4. ieee transactions on power delivery volume 29 issue 3 2014 [doi 10.1109%2ftpwrd.2014.2303482]...

1138 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 29, NO. 3, JUNE 2014

Accurate Estimation of Single-Phase Grid VoltageParameters Under Distorted ConditionsMd. Shamim Reza, Student Member, IEEE, Mihai Ciobotaru, Member, IEEE, and

Vassilios G. Agelidis, Senior Member, IEEE

AbstractThis paper presents an accurate technique for theestimation of single-phase grid voltage fundamental amplitudeand frequency. The technique consists of a quadrature signalgenerator (QSG) and a discrete Fourier transform (DFT). The fre-quency information required by the QSG based on a second-ordergeneralized integrator (SOGI) is estimated using the spectralleakage property of the DFT. The presented DFT operation doesnot require real-time evaluation of trigonometric functions. Thefrequency estimation is less affected by the presence of harmonicswhen compared to similar techniques based on QSG-SOGIsuch as the phase-locked loop and the frequency-locked loop.Moreover, unlike these techniques, the DFT-based QSG-SOGI(DFT-SOGI) technique does not create any interdependent loops,thus increasing the overall stability and easing the tuning process.The effectiveness of the proposed technique has been validated ona real-time experimental setup.

Index TermsDiscrete Fourier transform (DFT), grid voltagemonitoring, parameter estimation, phase-locked loop (PLL),quadrature signal generator (QSG), second-order generalizedintegrator (SOGI), single-phase system.

I. INTRODUCTION

T HE GRID voltage parameters, such as frequency, phaseangle, and amplitude are important information for manyareas of power system applications, such as the grid-connectedpower converters [1], uninterrupted power supply [2], activepower filters [3], and power system control and protection [4]to mention just a few. Usually, the estimation of the param-eters from an undistorted periodic grid voltage waveform isa relatively easy task. However, the grid voltage is distortedby harmonics due to the use of nonlinear loads [3]. The gridvoltage is also nonperiodic in nature due to the change of theload conditions and system configurations. The parameters es-timation from a distorted nonperiodic grid voltage waveformbecomes a relatively challenging task. Thus, a suitable digitalsignal processing (DSP) technique is required for accurate es-

Manuscript received January 02, 2013; revised July 09, 2013, September 12,2013, and November 17, 2013; accepted December 12, 2013. Date of publi-cation February 20, 2014; date of current version May 20, 2014. Paper no.TPWRD-00009-2013.The authors are with the Australian Energy Research Institute (AERI)

and School of Electrical Engineering and Telecommunications, The Univer-sity of New South Wales (UNSW), Sydney NSW 2052, Australia (e-mail:[email protected]; [email protected]; [email protected]).Color versions of one or more of the figures in this paper are available online

at http://ieeexplore.ieee.org.Digital Object Identifier 10.1109/TPWRD.2014.2303482

timation of the grid voltage parameters under nonperiodic anddistorted conditions.The discrete Fourier transform (DFT) [5] and the fast Fourier

transform (FFT) [6] are the commonly used window-basedtechniques for spectral analysis of the grid voltage waveform.The recursive DFT can also be used to reduce the computa-tional burden of the DFT [7]. However, the Fourier transform(FT)-based techniques assume that the grid voltage waveformis periodic and repetitive outside the window which maycause spectral leakage during the time-varying cases [6]. Thespectral leakage property of the DFT can be used to track thetime-varying parameters [8], [9]. The recursive DFT principlecan also be integrated with other techniques, such as the de-composition of single-phase voltage systems into orthogonalcomponents and the least square (LS) to track the time-varyingparameters [10]. However, the LS technique cannot deal witha singular matrix [11] and the recursive DFT is affected byaccumulation errors [7]. Nevertheless, the recursive DFT canbe carefully coded to avoid the cumulative numerical precisionerrors [4], [12]. Due to the improved frequency resolution andno spectral leakage effect, the prony method (PM) can be usedto provide better results compared to the FFT [13]. However,the PM is not suitable for real-time estimation due to its highercomputational burden required for the rooting of a high-orderpolynomial.The Kalman filter (KF) is a potential technique for instanta-

neous tracking of the single-phase grid voltage parameters [14].Nevertheless, the KF is a computationally demanding techniquefor real-time applications. The computationally efficient phase-locked loop (PLL) can be useful for instantaneous tracking ofthe single-phase grid voltage fundamental parameters [15], [16].However, the presence of harmonics introduces ripples into theestimated parameters [17], [18]. The ripples can be rejected byusing in-loop filters which may reduce the bandwidth of thePLL, thus leading to a slower dynamic response [19]. PLL sys-tems also require quadrature voltage waveforms and there isless information in single-phase systems than in three phase sys-tems for generating the quadrature voltagewaveforms. A single-phase quadrature signal generator (QSG) relying on a second-order generalized integrator (SOGI) can be used to implementthe PLL (SOGI-PLL) [20], [21]. Another drawback of the PLLis that the phase and frequency are estimated within a singleloop which causes large frequency transient during phase jumpsunder grid faults [22]. The effect of this undesired frequencyswing is also reflected back on the phase estimation and, hence,causes delay in the process of synchronization [22]. The fre-quency swing can be reduced by means of a frequency-locked

