′2

s2 + k · ω′ · s + ω′2 v(s). (11)

The estimate of the scaled VF χf at the filter terminals can thenbe expressed by

χf (s) =k · ω′2

s2 + k · ω′ · s + ω′2 · [vc(s) − r1 · ic(s)]

− ω′p.u. · l1 · ic(s). (12)

The frequency response of the transfer function in (11)is only marginally different from the second-order low-passfilter of (7), and they are both providing unity gain and 90◦

phase shift for fundamental frequency signals. However, themain functional difference is that the implementation of (11)according to Fig. 3 will be inherently frequency adaptive aslong as an estimate of the grid angular frequency ω′ is available.This frequency information can, for instance, be provided by aPLL as discussed in [31] or by a frequency-locked loop (FLL)as proposed in [32].

The proposed method for VF estimation can be considered asa general approach that can be used for grid synchronization ofboth three-phase and single-phase converters in voltage-basedas well as voltage-sensor-less control systems. The furtherfocus of this paper will, however, be voltage-sensor-less gridsynchronization of three-phase VSCs.

III. FREQUENCY-ADAPTIVE VF ESTIMATION UNDER

UNBALANCED CONDITIONS

As mentioned, only a limited number of studies have, un-til now, considered VF-based voltage-sensor-less grid syn-chronization under unbalanced conditions. From the studiesreported in [24]–[28] and [30], it can also be noticed thatthe applied strategies for VF estimation and the sensitivityto grid frequency variations are not discussed in detail. Thissection will therefore first show how the VF estimation methodproposed in Section II-C can be used to implement explicitlyfrequency-adaptive versions of traditional strategies for cascad-ing VF estimation and sequence separation under unbalancedconditions. Then, a new method for frequency-adaptive VFestimation with inherent sequence separation will be presented.

A. Traditional Approach With Cascaded VF Estimation andSequence Separation

Following the traditional approach, there are two ways oforganizing VF-based grid synchronization under unbalancedconditions.

1) Sequence Separation of Estimated VF: The most obviousand common approach is to first estimate the VF and thenapply a filtering technique, a PLL, or a sequence separationtechnique for tracking the corresponding PNS components, asreported in [25]–[28] and [30]. If measures are not taken toobtain frequency-adaptive operation of the VF estimation, theperformance of such strategies will, however, degenerate during

frequency variations, even if a fully frequency-adaptive methodlike the DDSRF-PLL from [29] is used to track the positive se-quence of the estimated VF. Frequency-adaptive operation mustalso be ensured in the case of sequence separation methodsimplemented in the stationary reference frame, for the systemto maintain its performance during grid frequency variations.

Explicitly frequency-adaptive voltage-sensor-less grid syn-chronization can, however, be obtained in a simple way byutilizing the proposed method for VF estimation described inSection II-C. The resulting structure is shown in Fig. 4, where itcan be seen that the scaled VF χg,αβ at the point of connectionto the grid is first estimated according to the definition and thedescriptions from Section II-C. Then, the PNS-VF componentsare estimated in the stationary αβ reference frame by usingthe SOGI-QSG as a phase-shifting operator [43], [44]. Thisis the same application of the SOGI-QSG as that proposed byRodríguez et al. [31], [32] for sequence separation of voltagemeasurements and can be expected to have similar dynamic per-formance as the DDSRF-PLL from [29] but with less demand-ing implementation [45]. In Fig. 4, the FLL from [46]–[48] isused to provide the grid frequency estimate to the SOGI-QSGs,but the source of the frequency information is of minor impor-tance in this context.

Considering Fig. 4, it can be observed that the estimationof PNS-VF components is achieved by using four SOGI-QSGblocks. However, if the PNS components of the measuredcurrents are needed in the control system of the converter,another two SOGI-QSG-blocks would be required. It can alsobe noticed that the filtering effect of the VF estimation is cas-caded with the filtering effect of the SOGI-QSGs used for thesequence separation and that this will slow down the dynamicresponse of the PNS-VF estimation.

