a method for synchronization

8/13/2019 A Method for Synchronization

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IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 19, NO. 3, AUGUST 2004 1263

A Method for Synchronization of PowerElectronic Converters in Polluted and

Variable-Frequency EnvironmentsMasoud Karimi-Ghartemani , Member, IEEE, and M. Reza Iravani , Fellow, IEEE

Abstract—This paper presents a new synchronization methodwhich employs an enhanced phase-locked loop (EPLL) system.The operational concept of the EPLL is novel and based ona nonlinear dynamical system. As compared with the existingsynchronization methods, the introduced EPLL-based syn-chronization method provides higher degree of immunity andinsensitivity to noise, harmonics and other types of pollutionsthat exist in the signal used as the basis of synchronization. Thesalient feature of the EPLL-based synchronization method overconventional synchronization methods is its frequency adaptivitywhich permits satisfactory operation when the centre frequency

of the base signal varies. The proposed EPLL-based method of synchronization is also capable of coping with the unbalancedsystem scenarios. Structural simplicity of the EPLL-based methodgreatly simplifies its implementation in digital software and/orhardware environments as an integral part of a digital controlplatform for power electronic converters. The primary applicationof the proposed synchronization method is for the distributedgeneration units, e.g., wind generation systems, which utilizepower electronic converters as an integral part of their systems.

Index Terms—Distributed generators, phase angle estimation,synchronization, PLL, power systems.

I. INTRODUCTION

INTERFACING power electronic converters to the utilitygrid, particularly at medium and high voltages, necessitates

proper synchronization for the purpose of operation andcontrol of the power electronic based apparatus [1], [2]. Thesynchronization is usually carried out with respect to the phaseangle of voltage (or current) signal(s) of the utility system.The signal(s) used for synchronization are often corrupted byharmonics, voltage sags and swells, commutation notches,noise, phase angle jump and unbalanced operating conditions[3]–[8]. A desired synchronization method must detect thephase of the utility signal as fast as possible while adequatelyeliminating the impacts of corrupting sources on the signal.The synchronization process should be updated not only at thesignal zero-crossing, but continuously over the fundamental

period of the signal [1].The need for improvements in the existing converter syn-

chronization approaches stems from rapid proliferation of distributed generation (DG) units in electric networks. Aconverter-interfaced DG unit, e.g., a wind generator unit, a

Manuscript received August 20, 2003.The authors are with the Centre for Applied Power Electronics (CAPE),

Department of Electrical and Computer Engineering, University of Toronto,Toronto, ON M5S 3G4, Canada (e-mail: [email protected]; [email protected]).

Digital Object Identifier 10.1109/TPWRS.2004.831280

photovoltaic-based unit and a micro-turbine-generator unit,under both grid-connected and micro-grid (islanding) scenariosrequires converter synchronization under polluted and/orvariable -frequency environment.

This paper presents a new synchronization method which notonly demonstrates a superior performance as compared with theexisting methods with respect to corrupting factors of the signal,it also provides frequency adaptivity and tolerance to unbal-anced system conditions. The main building block of the syn-chronization method is an enhanced phase-locked loop (EPLL)

systemwhich operates as a nonlinear dynamical system [9]. An-other salient feature of the proposed method is the simplicity of structure which renders itself for digital implementation in bothsoftware environment, e.g., a DSP, or a digital hardware envi-ronment, e.g., FPGA or ASIC, as an integral part of a digitalcontrol platform for power electronic converters.

The paper is organized as follows. Section II is devotedto a brief study of the existing synchronization schemes.They are categorized into two general branches of open-loopand closed-loop strategies. Principles of operation of fouropen-loop and two closed-loop methods are explained andtheir advantages and shortcomings are described. The proposedmethod of synchronization is presented in Section III. Sec-

tion IV is devoted to overview the EPLL system which is themain building block of the proposed synchronization method.Performance of the method is investigated with referenceto different conditions and its advantages over the existingmethods are shown in Section V. Some properties of the methodwhich make it advantageous for digital implementation areexplained in Section VI. Section VII provides a comparisonsummary and conclusions are stated in Section VIII.