0885-8977 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

REZA et al.: ACCURATE ESTIMATION OF SINGLE-PHASE GRID VOLTAGE PARAMETERS UNDER DISTORTED CONDITIONS 1139

loop (FLL) based on the QSG-SOGI (SOGI-FLL) [1], [23],[24]. A network consisting of an FLL and multiple QSG-SOGI(MSOGI) connected in parallel can be used to reject the har-monics effect [24]. However, the MSOGI technique is sensitiveto the presence of dc offset [25], [26].The technical literature shows that the standard PLL,

SOGI-FLL and SOGI-PLL techniques require proper tuningfor tracking the grid voltage dynamics and for rejecting thenegative effects caused by harmonics. A narrow bandwidth hasto be chosen for the rejection of harmonics at the expense of aslower dynamic response. Moreover, there are interdependentloops and, hence, each loop influences the other one at thesame time. As a result, the tuning of the controller parametersis more sensitive, thus reducing the stability margins. In orderto remove the previously mentioned shortcomings, a separatefrequency estimation technique can be used to obtain the tuningfrequency of the QSG-SOGI. For this purpose, a frequencyestimation technique relying on three consecutive samplesof the filtered grid voltage waveform can be used [27][31].However, the three consecutive samples-based technique isill-conditioned when the instantaneous value of the middlesample is zero [31]. Nevertheless, the ill-condition can be re-moved by holding the previously estimated frequency when theinstantaneous value of the middle sample is zero [31]. The threeconsecutive samples-based technique also presents large over-shoot/undershoot during transients. Moreover, the performanceof the three consecutive samples-based technique is affectedif the dc offset and harmonics are not properly rejected byfiltering. Therefore, a fixed-size window-based DFT technique[32], which is used in [8] and [9], for tracking the frequency ofa three-phase system can be used to obtain the single-phase gridvoltage frequency which is used by the QSG-SOGI to trackthe grid voltage fundamental amplitude [33]. The performanceof the fixed window DFT-based QSG-SOGI (DFT-SOGI)technique is discussed in [33] by using simulation results inMATLAB/Simulink. However, the real-time experimentalverification is not reported in [33].The objective of this paper is to report an accurate estimation

technique (DFT-SOGI) and its implementation on a real-timeexperimental setup. In the DFT-SOGI technique, the spectralleakage property of the fixed window DFT is used to track thetime-varying single-phase grid voltage fundamental frequencywhich is used as a tuning frequency for the QSG-SOGI. The sizeof the DFTwindow is chosen based on nominal fundamental pe-riods. The trigonometric functions required for DFT operationcan be estimated offline and, hence, can be stored for real-timeapplications. The DFT operation is less sensitive to the presenceof harmonics, thus providing improved estimation of frequencycompared to the SOGI-FLL [1] and SOGI-PLL [21] techniques.Moreover, unlike the SOGI-PLL and SOGI-FLL techniques,the DFT-SOGI technique does not produce any interdependentloops, thus offering an easy tuning process.The rest of the paper is organized as follows. In Section II,

the DFT-SOGI technique is briefly described. Simulationresults are presented in Section III. Section IV contains theexperimental performance comparison of the DFT-SOGI,SOGI-FLL and SOGI-PLL techniques. Finally, the conclusionsof this paper are summarized in Section V.

Fig. 1. DFT-SOGI technique for tracking the single-phase grid voltage funda-mental frequency and amplitude.

II. DFT-SOGI TECHNIQUEThe single-phase grid voltage waveform , distorted by

harmonics at the sampling instant, can be expressed by

(1)

where and are the maximum order of harmonics and sam-pling period, respectively, and ,and are the amplitude, instantaneous, and initial phase angleof the frequency component ( and

), respectively.The DFT-SOGI technique, as shown in Fig. 1, is used to

estimate the single-phase grid voltage fundamental amplitudeand frequency, where and are the estimatedfrequency, amplitude, phase angle, in-phase, and in-quadraturecomponents of the fundamental voltage waveform, respec-tively. As can be seen, the QSG-SOGI provides the orthogonalcomponents of the fundamental voltage waveform at thetuning frequency estimated by the DFT. A moving averagefilter (MAF) is used to remove the ripples from the estimatedamplitude. The window size of the MAF is updated using theestimated frequency. The DFT-SOGI technique is designed formonitoring the voltage of the distribution electricity networkwhere the fundamental frequency does not vary significantlyfrom its nominal value. According to the European standardEN-50160 [34], under normal operating conditions, the meanvalue of the fundamental frequency measured over 10 s shallbe within a range of 50 Hz 6 4% (i.e., 47 to 52 Hz) during100% of the time, for systems with a synchronous connection toan interconnected system. Therefore, the DFT-SOGI techniqueis used to estimate the fundamental voltage amplitude and thefrequency range of 47 to 52 Hz.