2) Sequence Separation of Converter Output Voltages andIndividual Estimation of PNS-VF Components: The other pos-sible configuration for PNS-VF estimation is to first carry outsequence separation of the converter output voltage, beforeestimating the VF signals. This approach was proposed, for thefirst time, by Kulka [24], based on utilization of the second-order low-pass filter in (7). An explicitly frequency-adaptiveimplementation can be achieved by using the SOGI-QSG asdescribed in Section II-C to replace the second-order low-passfilters. The resulting structure is shown in Fig. 5, with the FLLfrom [46]–[48] providing the grid frequency estimate to theSOGI-QSGs.

Considering the block diagram in Fig. 5, it is seen that thisstructure is more complex than the structure in Fig. 4 and thata total number of eight SOGI-QSG-blocks are needed for theimplementation. The same number of second-order filters wasalso needed in the original implementation proposed in [24], asa consequence of the fact that two sets of second-order filterswere needed for sequence separation of voltages and currents,while four second-order filters were needed for estimatingthe individual PNS-VF components. An interesting feature ofthis structure is, however, that it allows for using differentinductance values in the estimation of the PNS components ofthe VF [8].

From Fig. 5, it is noted that the sequence separation andthe VF estimation are cascaded also in this case. The dynamic

2914 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 59, NO. 7, JULY 2012

Fig. 4. Frequency-adaptive VF estimation cascaded with SOGI-QSG-based sequence separation of the estimated VF.

Fig. 5. Frequency-adaptive sequence separation of voltages cascaded with separate estimation of PNS-VF components.

SUUL et al.: VOLTAGE-SENSOR-LESS SYNCHRONIZATION TO UNBALANCED GRIDS BY VF ESTIMATION 2915

response should therefore be the same as for the estimationmethod shown in Fig. 4. With the implementation in [24],based on (7), only 90◦ phase-shifted values are available fromthe filter, and the unfiltered input values were therefore usedfor the sequence separation. To increase the bandwidth ofthe estimation, the unfiltered values can also be used for thesequence separation in Figs. 4 and 5, but the difference intransient response will not be significant.

B. New Method for VF Estimation With InherentSequence Separation

The SOGI-based method for VF estimation discussed inSection II-C has all the features needed for bandpass filtering,VF estimation, and generation of in-quadrature signals forsequence separation. A conceptually new strategy for merg-ing all these functions into one frequency-adaptive operation,based on two parallel SOGI-QSGs, has therefore been devel-oped in [33].

1) Structure of the Proposed Estimation Method: Consider-ing that the in-quadrature output signal qv′ of the SOGI-QSGin Fig. 3 represents the VF χ, a signal phase shifted by 90◦ isneeded for sequence separation. This is already available fromthe same SOGI-QSG in the form of the filtered input signalv′. The inverse of this signal corresponds to a phase lag of90◦ with respect to the VF signal and can be used directly forsequence separation following the same approach as used in[31] and [32].

A method for VF estimation based on these simple consider-ations is shown in Fig. 6. As shown, the VF integration and thesequence separation are based on two single SOGI-QSGs, andthis structure can therefore be labeled as dual SOGI-based VF(DSOGI-VF) estimation. The same number of SOGI-QSGs isalso needed for DSOGI-based sequence separation of measuredvoltages as described in [31] and [32]. Two SOGI-QSGs, orother similar filters, will also be needed for practical imple-mentation of the simple conventional VF estimation shown inFig. 2.

When PNS-VF components are estimated by the methodshown in Fig. 6, the current-induced fluxes have to be sub-tracted separately for all sequence components. Sequence sep-aration of the current measurements is therefore necessaryas shown in the figure. However, only four SOGI-QSGs areneeded for the total implementation, and there are no cascadedfiltering effects in the VF estimation. Therefore, this modelwill have faster dynamic response than the techniques basedon the conventional approach for PNS-VF estimation, like themethods shown in Figs. 4 and 5.

In Fig. 6, the FLL from [46]–[48] is used to track the gridangular frequency and, by that, to keep the PNS-VF estimationinherently frequency adaptive, although any other technique forfrequency estimation could be used. As for the structure shownin Fig. 5, different points of synchronization to the grid can beselected for the PNS-VF components.