II. EXISTING METHODS OF SYNCHRONIZATION

This section outlines various existing methods of synchro-

nization. They are categorized into open-loop and closed-loop

methods. Open-loop methods directly estimate phase angle of the voltage based on -frame signals. In closed-loop methods,

while the -frame voltages are being processed, the estimation

of the phase is adaptively updated through a loop mechanism.

This loop is aimed at locking the estimated value of the phase

angle to its actual value.

A. Open-Loop Synchronization Methods

In an ideal case that no distortion/unbalance is present,

represent the grid voltages for which the transformed

0885-8950/04$20.00 © 2004 IEEE


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KAR IM I- GHART EM ANI AND I RAVANI : A ME THOD FOR S YNCHRONI ZAT ION OF P OW ER ELE CT RONI C CONVERTE RS 1 265

Fig. 3. Block diagram of the three-phase PLL system.

should also take into account the PLL environment. More

specifically, distortion types, noise level, and the rates of phase

and frequency variations should not be overlooked.

2) Extended Three-Phase PLL-Based Method: The major

disadvantage of the three-phase PLL is its sensitivity to grid

voltage unbalance. Some attempts have been made to extendthis method for unbalanced voltages based on the concept of

symmetrical components.

Although the concept of symmetrical components is origi-

nally defined with respect to phasors, one can extend it to the

signals as functions of time. The idea is to replace the com-

plex phasor with a phase-shift operator in

time domain [6]. The phase-shift operator of 90-degree is easier

to implement [7]. Using , one

can derive the time-domain positive sequence components. The

time-domain positive sequence system is defined as

(2)

where superscript stands for the fundamental component

Rewriting (2) in terms of 90-degree phase-shift operator yields

(3)

In (3), is a 90-degree phase-shift operator. A block dia-

gram of the positive sequence extractor based on (3) is shown

in Fig. 4, [7]. This block diagram is a modified version of the

one presented in [7]. In [7], (5) does not fully take care of unbal-

ance. More specifically, it ignores the unbalance at some points.

The filters in Fig. 4 should be all-pass and generate a 90-degree

phase-shift at the center frequency . A simple first-order filter

such as can be used for this purpose.

The idea of using the positive sequence component for robust

phase detection, under unbalanced conditions, is conceptually

Fig. 4. Positive sequence extractor based on all-pass filters with 90-degreephase shift at the center frequency.

interesting. However, the method of [7] for detecting the instan-

taneous positive sequence has the following shortcomings.

1) All-pass filters are not frequency-adaptive. Therefore,

they can not make appropriate 90-degree phase shift

when the frequency varies from its nominal value of .

2) All-pass filters do not block harmonics and distortions.

Therefore, the performance of the phase detection scheme

to some degree is compromised. A low-pass filter is rec-

ommended to be used after -component extraction to re-

duce the impact of harmonics, [7].

III. PROPOSED METHOD OF SYNCHRONIZATION

A block diagram of the proposed method is shown in Fig. 5.

The positive sequence component is extracted by the first block

and then is passed to the EPLL to estimate its phase angle. In

other words, this structure is based on extracting the positive se-quence of the input voltages and then extracting the phase angle

based on this component. This strategy considers the effect of

all three phases of the system while maintaining adequate in-

sensitivity with respect to unbalanced conditions.

The block diagram for extracting the positive sequence com-

ponent is also shown in Fig. 5. This unit is comprised of three

EPLLs and arithmetic operations. The EPLLs adaptively extract

the fundamental components of the system voltages and their

90-degree phase-shifted versions. The arithmetic blocks receive

the fundamental components and the corresponding 90-degree

phase-shifted components and calculates the positive sequence

component of the utility voltages based on (3). The computa-

tional procedure is the same as the computational unit shown inFig. 4.