A. Estimation of Grid Voltage FrequencyA fixed-size window with a fixed sampling frequency

is used in the DFT operation to track the time-varyinggrid voltage fundamental frequency. The window size of theDFT is chosen based on nominal fundamental frequency .During the time-varying cases, the fixed-size window of theDFT causes spectral leakage and, hence, the actual spectrumof one frequency spreads its energy to its neighbor frequencies[6]. The time-varying grid voltage fundamental frequency canbe estimated adaptively using the spectral leakage information[8], [9], [32], [33]. The short range of leakage is preferred toestimate the grid voltage fundamental frequency, as it spreadsenergy in a short range of neighboring frequencies [8], [9]. Forlong-range leakage, large errors may be incurred due to the in-terference caused by neighboring harmonics [8], [9]. To avoidlong-range leakage, a Hanning window can be used to obtain a


smooth truncation of the analyzed portion of the grid voltagewaveform. The DFT of the Hanning windowed grid voltagewaveform can be expressed by

(2)

where; and are the constant integer number of voltage samples;number of nominal fundamental voltage cycles; frequency reso-lution; frequency index and complex operator, respectively; and

is the Hanning window as given by

(3)

From the DFT operation, as given by (2), the amplitudes corre-sponding to the nominal fundamental frequencyand two neighbor frequencies, such asand , are estimated. These three esti-mated amplitudes can be used to obtain the actual fundamentalfrequency and are given by [8], [9], [32], and [33]

(4)where

and is the estimated amplitude at the frequency . Themathematical derivation of for the window size of sam-ples is reported in[8] and [32]. The actual fundamental frequency is higher thanthe nominal value when the amplitude at the frequency

is higher than the amplitude at the frequencyand vice-versa, as shown in cases I and II of Fig. 2, respec-tively. In the DFT operation with a fixed-size window, the fre-quency deviation tracking range can be expressed by

[8]. The frequency tracking range can also beincreased by incorporating more neighboring spectral lines atthe expense of higher computational burden [8].As the size of the window is fixed, the trigonometric functions

required for DFT operation can be estimated offline and can bestored for real-time applications. Therefore, the DFT operation,as given by (2), can also be expressed as

(5)

where

and . For constant values ofand , as expressed by (5), can be consideredas the output of a digital filter (DF) with constant coefficients

Fig. 2. Spectral leakage property of the fixed window DFT operation duringthe time-varying cases, where is the amplitude at the frequency .

Fig. 3. Digital filter implementation of the fixed window DFT operation forfundamental frequency estimation.

given by , where is the input of the DF. The imple-mentation of the fixed-size window-based DFT operation fortracking the grid voltage frequency is shown in Fig. 3, wherethree DFT-based DFs are used to track the three spectral ampli-tudes, respectively. As can be noticed, the computational com-plexity of the presented frequency estimation technique mainlydepends on the implementation of three DFT-based DFs withconstant coefficients.The presented DFT-based frequency tracking strategy re-

quires a fixed-size memory buffer to store the samples ofthe grid voltage waveform. The sliding window strategy isfollowed to estimate the instantaneous fundamental frequencyand, hence, the memory buffer is updated at every new ac-quired sample and the oldest one is discarded. A large fixed-sizewindow improves the frequency resolution of the DFT at theexpense of higher computational burden and reduced frequencytracking range. Moreover, the large size window causes anarrower bandwidth of the DFT operation, as shown in Fig. 4and, hence, it degrades the dynamic response. On the otherhand, a small-size window improves the dynamic response dueto the higher bandwidth of DFT operation and decreases thecomputational burden, but it degrades the frequency resolu-tion. For small-size window-based DFT operation, harmonicsinterference may also occur due to the spectral line next tothe nominal fundamental frequency which might correspondto some harmonics [8], [9]. The choice of window size of theDFT also depends on the expected variation zone of the gridvoltage fundamental frequency. Thus, in order to estimate thetime-varying grid voltage fundamental frequency, a compro-mise is required when choosing the window size of the DFT.

B. Estimation of Grid Voltage Amplitude

In the DFT-SOGI technique, the fundamental voltage ampli-tude is estimated by an QSG-SOGI system whose tuning fre-quency is provided by the fixed window DFT operation as de-scribed earlier. The QSG-SOGI method is shown in Fig. 5(a),


Fig. 4. Magnitude responses of the different fixed-size window-based DFT op-eration at the nominal fundamental frequency (50 Hz).

Fig. 5. (a) Quadrature signal generator based on the second-order generalizedintegrator. (b) Discrete implementation of the third-order integrator.

where the tuning frequency sets the resonance fre-quency of the SOGI and the gain determines the bandwidthof the in-phase component and the static gain of the in-quadra-ture component [1], [21], [23], [24]. The transfer functions ofthe SOGI, in-phase, and in-quadrature components of the QSG-SOGI are given by (6)(8), respectively

(6)

(7)

(8)

The bode plots of (7) and (8) are shown in Figs. 6(a) and(b), respectively, where the transfer functions (7) and (8) behavelike a band-pass filter (BPF) and a low-pass filter (LPF), respec-tively. It can be seen from Fig. 6 that a tradeoff is required be-tween good dynamics and harmonics rejection capability whenchoosing the value of , where and represent thedamping factor of the QSG-SOGI [1], [21], [23], [24]. There-fore, the instantaneous estimation of the fundamental voltageamplitude and phase angle by the QSG-SOGI can be expressedby (9) and (10), respectively

(9)

(10)

The discrete implementation of the SOGI is presented inFig. 5(a), where the integrator blocks are replaced by thethird-order integrator shown in Fig. 5(b). The QSG-SOGIbased on third-order integrators provides more accurate re-sults compared to the QSG-SOGI relying on Euler, Tustin, orsecond-order integrators and, hence, the third-order integratorsare used for discrete implementation of the SOGI [21], [35],[36].

Fig. 6. Bode plots of the (a) in-phase transfer function and (b)in-quadrature transfer function of the QSG-SOGI, whererad/s.