2) Properties of the Proposed Estimation Method: The uti-lization of SOGI-QSGs for VF estimation has already beendiscussed in Section II-C, but the influence of the sequenceseparation must be included to study the performance of the

estimation method in Fig. 6. Thus, the transfer function fromthe voltage reference input to the sequence-separated flux com-ponents should be investigated.

In balanced conditions, the α and β voltage componentshave equal amplitude, and the β component is lagging the αcomponent by 90◦. For the steady-state frequency response, thisphase displacement can be described by [32]

vref,β(s) = − s

ωvref,α(s). (13)

Considering the previous discussion of the proposed VFestimation and the block diagram in Fig. 6, it can be seen thatthe positive-sequence flux component can be described by

χ+α (s) =

12

(χα(s) − q · χβ(s)) =12

(ω′

sv′

α(s) + v′β(s)

).

(14)

Substituting the expression from (13) into this equation re-sults in

χ+α (s) =

12

(ω′

sv′

α(s) − s

ωv′

α(s))

(15)

which can be further expanded, by using (8), into the fullexpression given by

χ+α (s) =

12

(k · ω′2

s2 + k · ω′ · s + ω′2 − s

ω

· k · ω′ · ss2 + k · ω′ · s + ω′2

)vref,α(s). (16)

Analyzing the steady-state frequency response, the resultingtransfer function from vref,α to χ+

α is given by

χ+α (jω)

vref,α(jω)=

12

(k · ω′ · (ω′ + ω)

ω′2 − ω2 + j · k · ω′ · ω

). (17)

Evaluating (17), it can be easily verified that the investi-gated sequence separation strategy results in unity gain and−90◦ phase shift for fundamental frequency positive-sequencesignals. For negative-sequence components, corresponding tonegative fundamental frequency, (17) results in zero ampli-tude, effectively eliminating the influence of negative-sequencecomponents on the estimated positive-sequence VF. The fre-quency response of this transfer function in the case of PNScomponents has been shown and discussed in [33], and similarexpressions can be derived for the estimation of negative-sequence VF components.

Considering the characteristics of (17), it is clear that bothVF estimation and sequence separation will be achieved withthe proposed estimation method under steady-state operation,as long as the estimated frequency ω′ is equal to the funda-mental frequency of the grid. Correct steady-state operation willalso be achieved with the estimation strategies shown in Figs. 4and 5, but with a slower transient response as demonstrated inthe following section.

2916 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 59, NO. 7, JULY 2012

Fig. 6. Frequency-adaptive DSOGI-VF estimation with inherent sequence separation.

IV. EVALUATION AND COMPARISON OF DIFFERENT

VF ESTIMATION METHODS

To investigate the dynamic performance of the proposedDSOGI-VF estimation method compared to the conventionalapproaches for PNS-VF estimation, all the configurations pre-sented in Section III have been evaluated and simulated withthe PSCAD/EMTDC simulation software.

A. Simulation Studies

To compare the operation of the different estimation meth-ods, a converter is simulated in the simple grid configurationshown in Fig. 1. The converter is simulated by an averagemodel neglecting the semiconductor switching operation, andthe rated operation is specified to 2.26 MVA at a 690-VRMS

line voltage. The converter is operated with a filter inductanceof 0.05 p.u. and is connected to an ideal transformer with a0.07-p.u. leakage inductance. For all conditions, the converteris operated with about 0.5-p.u. active power fed to the dc link.

The converter is controlled to give balanced sinusoidal cur-rents, independent of possible grid voltage unbalance. In thesimulation model, this is achieved by using dual-frame PIcurrent controllers where the positive-sequence d-axis currentis used to maintain the power balance while all other currentsare controlled to zero [49]. For the presented simulations, theVF estimation is synchronized to the high-voltage side of thetransformer. This is achieved by specifying the resistance andinductance used for VF estimation to be given by the seriesconnection of the parameters for the filter inductor and theleakage inductance and conduction losses of the transformer.Thus, the estimated VF values χ+,−

g αβ in Figs. 4–6 will becorresponding to the voltage Vg in Fig. 1.