Advantages of this method with respect to the extended three-

phase PLL-based method are as follows. The all-pass filters

are replaced with EPLLs in the proposed structure. EPLL is

an adaptive notch filter whose frequency moves based on the

center frequency of the grid. This prevents sensitivity of the

method with respect to frequency variations which is a major

deficiency of the method of [7]. Moreover, since the EPLL is a

bandpass filter rather than an all-pass filter, the extracted posi-

tive sequence is highly distortion-free. Indeed, the input signal

undergoes two stages of filtering: one in the positive sequence

extraction stage and then in the phase estimation stage.


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1266 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 19, NO. 3, AUGUST 2004

Fig. 5. Block diagram of the proposed method of phase detection.

Fig. 6. EPLL Structure.

IV. EPLL SYSTEM

This section is devoted to the EPLL of [9] which isused asthe

building block of the proposed synchronization scheme of this

paper. EPLL is well suitedfor powersystem applications since it

not only provides an output signal whose phase is locked to that

of the fundamental component of the input signal, the output

signal is also locked to the fundamental component of the input

signal in its amplitude and frequency. In other words, EPLL

is capable of providing an on-line estimate of the fundamentalcomponent of the input signal while following its variations in

amplitude, phase, and frequency.

In addition to the on-line estimate of the fundamental compo-

nent, EPLL also provides an on-line estimate of the basic param-

eters of this component including its amplitude, phase, and fre-

quency. This is the salient feature of EPLL. Another important

feature of EPLL is that it provides the 90-degree phase-shifted

version of the fundamental component. This is readily done by

EPLL since it directly estimates the phase angle of the funda-

mental component of its input.

An implementation of EPLL of [9] is shown in Fig. 6, in ac-

cordance with the conventional PLL structure which consists of

a PD, LF, and VCO. The input signal is compared with itsextracted smooth version to generate an error signal

which is used by LF to generate a driving signal for VCO.

The basic structure of Fig. 6 has three independent internal

parameters: , and . Parameter dominantly

controls the speed of convergence of amplitude . Parameters

and control the rates of convergence of phase

and frequency. A low-pass filter can be incorporated after the

integration unit in the VCO to obtain a smoother estimate of

the phase angle when the utility signal is distorted.

The EPLL is originally applicable to a single-phase signal.

All the previous methods, except EKF, are suited only for three-

phase situations. However, four units of similar EPLL units are

Fig. 7. Performance comparison of five existing methods and the EPLL-basedmethod in the presence of noise.

Fig. 8. Performance comparison of five existing methods and the EPLL-basedmethod in the presence of harmonics.

linked together in the proposed synchronization method to build

a three-phase structure which is highly immune to distortions

and unbalanced conditions.

V. PERFORMANCE EVALUATION

Performance of the EPLL-based method of synchronization

is evaluated by means of a number of simulations.

Fig. 7 shows the steady-state error which occurs in phase

angle detection due to the presence of noise. For a high

signal-to-noise-ratio (SNR) of 0 dB, the error is almost 5degrees and decreases to less than one degree as SNR goes

above 10 dB. Among the existing methods, the LPF-based

method generates the largest error while the EKF-based,

the PLL-based, the SVF-based, and the LSE-based methods

perform better, respectively. Comparing with the conventional

three-phase PLL-based method, the proposed method performs

almost twice as good.

The proposed method provides a highly distortion-free esti-

mate of the phase angle in the presence of harmonic pollution. A

set of study results are shown in Fig. 8. The input signal is com-

prised of a fundamental component and a fifth harmonic com-

ponent. The amplitude of this harmonic is taken as the variable,


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Fig. 9. Response of the EPLL-based method to a phase jump of 10 degrees at ms.