Fig. 7. Block diagram of the MAF.

The estimation of the fundamental voltage amplitude using(9) may contain ripples due to the presence of harmonics anddc offset. The MAF, as shown in Fig. 7, is used to remove theripples from the estimated amplitude, where deter-mines the window size of the MAF and . Thevalue of is made equal to the fundamental frequency to re-ject the ripples at the fundamental and harmonic frequencies.The third-order integrator, as shown in Fig. 5(b), is also usedfor discrete implementation of the MAF. The value of canbe noninteger, that is, , where is a positiveinteger and . Linear interpolation is used to obtainthe value of and is given by [31]

(11)

III. SIMULATION RESULTS

To evaluate the performance of the fixed-size window-basedDFT operation, a step change of frequency is considered in thegrid voltage fundamental component. The effect of the differentfixed-size window in the DFT operation for frequency estima-tion is shown in Fig. 8, where 1-Hz step change of frequencyoccurs at 1 s. As can be seen, the presented DFT oper-ation provides faster response for the smaller size window andvice-versa. However, DFT operation with a smaller size window


Fig. 8. Frequency step (50 to 51 Hz) estimation using DFT operation with adifferent fixed-size window.

Fig. 9. Steady-state error of the estimated frequency using DFT operation witha different fixed-size window.

produces higher ripples for offnominal frequency (51 Hz) esti-mation, as depicted by the magnified plots in Fig. 8.The IEEE standard C37.118.1 [37] specifies the fundamental

frequency range of 50 Hz 5 Hz (45 to 55 Hz) for an M classphasor measurement unit (PMU) [38], [39]. The estimatedsteady-state frequency error for the fundamental frequencyrange of 45 to 55 Hz by using DFT operation with a differentfixed-size window is shown in Fig. 9. As can be noticed, thewindow size that is equal to three nominal fundamental cyclescan be used to estimate the fundamental frequency range of47 to 52 Hz, as specified by the standard EN-50160, with asteady-state error of less than 0.01 Hz. Therefore, in this paper,the DFT with a window size that is equal to three nominal fun-damental cycles is used to estimate the fundamental frequencyrange of 47 to 52 Hz.In the presented DFT-SOGI technique, the QSG-SOGI pro-

vides errors in the amplitude and phase-angle estimation duringthe inaccurate tuning frequency. Figs. 10 and 11 show the am-plitude and phase-angle estimation errors due to the inaccuratetuning frequency of the QSG-SOGI for 2-Hz and 3-Hz fre-quency steps, respectively, where 3, and .As can be seen, the DFT operation takes some time to esti-mate the frequency steps and, hence, the tuning frequency of theQSG-SOGI is not equal to the input voltage frequency duringdynamics. It can also be observed that the estimated errors dis-appear when the tuning frequency of the QSG-SOGI estimatedby DFT operation is equal to the input voltage frequency. How-ever, the MAF introduces an additional delay to remove the esti-mated amplitude errors, as can also be noticed from Figs. 10(b)and 11(b), respectively.

Fig. 10. Effects of the inaccurate frequency tracking on the amplitude andphase-angle estimation. (a) Frequency step from 50 to 52 Hz. (b) Fundamentalvoltage amplitude error. (c) Phase-angle error.

Fig. 11. Effects of the inaccurate frequency tracking on the amplitude andphase-angle estimation. (a) Frequency step from 50 to 47 Hz. (b) Fundamentalvoltage amplitude error. (c) Phase-angle error.

IV. REAL-TIME EXPERIMENTAL RESULTS

The performance of the DFT-SOGI technique is comparedwith the SOGI-FLL and SOGI-PLL techniques on a real-timeexperimental setup. Similar to the DFT-SOGI technique,the frequency-adaptive MAF filter is also included in theSOGI-FLL and SOGI-PLL techniques for rejecting amplituderipples. The real-time experimental setup is shown in Fig. 12,which consists of hardware and software parts. The hardwarepart contains a programmable ac power supply, voltage sensor,dSPACE1103 (DS1103) control board, and a personal computer(PC). The programmable ac power supply is used to generatethe real-time single-phase grid voltage waveform ( , wheresubscript indicates line to neutral) under different condi-tions, such as harmonics, frequency drifts, voltage sag, andvoltage flicker. The voltage sensor measures the voltage andsends it to the 16-b analog-to-digital converter (ADC) of theDS1103 control board. On the other hand, the software partcontains MATLAB/Simulink, DS1103 Real-Time Interface


Fig. 12. Laboratory setup for the real-time experiment.

TABLE IPARAMETERS OF DFT-SOGI, SOGI-FLL, AND SOGI-PLL TECHNIQUES

(RTI) and Control Desk Interface. The DFT-SOGI, SOGI-FLL,and SOGI-PLL techniques for single-phase systems are im-plemented in a single MATLAB/Simulink model which isuploaded to the DS1103 control board using automatic codegeneration. The Control Desk Interface running on the PC isused to control the parameters in real time and to monitor theestimated values.The parameters, as specified in Table I, are tuned so that ap-

proximately an equal settling time is obtained for the presentedtechniques. The nominal grid voltage and sampling frequenciesare chosen to be 50Hz and 10 kHz, respectively. The amplitudesof the grid voltagewaveforms are considered on a per-unit basis.The grid voltage fundamental component presented in all casestudies is distorted by 0.05 p.u. of the 3rd, 0.05 p.u. of the 5th,0.05 p.u. of the 7th, and 0.05 p.u. of the 9th harmonic, leadingto a total harmonic distortion (THD) of 10%.Case-1: Steady State With Harmonics: The steady-state