Under the initial operating conditions, the grid voltage atthe high-voltage side of the transformer is kept constant witha 1.0-p.u. positive-sequence component. A negative-sequencecomponent of 0.01 p.u. is also added to the voltage to test thecapabilities of tracking low values of unbalance.

1) Transient Response of Proposed DSOGI-VF Estimationin the Case of Unbalanced Grid Voltage Sag: The transient

SUUL et al.: VOLTAGE-SENSOR-LESS SYNCHRONIZATION TO UNBALANCED GRIDS BY VF ESTIMATION 2917

Fig. 7. Simulation results showing the operation of the DSOGI-VF estimationin the case of an unbalanced sag in the grid voltage.

response of the DSOGI-VF estimation method has been inves-tigated by imposing an unbalanced voltage dip in the grid at thehigh-voltage side of the transformer in the simulation model.When a fault occurs, the positive-sequence voltage is steppeddown to 0.733 pu, and the phase angle is shifted by 5◦. At thesame time, the negative-sequence component of the voltage isset to 0.210 pu, while the phase angle is shifted by 50.4◦.

The main simulation results are shown in Fig. 7, where thefault is applied at t = 0.04 s while the system is operatingunder steady-state conditions. From Fig. 7(a), it can be seenhow the voltage references for generation of PWM signalsbecome unbalanced as the converter is injecting balanced cur-rents during the unbalanced conditions. From these unbalancedvoltage references and the measured currents, PNS-VF signalsare estimated by the proposed strategy as shown in Fig. 7(b)and (c), respectively. In Fig. 7(d), the amplitudes of the PNS-VF components are calculated and compared to the amplitudesof the grid voltage imposed to the system. It can be seenthat the VF estimation is relatively fast and accurate, withabout 5-ms rise time and very little overshoot. It can also benoted that this response time is similar to what is usual forsequence separation methods based on voltage measurementsas discussed, for instance, in [31], [32], and [50].

Fig. 8. Amplitudes of estimated PNS-VF components for different VF esti-mation methods when exposed to an unbalanced drop in grid voltage.

The phase angles θ+χ and θ−χ , calculated directly from the

PNS-VF components, are shown in Fig. 7(e) and (f), respec-tively, phase shifted by 90◦ for comparison to the phase anglesθ+

v and θ−v of the voltage components. The phase angles ofthe PNS voltage components are obtained by DSOGI-basedsequence separation of voltages measured at the point of syn-chronization, according to [31] and [32]. The curves showthat the values obtained from the VF estimation are closelycorresponding to the values obtained from the voltage measure-ments. This verifies that the proposed DSOGI-VF estimationmethod can achieve the same transient response as conventionalgrid synchronization based on measured voltages.

2) Comparison of Transient response for Different PNS-VFEstimation Methods: The amplitudes of the PNS-VF compo-nents, calculated by vector summation of the sinusoidal αβquantities, can serve as an index for comparing the transientresponse of different methods for VF estimation, as shown inFig. 8. The plotted curves are obtained by simulating the sameunbalanced voltage sag as described in the previous section,and the PNS voltage components |v+

g | and |v−g |, imposed to the

simulation model, are used as the reference for comparing thetransient response of the different estimation methods.

Since the methods shown in Figs. 4 and 5 have the samedynamic response, only the results from Fig. 4 are shown bythe blue lines in Fig. 8. As can be seen, the response of boththe PNS components has a significant overshoot and a settlingtime in the range of 30–40 ms. As a contrasting example withfilter-based estimation in a cascaded structure, results obtainedwith the method proposed in [24], based on (7), are also shownwith green dashed lines in Fig. 8. In this case, the response is abit more damped due to the higher damping of the second-orderlow-pass filter, and the speed of response is slightly increasedby using unfiltered input signals together with the phase-shiftedsignals when carrying out the sequence separation. However,the speed of response for the estimation methods in Figs. 4 and5 can also be improved in a similar way by using unfilteredsignals instead of the bandpass-filtered signals in the sequence

2918 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 59, NO. 7, JULY 2012

Fig. 9. Amplitudes of estimated PNS-VF components for different VF esti-mation methods when exposed to a step in the grid frequency.

separation, and the damping can be increased by increasing thegain parameter k in Fig. 3. However, the overshoot and therelatively long settling time of all these methods are mainlya consequence of the conventional approach of cascadingsecond-order filters used for both sequence separation and VFestimation.