Fig. 10. Response of the EPLL-based method to a frequency jump of 5 Hz at ms.

and its effect on the steady-state performance is shown. As the

parameter varies from zero to 0.4, a maximum error of almost

0.2 degrees is generated by the EPLL-based method. The LSE-

based method generates an error which is almost twice. Theerror associated with the conventional three-phase PLL-based

method is around 20 times larger.

Effects of jumps in phase and frequency are shown by Figs. 9

and 10. A phase jump of 10 degrees occurs in the input signal at

time msec and the error in tracking this variation by the

EPLL-based method is shown in Fig. 9. A transient error with

a peak of about 10 degrees is observed which dies out in a few

cycles. In Fig. 10, a frequency step of 5 Hz occurs in the input

voltage at time msec and the error introduced in the

estimated phase angle using the EPLL-based method is shown.

Similarly, a transient error is generated which decays to zero in

a few cycles. The EPLL-based method adaptively follows the

phase and frequency variations with no steady-state errors.Unbalance tolerance is another main feature of the

EPLL-based synchronization scheme. In Fig. 11, a 50% voltage

sag occurs simultaneously in phases and at msec.

The method is able to adjust itself to the new condition with

no steady-state error. In a very significant unbalance scenario

(Fig. 12), a random voltage sag is imposed on all three phases

of the utility voltages. Fig. 12(a) shows the input signals. The

estimated phase angle has no steady-state error, Fig. 12(b).

In the last case, a step-up of 10 degrees occurs in the phase

angle of at ms. Fig. 13 shows that the method

adjusts itself to the new condition within a few cycles and no

steady-state error.

Fig. 11. Response of the EPLL-based method to 50% voltage sag on phases and at ms.

Fig. 12. Response of the EPLL-based method to a random voltage sag on allthree phases at m: (a) input signals and (b) error in estimated phaseangle.

Fig. 13. Response of the EPLL-based method when the phase angle of undergoes a 10-degree step-up at ms.

The proposed system is employed for synchronization pur-

pose in a DG system to investigate micro-grid operational sce-

narios [17]. The system of Fig. 14 is a single-line diagram of a

three-phase system which is used to investigate micro-grid op-

erational scenarios [17]. The basic configuration and parameters

come from the IEEE Standard 399-1997. This system is com-

posed of a 13.8 kV, three-feeder distribution subsystem which

is connected to a large network through a 69-kV radial line. A

combination of conventional and nonconventional loads ( to

) are supplied through three radial feeders. Loads to

are composed of linear RL loads. Load is a diode-rectifier

load. The aggregate of and constitutes a sensitive load


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Fig. 14. Single-line diagram of the DG system.

within the distribution system. The system includes two gen-

eration units: DG1 (5 MVA) and DG2 (2.5 MVA) located on

the first and third feeders. A voltage-source converter (VSC) is

utilized by DG2 as an interface to control exchange of active

and reactive powers for the sensitive load [17]. Conventional

three-phase PLL [3], [15] is optimally set and its performance

is compared with the proposed EPLL-based system in this sec-

tion. To make the comparison, both the PLL and the EPLL areused to measure the frequency. The DG1 speed is used as an

index to judge accuracy and convergence. The power system is

modeled in PSCAD/EMTDC environment and the EPLL-based

system is simulated in Matlab/Simulink and is properly inter-

faced to the power system.

A line-to-ground fault occurs on the 69-kV line at s.

The fault is cleared by triple-pole operation of CBs at both ends

of the line, five cycles after the fault inception, i.e., at

s, and a micro-grid is formed due to the accidental islanding.

The islanding phenomenon is detected five cycles after the CBs

open, i.e., at s, at which time the micro-grid control

strategy of the DG units is activated. Results of frequency and

phase angle estimation are shown in Fig. 15 that confirms closebehavior of the PLL and EPLL. However, the zoomed version

of the graph over the fault period, Fig. 16, reveals that the PLL

is not capable of providing an accurate estimate for frequency

neither for phase angle. The reason isdue to the presence of fault

which makes the voltages unbalanced. Oscillatory behavior in

estimated frequency by the PLL is observed [Fig. 16(a)] even

though some low-pass filters are already employed to smoothen

its response. On the contrary, the EPLL is capable of providing

a smooth and accurate estimate of the frequency [Fig. 16(a)].