grid voltage waveform, as shown in Fig. 13(a), contains10% THD. The estimations of the fundamental voltageamplitude, frequency, and phase-angle error by using theDFT-SOGI, SOGI-FLL, and SOGI-PLL techniques are de-picted in Fig. 13(b)(d), respectively. As can be seen, theamplitude and frequency estimations at steady state using theDFT-SOGI technique are less affected by the harmonic contentcompared to the SOGI-FLL and SOGI-PLL techniques. Sincethe SOGI-FLL and SOGI-PLL techniques provide large ripplesin frequency estimation, the MAF cannot reject the amplituderipples effectively compared to the DFT-SOGI technique whichcan be noticed in Fig. 13(b). On the other hand, the presentedtechniques provide little phase-angle error due to the presenceof harmonics, as can be seen in Fig. 13(d).Case-2: Frequency SweepWith Harmonics: In a real network

scenario, the grid frequency varies slowly due to the large inertiaof the rotating shaft of power generators [38], [39]. A 10-Hz/sfrequency sweep with a duration of 0.2 s is considered in thegrid voltage waveform containing 10% THD. The estimationsof the fundamental voltage amplitude, frequency sweep, andphase-angle error by the investigated techniques are shown inFig. 14. As can be seen, the DFT-SOGI technique can track thefrequency sweep accurately while being less affected by har-monics compared to the SOGI-FLL and SOGI-PLL techniques.On the other hand, all of the presented techniques provide smallamplitude error due to the inaccurate tuning frequency of theQSG-SOGI during the frequency-sweep condition. The esti-mated phase-angle errors are also similar for the presented tech-niques, as can be noticed in Fig. 14(c).

Fig. 13. Case-1: Steady state with harmonics. (a) Grid voltage waveform.(b) Fundamental voltage amplitude. (c) Fundamental frequency. (d) Phase-angleerror.

Fig. 14. Case-2: Frequency sweep with harmonics. (a) Fundamental voltageamplitude. (b) Fundamental frequency. (c) Phase-angle error.

Case-3: Frequency Step With Harmonics: For this case,a worst case scenario of grid frequency variation, such as astep change, is considered for comparing the performance ofthe DFT-SOGI, SOGI-FLL, and SOGI-PLL techniques. Thefrequency step could also be observed in a stand-alone or asmall microgrid system. Fig. 15 illustrates the estimations offundamental voltage amplitude, 3-Hz frequency step, andphase-angle error by using the presented techniques, where the


Fig. 15. Case-3: Frequency step with harmonics. (a) Fundamental voltage am-plitude. (b) Fundamental frequency. (c) Phase-angle error.

grid voltage waveform contains 10% THD. It can be seen inFig. 15(b) that the DFT-SOGI technique takes an equal settlingtime for tracking the frequency step and is less disturbed byharmonics compared to the SOGI-FLL and SOGI-PLL tech-niques. Similar to simulation results presented in Fig. 11(b), theDFT-SOGI technique provides 0.05-p.u. amplitude error duringthe 3-Hz frequency step, as can be noticed in Fig. 15(a). Onthe other hand, phase-angle estimation is affected due to thefrequency step for all of the presented techniques, as can beobserved in Fig. 15(c).Case-4: Voltage Flicker With Harmonics: In this case,

voltage flicker is introduced in the grid voltage waveformcontaining 10% THD, as shown in Fig. 16(a). The frequencyand the amplitude of the triangular voltage flicker are 2.5 Hzand 0.05 p.u., respectively. The estimations of fundamentalamplitude, frequency, and phase-angle error are shown inFig. 16(b)(d), respectively. As can be seen, the presentedtechniques can track the voltage flicker accurately. However,the performance of the DFT-SOGI technique for amplitude andfrequency estimation is less affected by harmonics comparedto the SOGI-FLL and SOGI-PLL techniques. It can be seenfrom Fig. 16(d) that the presented techniques provide similarphase-angle estimation error during the voltage flicker andharmonic conditions.Case-5: Voltage Sag With Harmonics: A voltage sag of 50%

and 10% THD is shown in Fig. 17(a). The estimations of thefundamental amplitude, frequency, and phase-angle error byusing the DFT-SOGI, SOGI-FLL, and SOGI-PLL techniquesare shown in Fig. 17(b)(d), respectively. As can be noticed,the presented techniques can track the voltage sag accurately.However, it can be noticed from Fig. 17(c) that the DFT-SOGItechnique presents less overshoot/undershoot in the frequencyestimation during voltage sag compared to the SOGI-FLL andSOGI-PLL techniques. On the other hand, the performanceof the presented techniques for phase-angle estimation is alsoaffected by voltage sag, as can be observed in Fig. 17(d).Case-6: DC Offset With Harmonics: In this case, 5% DC

offset is added with the grid voltage waveform containing 10%THD and is shown in Fig. 18(a). The estimated fundamental

Fig. 16. Case-4: Voltage flicker with harmonics. (a) Grid voltage waveform.(b) Fundamental voltage amplitude. (c) Fundamental frequency. (d) Phase-angleerror.