A faster and more damped response of both the PNS am-plitudes is clearly achieved with the proposed DSOGI-VFestimation method from Fig. 6 as plotted by red dashed linesin Fig. 8. The observed rise time of about 5 ms, and the settlingtime of around 20 ms, is in accordance with the characteristicsof the SOGI-QSG as discussed in [46] and [47] and withtraditional approximations for second-order systems. This isbecause the DSOGI-VF estimation method effectively reducesthe PNS-VF estimation to a second-order system, as long asthe grid frequency is constant. With purely sinusoidal signalsand accurately identified system parameters, as in an idealsimulation model, the amplitude response of the estimationmethod from Fig. 6 is exactly corresponding to the amplituderesponse of the DSOGI-based sequence separation of measuredvoltages from [32].

Fig. 9 shows the results when the estimation methods com-pared in Fig. 8 are exposed to a step in the grid frequency from50 to 60 Hz during the unbalanced conditions. Although it isan unrealistic frequency change for real grid conditions, thiscase gives useful illustration of the properties of the differentestimation methods. From the curves in Fig. 9, it can be clearlyseen how the filter-based method for sequence separation andVF estimation based directly on (7) is unable to estimate thecorrect amplitude when the grid frequency is different fromthe nominal frequency. Since VF estimation and sequenceseparation based on SOGI-QSGs will be explicitly frequencyadaptive, the estimation method in Fig. 4 is, however, reachinga new steady state after a transient period of about 120 ms. Thissettling time will be determined by the dynamics of the gridfrequency tracking and its interaction with the VF estimation.

The DSOGI-VF estimation in Fig. 6 shows a faster responseand a significantly lower maximum deviation from the real

grid voltage amplitude compared to what can be obtained withthe methods in Figs. 4 and 5. Again, this improvement in thedynamical response is mainly because cascaded operation ofsequence separation and VF estimation is avoided.

B. Comparison of Characteristics and ImplementationComplexity of different Methods for Grid Synchronization

Information characterizing different strategies for VF-basedvoltage-sensor-less grid synchronization is collected in Table Ias a basis for discussion and comparison. Corresponding infor-mation about grid synchronization by DSOGI-based sequenceseparation of measured voltages, based on [32], is included inthe table as a point of reference.

The first column of the table is concerning the possibilityfor frequency-adaptive operation. As already mentioned, this isnot automatically achieved with traditional filter-based methodsfor sequence separation and VF estimation but will be aninherent feature if SOGI-QSGs are used for implementation ofthe synchronization method.

The next column of the table is summarizing how thedifferent synchronization methods behave during unbalancedconditions. As implied by the previous descriptions, conven-tional methods for VF estimation based on Fig. 2 will not beable to maintain the intended performance during unbalancedconditions, while the methods discussed in Section III areexplicitly designed to estimate PNS components. The table isalso summarizing the order of signal processing in cascadefor the different methods, as discussed in Section III, and theasymptotic frequency response of the synchronization methodsin the range above the grid frequency.

Considering the transient response of the different synchro-nization methods, it is seen that the proposed DSOGI-VFestimation achieves the same rise time and settling time asthe voltage-based synchronization method from [32] and as theconventional VF estimation implemented by SOGI-QSGs. Thisis because the DSOGI-VF estimation is configured to achievesequence separation and VF estimation in one single operationand therefore exhibits predominantly second-order dynamics.The PNS-VF estimation methods based on cascaded operationof flux estimation and sequence separation exhibit fourth-orderdynamics due to the series connection of two second-orderstructures, and the transient response will therefore be slowerand more oscillatory as already demonstrated by the presentedsimulation results. The transient response of such cascadedmethods will, however, depend on the implementation andtuning, and therefore, only values for implementations basedon SOGI-QSGs with the tuning discussed in Section II-C aregiven in Table I.

The last columns of Table I are giving details regarding thecomplexity of implementation for the different synchronizationmethods, based on the diagrams shown in Figs. 3–6. The statevariables and the mathematical operations related to tracking ofthe grid frequency are not included in the table since they canbe the same for all the different methods.