Similar error is also observed in the estimated phase angle by

the PLL, which is shown in Fig. 16(b).

Another case study investigates the micro-grid for-

mation and its electrical transients due to a permanentline-to-line-to-line-to-ground (L-L-L-G) fault on the 69-kV

line. The time intervals corresponding to fault clearing, is-

landing detection and reclosure attempts are the same as those

of the previous case studies except that system islanding is

detected in two cycles (as opposed to five cycles in the previous

cases). Islanding detection in two cycles is possible in this case

because of the severe voltage drop due to the L-L-L-G fault.

Fig. 17 shows the estimated frequency and phase angle by the

PLL and the EPLL. The EPLL provides more accurate results

with better transient response. A zoomed version of this graph

is shown in Fig. 18 for better view of the performance of PLL

and EPLL during unbalanced conditions.

Fig. 15. Temporary line-to-ground fault at s, islanding at s, and reclosure at s: (a) DG1 speed, estimated frequency by PLL,and estimated frequency by EPLL and (b) difference between estimated phaseangles by PLL and EPLL.

Fig. 16. Zoomed version of Fig. 15 over the fault period of [0.5 0.583] s.

Fig.17. Three-phase line-to-ground fault. (a) DG1 speed, estimatedfrequencyby PLL, and estimated frequency by EPLL. (b) Difference between estimatedphase angles by PLL and EPLL.

VI. DIGITAL IMPLEMENTATION

This section studies advantages of the EPLL-based method

from the standpoint of digital implementation. The proposed

method is fundamentally comprised of a number of EPLLs. The


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Fig. 18. Zoomed version of Fig. 17.

continuous-time differential equations governing an EPLL are

derived from the block diagram of Fig. 6 as

(4)

where d ot o n top s tands f or t ime d erivative, is

the error signal, is the input signal,

is its fundamental component, and , and are the

amplitude, frequency, and phase angle, respectively.

A discrete-time version of (4) can be derived based on the first

approximation of the derivative for digital implementation pur-

poses. The investigations show that the first-order approximated

system adequately maintains the desired properties of the algo-

rithm due to the structural robustness of the EPLL. Assuming

sampling period of , the discrete-time recursive equations are

(5)

where , and are called

step sizes. These equations resemble the LMS algorithm used

in signal processing applications. The LMS algorithm is known

for its simple structure and efficient performance in many ap-

plications.

Equations (5) are well suited for implementation on software

(e.g., DSP) platforms or hardware (e.g., FPGA or ASIC) plat-

forms due to their simplicity of structure. An important feature

of this algorithm is that its three parameters arequalitative parameters. These parameters are directly related to

, and , respectively. This indicates that small varia-

tions of these parameters do not affect theperformance of EPLL.

This is very important in fixed-point implementations for which

bit-length limitations exist.

The feasibility of the EPLL algorithm is verified in laboratory

using the TMS320C6711 Texas Instruments™ floating point

platform. It comprises an on-board power supply, peripherals

providing A/D and D/A units and the shell program through

which the DSP is controlled. The C programming language is

used to write the code. Fig. 19 shows a distorted signal whose

phase angle is extracted by the proposed method.

Fig. 19. Implementation on DSP: (a) distorted input and (b) extracted phaseangle.

Further evaluations have been carried out regarding the per-

formance of the discrete version of the synchronization method

using Fixed-Point Blockset in Matlab Simulink environment.

The results confirm that the method performs well even when

it is implemented with a relatively low number of bits, e.g., 8 or

10 bits.

VII. SUMMARY OF COMPARISONThis section provides a qualitative comparison of the EPLL-

based method with the existing synchronization methods. The

methods are compared from the following standpoints.