Fig. 17. Case-5: Voltage sag with harmonics. (a) Grid voltage waveform. (b)Fundamental voltage amplitude. (c) Fundamental frequency. (d) Phase-angleerror.

voltage amplitude, frequency, and phase-angle error by usingthe presented techniques are depicted in Fig. 18(b)(d), respec-tively. As can be seen, the performance of the DFT-SOGI tech-nique for amplitude and frequency estimation is less sensitiveto the presence of the dc offset and harmonics compared to theSOGI-FLL and SOGI-PLL techniques. However, it can be ob-served from Fig. 18(d) that the phase-angle estimation by using


Fig. 18. Case-6: dc offset with harmonics. (a) Grid voltage waveform. (b) Fun-damental voltage amplitude. (c) Fundamental frequency. (d) Phase-angle error.

the presented techniques is affected due to the presence of dcoffset and harmonics.Computational Burden Comparison: It can be seen from the

experimental results presented in case studies 16 that the per-formance of the DFT-SOGI technique for frequency estimationis less affected by the presence of harmonics compared to theSOGI-FLL and SOGI-PLL techniques. In addition, the DFT-SOGI technique avoids the use of interdependent loops. Onthe other hand, all of these advantages of using the DFT-SOGItechnique come at the expense of being more computationallydemanding compared to the SOGI-FLL and SOGI-PLL tech-niques. Although the presented fixed-size window-based DFToperation does not require the evaluation of trigonometric func-tions in real time, the use of three high-order DFT filters in-creases the computational burden of the DFT-SOGI techniquecompared to the SOGI-FLL and SOGI-PLL techniques. There-fore, a compromise is made between high-accuracy frequencyestimation and digital resources consumption.

V. CONCLUSIONThis paper presents a DFT-based QSG-SOGI technique to

estimate the fundamental voltage amplitude and frequencyfrom a distorted grid voltage waveform. The DFT operationdoes not need to adjust the window size corresponding tothe actual frequency. The fixed-size window based on nom-inal fundamental periods enables offline computation of thetrigonometric functions required for DFT operation. The use ofthree high-order DFT filters increases the computational burdenof the DFT-SOGI technique compared to the SOGI-FLL andSOGI-PLL techniques. However, frequency estimation usingthe DFT-SOGI technique is less sensitive to the presence ofharmonics and does not depend on the generation of the quadra-ture waveforms compared to the SOGI-FLL and SOGI-PLLtechniques. Moreover, unlike the SOGI-FLL and SOGI-PLL

techniques, the DFT-SOGI technique does not create any in-terdependent loops, thus increasing overall stability and easingthe tuning process.

REFERENCES[1] P. Rodriguez, A. Luna, R. S. Munoz-Aguilar, I. Etxeberria-Otadui, R.

Teodorescu, and F. Blaabjerg, A stationary reference frame grid syn-chronization system for three-phase grid-connected power convertersunder adverse grid conditions, IEEE Trans. Power Electron., vol. 27,no. 1, pp. 99112, Jan. 2012.

[2] R. M. S. Filho, P. F. Seixas, P. C. Cortizo, L. A. B. Torres, and A. F.Souza, Comparison of three single-phase PLL algorithms for UPS ap-plications, IEEE Trans. Ind. Electron., vol. 55, no. 8, pp. 29232932,Aug. 2008.

[3] L. Asiminoaei, F. Blaabjerg, and S. Hansen, Detection is keyHar-monic detection methods for active power filter applications, IEEEInd. Appl. Mag., vol. 13, no. 2, pp. 2233, Jul./Aug. 2007.

[4] A. J. Roscoe, G. M. Burt, and J. R. McDonald, Frequency and fun-damental signal measurement algorithms for distributed control andprotection applications, IET Gen. Transm. Distrib., vol. 3, no. 5, pp.485495, 2009.

[5] E. Jacobsen and R. Lyons, The sliding DFT, IEEE Signal Proc. Mag.,vol. 20, no. 2, pp. 7480, Mar. 2003.

[6] A. A. Girgis and F. M. Ham, A quantitative study of pitfalls in theFFT, IEEE Trans. Aerosp. Electron. Syst., vol. AES-16, no. 4, pp.434439, Jul. 1980.

[7] H. A. Darwish and M. Fikri, Practical considerations for recursiveDFT implementation in numerical relays, IEEE Trans. Power Del.,vol. 22, no. 1, pp. 4249, Jan. 2007.

[8] E. Lavopa, P. Zanchetta, M. Sumner, and F. Cupertino, Real-time esti-mation of fundamental frequency and harmonics for active shunt powerfilters in aircraft electrical systems, IEEE Trans. Ind. Electron., vol.56, no. 8, pp. 28752884, Aug. 2009.

[9] F. Cupertino, E. Lavopa, P. Zanchetta, M. Sumner, and L. Salvatore,Running DFT-based PLL algorithm for frequency, phase, and ampli-tude tracking in aircraft electrical systems, IEEE Trans. Ind. Electron.,vol. 58, no. 3, pp. 10271035, Mar. 2011.

[10] I. Sadinezhad and V. G. Agelidis, Frequency adaptive least-squares-Kalman technique for real-time voltage envelope and flicker estima-tion, IEEE Trans. Ind. Electron., vol. 59, no. 8, pp. 33303341, Aug.2012.

