observer pll

10
Copyright (c) 2013 IEEE. Personal use is permitted. For any other purposes, permission must be obtained from the IEEE by emailing [email protected]. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Phase Locked Loop Based on an Observer for Grid Synchronization Yongsoon Park Student member, IEEE Seoul National University, Seoul, Korea. Seung-Ki Sul Fellow, IEEE Seoul National University, [email protected] Woo-Chull Kim LG Uplus Corp., Seoul, Korea. Hyun-Young Lee PLASPO Co., Ltd. Goyang City, Korea Abstract— A grid synchronization technique is essential for grid-connected power converters. Phase locked loop (PLL) has been widely exploited as an implementation technique, but additional efforts are required to deal with severely distorted grid voltages. In this paper, an observer is proposed to enhance the performance of PLL. A state equation is newly formulated to construct the observer, which extracts positive-sequence voltage from the distorted grid voltage. Additionally, guidelines are suggested to set the observer gains by considering its internal transfer functions. The PLL and proposed observer have been tested in simulations and experiments in contrast to dual second order generalized integrator frequency locked loop (DSOGI-FLL). The results have shown that the proposed method reveals better phase-tracking performance for grid synchronization. Index terms – digital signal processing, grid-tied converter, grid synchronization, observer, phase locked loop, positive- sequence voltage. I. INTRODUCTION Electricity is delivered from suppliers to consumers via an electrical grid. The grid voltage is expected to be sinusoidal, whose frequency is fundamentally 50 or 60 Hz. This normal voltage is called a positive-sequence voltage. In particular, electrical power is mainly transferred by modulating the AC current corresponding to the positive-sequence voltage, and it is useful to separate this from the rest of ‘apparent power’ [1]. The grid voltage phase angle should be detected to elaborately modulate active and reactive powers when a grid- connected converter participates in power delivery. For this purpose, the method based on phase locked loop in the synchronous reference frame (SRF-PLL) has been widely used [2], [3]. However, since the grid voltage is usually polluted by unexpected distortions such as harmonics, unbalances, and glitches, the detection of its phase angle may not be easy with the simple PLL method. Therefore, many attempts have been made to enhance the detection performance under polluted grid conditions [4]-[15]. When the recent researches are considered, a better method for grid synchronization is to fulfill the following requirements simultaneously. First, the mitigation of unbalance and harmonics should be achieved under higher dynamics to track the phase angle variation. Second, the consistency of grid synchronization has to be guaranteed even if grid frequency varies. In general, each required function can be implemented in several stages with filter-type blocks [4]-[9]. In some cases, the implementation can be based on parallel structure [12], [13]. Even if all these methods have already presented effective performances in functional aspects, the computational efficiency is not high due to the distributed structures. Moreover, the integrated system design becomes more complicated when the number of separate parts increases. By using a specialized filter, the rejection at every harmonic has been attempted with the relatively simple structure [14], [15]. However, this method should save the previously sampled values, and its sampling frequency must be set carefully in conjunction with the grid frequency. Therefore, an appropriate compromise is required between the implementation effort and the grid synchronization performance. In this paper, an observer is proposed to clearly extract the positive-sequence component of the grid voltage. The required functions for grid synchronization can be unified into a single observer by virtue of its state equation, which has been newly derived in this paper. As a result, the proposed method has a relatively simple structure while presenting the phase detection performance comparable to the dual second order generalized integrator frequency locked loop (DSOGI-FLL) [10]. In terms of design and analysis, the following points can be further noted: although the observer gains are generally set on the basis of the heuristic insight of the designer, this paper suggests explicit guidelines in setting the gains considering the internal transfer functions. In addition, the analyzing tools are newly introduced to discuss the unified effect of the proposed 4th order observer and to examine the distortions from digital implementation. The organization of this paper is as follows. In section II, how the observer can extract positive-sequence voltage with less distortion is described. After the observer gains are set, the observer to PLL attachment is detailed in section III. The proposed method is then assessed via simulation and experimental results under grid fault situations in section IV. Finally, concluding remarks are noted in section V. II. EXTRACTION OF POSITIVE-SEQUENCE VOLTAGES A. Definitions of Symmetrical Components In general, the three-phase voltage can be decomposed into symmetrical components: positive-, negative-, and zero- sequence voltages [18]. Among them, negative-sequence voltage arises mainly when the grid is under abnormal operating conditions such as phase-to-ground faults and unbalanced loading conditions. In SRF-PLL, it is hard to filter out the negative-sequence voltage in the synchronous reference frame even though the bandwidth of PLL is quite reduced. [3], [4]. To effectively remove the negative-

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Page 1: Observer PLL

Copyright (c) 2013 IEEE. Personal use is permitted. For any other purposes, permission must be obtained from the IEEE by emailing [email protected].