From Table I, it is seen that all the methods for PNS-VFestimation require a significantly higher number of mathe-matical operations than the DSOGI-based sequence separation

SUUL et al.: VOLTAGE-SENSOR-LESS SYNCHRONIZATION TO UNBALANCED GRIDS BY VF ESTIMATION 2919

TABLE ISUMMARY OF PERFORMANCE CHARACTERISTICS AND IMPLEMENTATION COMPLEXITY FOR DIFFERENT SYNCHRONIZATION METHODS

from [32], but this is mainly due to the flux estimation ac-cording to (5). The lowest number of mathematical operationsis required by the method in Fig. 4, since this method doesnot include sequence separation of the currents. However, thetransient response is significantly slower than that for the pro-posed DSOGI-VF estimation due to the cascaded operation ofVF estimation and sequence separation, and it can be noticedthat two of the state variables are not directly utilized. TheDSOGI-VF estimation is resulting in a slightly higher numberof mathematical operations, because the PNS-VF componentsare calculated individually. However, since this method impliesparallel operation of SOGI-based sequence separation of VFand currents, all the eight state variables are utilized, andas already discussed, the transient response is predominantlyshowing second-order characteristics. The PNS-VF estimationin Fig. 5 results in a significantly more complex implementationwhile achieving the same dynamic response as the method inFig. 4.

From this information, it is clear that the proposedDSOGI-VF estimation can be an effective method for voltage-sensor-less grid synchronization with good dynamic per-formance and inherent ability to operate under unbalancedconditions as well as grid frequency variations. The methodadds little to the complexity of the grid synchronization whileachieving fast transient response and effective utilization of thecomputational efforts. It should also be noticed that, in casesequence separation of the current measurements is needed inother parts of the converter control system, the computationalefforts of the DSOGI-VF estimation can be utilized even moreeffectively.

V. EXPERIMENTAL VERIFICATION OF THE PROPOSED

DSOGI-VF ESTIMATION METHOD

Since the proposed DSOGI-VF estimation method in Fig. 6and [33] has been shown to have beneficial features in com-parison with other methods, experiments on a small-scale lab-oratory setup have been carried out to verify its operationand performance. The experimental setup consisted of a grid-connected 5-kVA power converter module with an LC filteron the ac side. Power to the dc capacitor of the converter wasprovided by a controllable dc source. The ac grid voltage wascontrolled by a grid emulator based on adjustable transformersand contactors that could be configured to generate balanced orunbalanced voltage sags. For this study, the grid emulator wasoperated with a prefault line-to-line voltage of 110 VRMS.

The control algorithms needed to operate the converter, andthe proposed DSOGI-VF estimation, were implemented on adSPACE DS1103 platform. In this case, the sampling intervalwas set to 100 μs, and the control system was generating dutycycles for PWM operation of the converter with a 10-kHzswitching frequency. The duty-cycle signals were transmittedfrom the dSPACE platform to the converter module by fiber-optic connections. The layout of the laboratory setup and theimplemented control system is shown in Fig. 10, with the mainparameters listed in Table II.

A. Control System and Fault Sequence

In these experiments, the converter was operated by a controlsystem based on instantaneous power theory according to [51]

2920 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 59, NO. 7, JULY 2012

Fig. 10. Overview of laboratory setup.

TABLE IIDETAILS OF LABORATORY SETUP

and with grid synchronization based on voltage measurementsas described in [32]. For the presented results, the setup wasconfigured to inject a constant average power of 350 W to thegrid by balanced three-phase currents. To impose an unbal-anced disturbance to the system, the voltage-sag generator wascontrolled to generate a voltage drop of about 50% in two ofthe phases, while the converter was operating in steady-stateconditions.

The DSOGI-VF estimation was implemented in parallel tothe voltage-based synchronization strategy and was not used inthe closed-loop control of the converter as shown in Fig. 10.This parallel operation of the two synchronization strategiesallowed for direct comparison of signals obtained from mea-surements and from the VF estimation.