[11] M. S. Reza, M. Ciobotaru, and V. G. Agelidis, Accurate estimationof grid voltage parameters using singular value decomposition tech-nique, inProc. 3rd IEEE Symp. Power Elect. Distrib. Gen. Syst., 2012,pp. 794800.

[12] A. J. Roscoe, I. F. Abdulhadi, and G. M. Burt, P and M class phasormeasurement unit algorithms using adaptive cascaded filters, IEEETrans. Power Del., vol. 28, no. 3, pp. 14471459, Jul. 2013.

[13] M. S. Reza, M. Ciobotaru, and V. G. Agelidis, Power quality analysisusing piecewise adaptive Pronys method, in Proc. of IEEE Int. Conf.Ind. Tech., 2012, pp. 926931.

[14] M. S. Reza, M. Ciobotaru, and V. G. Agelidis, Instantaneous powerquality analysis using frequency adaptive Kalman filter technique, inProc. IEEE Int. Power Elect. Motion Cont. Conf. -ECCE Asia, 2012,pp. 8187.

[15] M. Karimi-Ghartemani, H. Karimi, and M. R. Iravani, A magni-tude/phase-locked loop system based on estimation of frequency andin-phase/quadrature-phase amplitudes, IEEE Trans. Ind. Electron.,vol. 51, no. 2, pp. 511517, Apr. 2004.

[16] M. Karimi-Ghartemani and M. R. Iravani, Robust and fre-quency-adaptive measurement of peak value, IEEE Trans. PowerDel., vol. 19, no. 2, pp. 481489, Apr. 2004.

[17] S.-K. Chung, Phase-locked loop for grid-connected three-phasepower conversion systems, Proc. Inst. Elect. Eng., Elect. Power App.,vol. 147, no. 3, pp. 213219, 2000.

[18] M. Karimi-Ghartemani and M. R. Iravani, Measurement of har-monics/inter-harmonics of time-varying frequencies, IEEE Trans.Power Del., vol. 20, no. 1, pp. 2331, Jan. 2005.

[19] M. Karimi-Ghartemani, S. A. Khajehoddin, P. K. Jain, and A.Bakhshai, Derivation and design of in-loop filters in phase-lockedloop systems, IEEE Trans. Instrum. Meas., vol. 61, no. 4, pp.930940, Apr. 2012.

[20] B. Burger and A. Engler, Fast signal conditioning in the single phasesystems, presented at the Eur. Conf. Power Elect. Appl., Graz, Austria,2001.


[21] M. Ciobotaru, R. Teodorescu, and F. Blaabjerg, A new single-phasePLL structure based on second order generalized integrator, in Proc.37th IEEE Power Electron. Spec. Conf., 2006, pp. 16.

[22] M. K. Ghartemani, S. A. Khajehoddin, P. K. Jain, and A. Bakhshai,Problems of startup and phase jumps in PLL systems, IEEE Trans.Power Electron., vol. 27, no. 4, pp. 18301838, Apr. 2012.

[23] P. Rodriguez, A. Luna, M. Ciobotaru, R. Teodorescu, and F. Blaabjerg,Advanced grid synchronization system for power converters underunbalanced and distorted operating conditions, in Proc. IEEE 32ndAnnu. Conf. Ind. Elect., 2006, pp. 51735178.

[24] P. Rodriguez, A. Luna, I. Candela, R. Mujal, R. Teodorescu, and F.Blaabjerg, Multiresonant frequency-locked loop for grid synchroniza-tion of power converters under distorted grid conditions, IEEE Trans.Ind. Electron., vol. 58, no. 1, pp. 127138, Jan. 2011.

[25] M. Ciobotaru, R. Teodorescu, and V. G. Agelidis, Offset rejectionfor PLL based synchronization in grid-connected converters, in Proc.IEEE 23rd Annu. App. Power Elect. Conf. Expo., 2008, pp. 16111617.

[26] M. Karimi-Ghartemani, S. A. Khajehoddin, P. K. Jain, A. Bakhshai,and M. Mojiri, Addressing DC component in PLL and notch filteralgorithms, IEEE Trans. Power Electron., vol. 27, no. 1, pp. 7886,Jan. 2012.

[27] M. D. Kusljevic, A simple recursive algorithm for frequency estima-tion, IEEE Trans. Instrum. Meas., vol. 53, no. 2, pp. 335340, Apr.2004.

[28] A. Lopez, J.-C. Montano, M. Castilla, J. Gutierrez, M. D. Borras, and J.C. Bravo, Power system frequency measurement under nonstationarysituations, IEEE Trans. Power Del., vol. 23, no. 2, pp. 562567, Apr.2008.

[29] M. D. Kusljevic, A simple recursive algorithm for simultaneous mag-nitude and frequency estimation, IEEE Trans. Instrum. Meas., vol. 57,no. 6, pp. 12071214, Jun. 2008.

[30] M. D. Kusljevic, J. J. Tomic, and L. D. Jovanovic, Frequency esti-mation of three-phase power system using weighted-least-square algo-rithm and adaptive FIR filtering, IEEE Trans. Instrum. Meas., vol. 59,no. 2, pp. 322329, Feb. 2010.

[31] P. Roncero-Sanchez, X. del Toro Garcia, A. P. Torres, and V. Feliu,Robust frequency-estimation method for distorted and imbalancedthree-phase systems using discrete filters, IEEE Trans. Power Elec-tron., vol. 26, no. 4, pp. 10891101, Apr. 2011.