This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication.

Phase Locked Loop Based on an Observer for Grid Synchronization

Yongsoon Park Student member, IEEE

Seoul National University, Seoul, Korea.

Seung-Ki Sul Fellow, IEEE

Seoul National University, [email protected]

Woo-Chull Kim LG Uplus Corp.,

Seoul, Korea.

Hyun-Young Lee PLASPO Co., Ltd.

Goyang City, Korea

Abstract— A grid synchronization technique is essential for

grid-connected power converters. Phase locked loop (PLL) has been widely exploited as an implementation technique, but additional efforts are required to deal with severely distorted grid voltages. In this paper, an observer is proposed to enhance the performance of PLL. A state equation is newly formulated to construct the observer, which extracts positive-sequence voltage from the distorted grid voltage. Additionally, guidelines are suggested to set the observer gains by considering its internal transfer functions. The PLL and proposed observer have been tested in simulations and experiments in contrast to dual second order generalized integrator frequency locked loop (DSOGI-FLL). The results have shown that the proposed method reveals better phase-tracking performance for grid synchronization.

Index terms – digital signal processing, grid-tied converter,

grid synchronization, observer, phase locked loop, positive-sequence voltage.

I. INTRODUCTION

Electricity is delivered from suppliers to consumers via an electrical grid. The grid voltage is expected to be sinusoidal, whose frequency is fundamentally 50 or 60 Hz. This normal voltage is called a positive-sequence voltage. In particular, electrical power is mainly transferred by modulating the AC current corresponding to the positive-sequence voltage, and it is useful to separate this from the rest of ‘apparent power’ [1].

The grid voltage phase angle should be detected to elaborately modulate active and reactive powers when a grid-connected converter participates in power delivery. For this purpose, the method based on phase locked loop in the synchronous reference frame (SRF-PLL) has been widely used [2], [3]. However, since the grid voltage is usually polluted by unexpected distortions such as harmonics, unbalances, and glitches, the detection of its phase angle may not be easy with the simple PLL method.

Therefore, many attempts have been made to enhance the detection performance under polluted grid conditions [4]-[15]. When the recent researches are considered, a better method for grid synchronization is to fulfill the following requirements simultaneously. First, the mitigation of unbalance and harmonics should be achieved under higher dynamics to track the phase angle variation. Second, the consistency of grid synchronization has to be guaranteed even if grid frequency varies.

In general, each required function can be implemented in several stages with filter-type blocks [4]-[9]. In some cases, the implementation can be based on parallel structure [12], [13]. Even if all these methods have already presented

effective performances in functional aspects, the computational efficiency is not high due to the distributed structures. Moreover, the integrated system design becomes more complicated when the number of separate parts increases. By using a specialized filter, the rejection at every harmonic has been attempted with the relatively simple structure [14], [15]. However, this method should save the previously sampled values, and its sampling frequency must be set carefully in conjunction with the grid frequency. Therefore, an appropriate compromise is required between the implementation effort and the grid synchronization performance.

In this paper, an observer is proposed to clearly extract the positive-sequence component of the grid voltage. The required functions for grid synchronization can be unified into a single observer by virtue of its state equation, which has been newly derived in this paper. As a result, the proposed method has a relatively simple structure while presenting the phase detection performance comparable to the dual second order generalized integrator frequency locked loop (DSOGI-FLL) [10].

In terms of design and analysis, the following points can be further noted: although the observer gains are generally set on the basis of the heuristic insight of the designer, this paper suggests explicit guidelines in setting the gains considering the internal transfer functions. In addition, the analyzing tools are newly introduced to discuss the unified effect of the proposed 4th order observer and to examine the distortions from digital implementation.