B. Experimental Results

A set of results comparing signals obtained from the voltagemeasurements and from the VF estimation is shown in Fig. 11for the case when an unbalanced voltage sag occurs. Fig. 11(a)shows the measured three-phase voltages, while Fig. 11(b) and(c) shows the PNS components of the measured voltage asdetected by the DSOGI-based method from [32]. Fig. 11(d)and (e) shows the PNS components of the estimated VF. The90◦ phase shift between voltage and flux signals can be easilyidentified by studying the curves.

The phase angles of the PNS components of voltage and VFsignals are calculated by postprocessing of the data logged bythe dSPACE interface to the converter. The resulting angles

are shown in Fig. 11(f) and (g), where the phase angles ofthe VF components are shifted by +90◦ and −90◦ for PNScomponents, respectively, in order to simplify the comparison.

The results show that the phase angle of the positive-sequence grid voltage component is well estimated by theDSOGI-VF estimation, both under balanced and unbalancedconditions. In the normal operating condition before and afterthe fault, the negative-sequence components of the grid voltageand the corresponding VF are fluctuating around zero, andthe phase angles of these signals are therefore not containingrelevant information. When the fault occurs, it is, however,seen that the phase angle calculated from the negative-sequenceVF component is quickly tracking the negative-sequence phaseangle found from the voltage measurements.

In Fig. 12, the amplitudes of the PNS components of themeasured voltage and the estimated VF are compared for atime period of 0.5 s, including the unbalanced dip in thegrid voltage. These signals are also found by postprocessingvoltage and flux signals logged by the dSPACE interface to theconverter. It can be seen from this figure that the amplitudesare matching reasonably well and that there is no additionaldelay in the estimation of the PNS-VF components comparedto the sequence separation of the measured voltages. Thereis, however, a slight deviation in the amplitudes that is orig-inating from parameter mismatch in the VF estimation, sincenominal values for inductance and resistance of the filter in-ductor are used without further measurements or identificationroutines.

Fig. 12 also shows that there is more ripple in the amplitudesof the estimated VF components than in the amplitude ofthe PNS components of the voltage. This additional ripple isappearing due to the parameter deviations and because com-pensation for converter dead time and for the threshold voltageof the IGBTs is not included in the laboratory implementation.

VI. CONCLUSION

This paper has discussed methods for VF-based voltage-sensor-less grid synchronization of VSCs, under variable gridfrequency and unbalanced voltage conditions.

First, it has been shown how a SOGI-QSG can beused as a basic building block for achieving inherently

SUUL et al.: VOLTAGE-SENSOR-LESS SYNCHRONIZATION TO UNBALANCED GRIDS BY VF ESTIMATION 2921

Fig. 11. Laboratory results showing measured three-phase voltages, PNScomponents of measured voltage, and PNS components of the estimated VF,with corresponding phase angles.

frequency-adaptive VF estimation. The SOGI-QSG has thenbeen applied to replace traditional low-pass filters in conven-tional configurations of VF estimation and sequence separation.Although frequency-adaptive operation is achieved by the useof SOGI-QSGs, the conventional approach of cascading thesetwo functions results in complex structures with relatively slowdynamic response. Therefore, a new estimation method thatmerges the functions of frequency-adaptive bandpass filtering,VF estimation, and sequence separation into one operation hasbeen proposed and analyzed. Since the implementation of theproposed method is based on two parallel SOGIs for the PNS-VF estimation, it has been labeled as DSOGI-VF estimation.

Compared to conventional configurations of sequence sepa-ration and VF estimation, the proposed DSOGI-VF estimation

Fig. 12. Laboratory results showing amplitudes calculated from the PNS com-ponents of voltage and estimated VF before, during and after the unbalancedvoltage drop.

method has a minimum number of filter structures connected incascade and is therefore resulting in a faster and more dampedtransient response. The improved dynamic response comparedto other methods for PNS-VF estimation has been verifiedby simulations for both unbalanced grid conditions and largevariations in grid frequency. Laboratory experiments verifyingthe operation of the DSOGI-VF estimation method under bal-anced and unbalanced conditions have been presented, provingthat the dynamic performance is similar to the performance ofDSOGI-based synchronization to measured grid voltages.