[32] G. Andria, A. DellAquila, and L. Salvatore, Analysis of distorted un-balanced waveforms in inverter drives, IEEE Trans. Power Electron.,vol. 4, no. 2, pp. 298310, Apr. 1989.

[33] M. S. Reza, M. Ciobotaru, and V. G. Agelidis, Tracking of time-varying grid voltage using DFT based second order generalized inte-grator technique, in Proc. IEEE Int. Conf. Power Sys. Tech., 2012, pp.16.

[34] Voltage Characteristics of Electricity Supplied by Public DistributionSystems, European Standard EN-50160, 1999.

[35] F. J. Rodriguez, E. Bueno, M. Aredes, L. G. B. Rolim, F. A. S. Neves,and M. C. Cavalcanti, Discrete-time implementation of second ordergeneralized integrators for grid converters, in Proc. IEEE 34th Annu.Conf. Ind. Electron., 2008, pp. 176181.

[36] A. G. Yepes, F. D. Freijedo, J. Doval-Gandoy, O. Lopez, J. Malvar,and P. Fernandez-Comesana, Effects of discretization methods on theperformance of resonant controllers, IEEE Trans. Power Electron.,vol. 25, no. 7, pp. 16921712, Jul. 2010.

[37] IEEE Standard for Synchrophasor Measurements for Power Systems,IEEE Standard C37.118.1, 2011.

[38] I. Kamwa, M. Leclerc, and D. McNabb, Performance of demodula-tion-based frequency measurement algorithms used in typical PMUs,IEEE Trans. Power Del., vol. 19, no. 2, pp. 505514, Apr. 2004.

[39] I. Kamwa, S. R. Samantaray, andG. Joos, Wide frequency range adap-tive phasor and frequency PMU algorithms, IEEE Trans. Smart Grid,2013, to be published.

Md. Shamim Reza (S11) was born in Magura,Bangladesh. He received the B.Sc. and M.Sc. de-grees in electrical and electronic engineering (EEE)from Bangladesh University of Engineering andTechnology (BUET), Dhaka, Bangladesh, in 2006and 2008, respectively, and is currently pursuingthe Ph.D. degree in electrical engineering at TheUniversity of New South Wales (UNSW), Sydney,NSW, Australia.His research interests include adaptive and digital

signal processing, monitoring of power quality, andsmart metering in smart-grid power systems.

Mihai Ciobotaru (S04M08) was born in Galati,Romania. He received the B.Sc. andM.Sc. degrees inelectrical engineering from the University of Galati,Galati, Romania, in 2002 and 2003, respectively, andthe Ph.D. degree in electrical engineering from theInstitute of Energy Technology, Aalborg University,Aalborg, Denmark, in 2009.From 2003 to 2004, he was an Associate Lecturer

at the University of Galati. From 2007 to 2010, hewas an Associate Research Fellow at the Institute ofEnergy Technology, Aalborg University. From 2010

to 2013, he was a Research Fellow at the School of Electrical Engineering andTelecommunications, University of New South Wales (UNSW), Sydney, Aus-tralia. Currently, he is a Senior Research Associate with the UNSW, performinghis research activities under the Australian Energy Research Institute. His mainresearch activities and interests are in grid integration of PV systems, controldesign of grid-connected power converters, power management of hybrid en-ergy-storage systems, multilevel converters, and estimation of grid voltage pa-rameters in single- and three-phase systems.

Vassilios G. Agelidis (S89M91SM00) was bornin Serres, Greece. He received the B.Eng. degree inelectrical engineering from the Democritus Univer-sity of Thrace, Thrace, Greece, in 1988, the M.S. de-gree in applied science from Concordia University,Montreal, QC, Canada, in 1992, and the Ph.D. degreein electrical engineering from the Curtin University,Perth, WA, Australia, in 1997.From 1993 to 1999, he was with the School

of Electrical and Computer Engineering, CurtinUniversity. In 2000, he joined the University of

Glasgow, Glasgow, U.K., as a Research Manager for the Glasgow-Strath-clyde Centre for Economic Renewable Power Delivery. In addition, he hasauthored/co-authored several journal and conference papers as well as PowerElectronic Control in Electrical Systems in 2002. From 2005 to 2006, he wasthe inaugural Chair of Power Engineering in the School of Electrical, Energyand Process Engineering, Murdoch University, Perth. From 2006 to 2010,he was the Energy Australia Chair of Power Engineering at the Universityof Sydney, Sydney, Australia. Currently, he is the Director of the AustralianEnergy Research Institute, The University of New South Wales, Sydney,N.S.W., Australia.Dr. Agelidis received the Advanced Research Fellowship from the United

Kingdoms Engineering and Physical Sciences Research Council in 2004.He was the Vice President of Operations within the IEEE Power ElectronicsSociety for 20062007. He was an Associate Editor of the IEEE POWERELECTRONICS LETTERS from 2003 to 2005, and served as the Power Elec-tronics Society (PELS) Chapter Development Committee Chair from 2003to 2005. He was an AdCom Member of IEEE PELS for 20072009 andthe Technical Chair of the 39th IEEE Annual Power Electronics SpecialistsConference, Rhodes, Greece.

4. ieee transactions on power delivery volume 29 issue 3 2014 [doi 10.1109%2ftpwrd.2014.2303482]...

Documents