The organization of this paper is as follows. In section II, how the observer can extract positive-sequence voltage with less distortion is described. After the observer gains are set, the observer to PLL attachment is detailed in section III. The proposed method is then assessed via simulation and experimental results under grid fault situations in section IV. Finally, concluding remarks are noted in section V.

II. EXTRACTION OF POSITIVE-SEQUENCE VOLTAGES

A. Definitions of Symmetrical Components

In general, the three-phase voltage can be decomposed into symmetrical components: positive-, negative-, and zero-sequence voltages [18]. Among them, negative-sequence voltage arises mainly when the grid is under abnormal operating conditions such as phase-to-ground faults and unbalanced loading conditions. In SRF-PLL, it is hard to filter out the negative-sequence voltage in the synchronous reference frame even though the bandwidth of PLL is quite reduced. [3], [4]. To effectively remove the negative-

Page 2: Observer PLL

Copyright (c) 2013 IEEE. Personal use is permitted. For any other purposes, permission must be obtained from the IEEE by emailing [email protected].

This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication.

sequence voltbe considered

Initially, th

a+ +

b+ +

c+ +

v V sin

v V sin(

v V sin(

= −

= − = −where both thsequence, anvoltage.

As per theonly exists reference framthe coherenceusing the samvoltage can th

a

b

c

v V sin

v V sin

v V sin

− −

− −

− −

= −

= − = −where the subφn is the phapositive-seque

For exampin terms of thV+ in (1) wasIn addition, φn

negative-sequin Fig. 1.

B. An Obser

For the obmust first berelationship bthe grid voltavariation. In pthe synchrono

d

q

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= −

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he subscripts d θp is the p

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rver for Estim

server design,e established. between statesage should beparticular, theous reference f

p p

p p

ˆ ˆθ cos(θ 12

ˆ ˆnθ sin(θ 12

− −

‘^’ hereafter rphase, the sume of (3). Thecause it is naages can also uence compon

d +

q +

v V s

v V co−

− + =

pθ̂− .

metrical comp

quence voltage

‘+’ and ‘p’ rphase angle o

f (1), the positdrature axis onition has beenid and AC-mogle in (1), thlized into

)

)

resents the nee of negative-

age in (1) ande as shown in V, and V− in

et to 30 °. Thes presents an

mating Positive

, the state equThis state eq

s and their dere discussed in grid voltage frame by

p

p

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ˆ20 ) sin(θ

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ponent model

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Each negative other axis in

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cripts ‘s’ and

er observer canservable with

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cause

Page 3: Observer PLL

Copyright (c) 2013 IEEE. Personal use is permitted. For any other purposes, permission must be obtained from the IEEE by emailing [email protected].

This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication.

s m s m o m sˆ ˆ ˆV A V L [V C V ]

d

dt= + ⋅ − (9-a)

T

1 3 1 3m

2 4 2 4

p p q qL

p p q q

=

(9-b)

T

s d q d+ q+ˆ ˆ ˆ ˆ ˆV v v v v = (9-c)

where variables in Lm are observer gains. By virtue of the practical assumption on positive-sequence

voltage, the observer in (9) could be newly proposed, which can observe the positive-sequence voltage in its internal state.

C. Gain Settings for the Observer

The observer gains of Lm in (9) must be specified. In general, it is difficult to logically describe why a set of observer gains have to be selected since certain selections may have to rely on the insight of the designer. In this paper, the gain setting of the observer is described with the reason why they are selected. The internal transfer functions of the observer are used to explain the gain setting. These functions can be derived as follows. Initially, the state equation in (9) can be transformed into (10) when the derivative operator is replaced with the Laplace operator:

s m s m o m sˆ ˆ ˆs V A V L [V C V ]⋅ = + ⋅ − . (10)

Equation (10) can be rearranged in terms of Vo: 1

s m m m m m oV̂ [s I A L C ] L V−= ⋅ − + ⋅ (11)

where Im represents the identity matrix. Hence, the estimated states in (9-c) can be expressed with

respect to the measurable states in (8-b):

d t t d t t q

q t t d t t q

d+ t t d t t q

q+ t t d t t q

v̂ A /P v E /P v

v̂ B /P v F /P v

v̂ C /P v G /P v

v̂ D /P v H /P v

= ⋅ + ⋅ = ⋅ + ⋅ = ⋅ + ⋅ = ⋅ + ⋅

(12)

where all transfer functions in (12) are detailed with 3 2

t 1 p 3 3 1 4 2 3

2p 1 2 2 1 3 4 4 3 p 1 p 1 4 2 3

ˆA p s {2ω (p q ) p p p p }s

ˆ ˆ ˆ2ω (p q p q p q p q 2ω q )s 4ω (q q q q )