• Noise immunity.

• Distortion/disturbance rejection.

• Phase angle adaptivity.

• Frequency adaptivity.

• Unbalance robustness.

• Structural simplicity (ease of design, tuning and imple-

mentation),

An index is defined with respect to each item to relatively com-

pare performances of the methods. The possible range of per-formance is divided into six regions, as follows.

• (0) Lacking: means that the method takes no account of

that parameter and hence the performance of the method is

completely prone to that specific parameter. For example,

the LPF-based method does not consider frequency varia-

tions and its performance with respect to frequency varia-

tions is not acceptable.

• (1) Bad : means that although the method has not taken that

parameter into consideration in its structure, nevertheless,

its performance can be acceptable in some scenarios. Ex-

amples of this are all the open-loop methods with respect

to unbalance. Although they do not consider any precau-


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TABLE ICOMPARISON OF THE SYNCHRONIZATION METHODS

tions for unbalanced conditions, nevertheless, due to the

symmetry of the to transformation, they may re-

ject impact of some types of unbalance.

• (2) Average: means that the method inherently has the ten-

dency to improve its performance in this regard but it can

not reach the desired level, even though, some improve-

ments are achieved. For example, the extended SVF-based

method tries to accommodate frequency variations but it

can not perform a satisfactory job.

• (3) Good : means that the performance is “good enough”.For example, most of the methods offer a good harmonic

rejection. This is as far as some ordinary applications are

concerned, but the estimated value may not be sufficiently

precise for more crucial applications.

• (4) Very Good : means that the method performs very well,

however, there might still be some room for improvement.

• (5) Excellent : means that the method performs as good as

possible for the prescribed application and no further im-

provement is desired with regard to this specific factor. For

example, all the methods properly follow the step changes

in the phase angle. No more improvement in this regard is

needed.

Table I shows the comparison results. Major shortcomingsof the existing methods can be summarized as follows. The

LPF-based method is not capable of adjustment to frequency

variations. Its performance is also affected by the utility voltage

unbalance. The SVF-based method has the same shortcomings

as the LPF-based method while it performs better with respect

to utility distortions and noise. The main drawback of the three-

phase PLL method is that it cannot accommodate voltage un-

balance. Although the extended three-phase PLL method elim-

inates this shortcoming, it is sensitive to frequency variations.

The introduced EPLL-based method has no major shortcoming

comparable to the other methods.

VIII. CONCLUSION

A new synchronization method is proposed and its perfor-

mance is evaluated. The method is based on an EPLL system

which offers structural simplicity and robustness. The EPLL-

based method of synchronization is immune to noise, harmonics

and other types of distortion. It is capable of coping with unbal-

anced conditions and it is frequency adaptive. Its structural sim-

plicity and robustness makes it suitable for digital implementa-

tion as an integral part of digital controller platforms for power

electronic converters.

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Masoud Karimi-Ghartemani (M’01) received the B.Sc. and M.Sc. degrees inelectrical engineering from Isfahan University of Technology, Isfahan, Iran, in1993 and 1995 and the Ph.D. degree in electrical engineering from Universityof Toronto, Toronto, ON, Canada, in 2004.

He was with the Center for Applied Power Electronics (CAPE), Departmentof Electrical and Computer Engineering, University of Toronto, from 1998 to2001. His research is focused on developing control and signal processing algo-rithms for power systems protection, control and power quality.

M. Reza Iravani (M’85–F’03) received the B.Sc. degree fromTehranPolytech-nique University, Tehran, Iran, in 1976 and the M.Sc. and Ph.D. degrees fromthe University of Manitoba, Winnipeg, MB, Canada, in 1981 and 1985, respec-tively, all in electrical engineering.

He started his career as a Consulting Engineer in 1976. Presently, he is a Pro-fessor at the University of Toronto, Toronto, ON, Canada. His research interestsinclude power electronics and power system dynamics and control.

a method for synchronization

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