ACKNOWLEDGMENT

The authors would like to thank Prof. M. Molinas of theNorwegian University of Science and Technology (NTNU) forinitiating and facilitating the cooperation between NTNU andTechnical University of Catalonia (UPC). The authors wouldalso like to thank I. Candela and J. Rocabert of UPC for pro-viding equipment and facilitating the experimental verificationof the presented concept during a one-month research stay ofJ. A. Suul in Terrassa, Spain, in March 2010.

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Jon Are Suul (M’11) received the M.Sc. degreefrom the Norwegian University of Science andTechnology (NTNU), Trondheim, Norway, in 2006,where he is currently working toward the Ph.D.degree in the Department of Electric Power Engi-neering.

From 2006 to 2007, he was with SINTEF Energy,Trondheim, where he was engaged in the simulationof power electronic systems. In 2008, he was a guestPh.D. student for two months with the Energy Tech-nology Research Institute of the National Institute of

Advanced Industrial Science and Technology, Tsukuba, Japan. He was also avisiting Ph.D. student for two months with the Research Center on RenewableElectrical Energy Systems, within the Department of Electrical Engineering,Technical University of Catalonia (UPC), Terrassa, Spain, during 2010. Hisresearch interests are mainly related to control of power electronic convertersin power systems and for renewable-energy applications.

Alvaro Luna (S’07–M’10) received the B.Sc.,M.Sc., and Ph.D. degrees in electrical engineer-ing from the Technical University of Catalonia(UPC), Barcelona, Spain, in 2001, 2005, and 2009,respectively.

He joined the faculty of UPC, in 2005, wherehe is currently an Assistant Professor. His researchinterests include wind turbine control, integration ofdistributed generation, and power conditioning.

Dr. Luna is a student member of the IEEE PowerElectronics Society, the IEEE Industrial Electronics

Society, and the IEEE Industry Applications Society.

Pedro Rodríguez (S’99–M’04–SM’10) received theM.Sc. and Ph.D. degrees in electrical engineeringfrom the Technical University of Catalonia (UPC),Barcelona, Spain, in 1994 and 2004, respectively.

In 1990, he joined the faculty of UPC as anAssistant Professor, where he is currently an As-sociate Professor with the Department of ElectricalEngineering and the Head of the Research Centeron Renewable Electrical Energy Systems (SEER). In2005, he was a Visiting Researcher with the Centerfor Power Electronics Systems, Virginia Polytechnic

Institute and State University, Blacksburg. In 2006, he was a PostdoctoralResearcher with the Department of Energy Technology, Aalborg University,Aalborg, Denmark, where he has been a Part-time Professor since 2007,being a Cosupervisor in the Vestas Power Program. He has coauthored about100 papers in technical journals and conference proceedings. He is the holder ofseven licensed patents on wind and photovoltaic systems. His research interestsinclude integration of distributed energy systems, power conditioning, andcontrol of power converters.

Dr. Rodriguez is a senior member of the IEEE Power Electronics Society,IEEE Industrial Electronics Society, IEEE Industry Application Society, andIEEE IES Technical Committee on Renewable Energy Systems. He is anAssociate Editor of the IEEE TRANSACTIONS ON POWER ELECTRONICS andthe Committee Chair of the IEEE-IES Student and GOLD Members Activities.

Tore Undeland (M’86–SM’92–F’00) was born inBergen, Norway, in 1945. He received the M.Sc.and Ph.D. degrees from the Norwegian Universityof Science and Technology (NTNU), Trondheim,Norway, in 1970 and 1977, respectively.

Since 1970, he has been with NTNU, where hehas been in the position of Full Professor since 1984.He has also served as an Adjunct Professor withChalmers University of Technology, Gothenburg,Sweden, since 2000, and as a Scientific Advisor toSINTEF Energy, Trondheim. His research interests

include power electronics and wind energy systems. He is a coauthor of thewell-known textbook Power Electronics: Converters, Applications, and Design(Wiley, 1989, 1995, and 2003).

Dr. Undeland has served as the President of the European Power Electronicsand Drives Association (EPE) and is a member of the Norwegian Academy ofTechnological Sciences.