= + − + −

+ − + − + + −(13-a)

3 2 2t 3 p 1 1 p 3ˆ ˆB p s 2ω (q p )s 4ω q s= + − + (13-b)

3 2t 1 4 1 3 2

2p 1 2 2 1 p 1 p 1 4 2 3

C q s (p q p q )s

ˆ ˆ ˆ+2ω (p q p q 2ω q )s 4ω (q q q q )

= + −

− + + − (13-c)

3 2t 3 4 3 3 4

p 3 2 2 4 1 1 p 3

D q s (p q p q )s

ˆ ˆ2ω {q (q p ) q (p q ) 2ω q }s

= + −+ − + − +

(13-d)

3 2 2t 2 p 4 4 p 2ˆ ˆE p s 2ω (p q )s 4ω q s= + − + (13-e)

3 2t 4 p 2 2 1 4 2 3

2p 1 2 2 1 3 4 4 3 p 4 p 1 4 2 3

ˆF p s {2ω (q p ) p p p p }s

ˆ ˆ ˆ2ω (p q p q p q p q 2ω q )s 4ω (q q q q )

= + − + −

+ − + − + + −(13-f)

3 2t 2 1 2 2 1

p 2 3 3 1 4 4 p 2

G q s (p q p q )s

ˆ ˆ2ω {q (p q ) q (q p ) 2ω q }s

= + −+ − + − +

(13-g)

3 2t 4 1 4 2 3

2p 3 4 4 3 p 4 p 1 4 2 3

H q s (p q p q )s

ˆ ˆ ˆ+2ω (p q p q 2ω q )s 4ω (q q q q )

= + −

− + + − (13-h)

t m m m m

4 3 21 4 p 1 4 2 3

2 2p p 3 2 2 3 1 4 2 3

p 1 2 2 1 3 4 4 3 p 1 4

P det[s I A L C ]

ˆs (p p )s 4ω (q q q q )

ˆ ˆ{4ω 2ω (p p q q ) p p p p }s

ˆ ˆ2ω {p q p q p q p q 2ω (q q )}s

= ⋅ − +

= + + + −

+ + − + − + −

+ − + − + +

. (14)

Among the transfer functions in (12), the most important factors are Ct/Pt and Ht/Pt, which explain the influence of each axis voltage to its estimated positive-sequence voltage. Therefore, these transfer functions have been crucially considered in setting the observer gains. Initially, the roll-off rate of Ct/Pt and Ht/Pt can simply be increased by setting q1 and q4, the highest order coefficients in the numerators, to zero:

1 4q q 0= = . (15)

The settings of (15) are intended to enhance the filtering performance to high-frequency distortions. By (15), Ct and Ht are simplified into

2 2t 3 2 p 1 2 p 2 3ˆ ˆC p q s 2ω p q s 4ω q q= − + − (16)

2 2t 2 3 p 4 3 p 2 3ˆ ˆH p q s 2ω p q s 4ω q q= − − − . (17)

To prevent non-minimum phase responses, all coefficients must have the same sign in each of (16) and (17). This condition causes the roots of each equation to be placed in the left half plane (LHP) and is presented as

1 3 3 3 4 2 2 2p / p 0, q / p 0, p / p 0, q / p 0< > > > . (18)

Meanwhile, the observer poles can be determined by using the concept of the general second order system as follows:

2 2 2 2set 1 n1 n1 2 n2 n2P (s 2ζ ω s ω )(s 2ζ ω s ω )= + + + + (19)

where ζx is damping ratio and ωnx is natural frequency. After the damping ratios and natural frequencies are

determined, the observer gains are set by comparing the coefficients between (14) and (19). Considering that all the coefficients are positive in (19), the condition in (20) must be satisfied in the coefficient comparison after (15) is applied:

1 4 2 3p p 0, q q 0+ > < . (20)

The next design point is to set the observer gains so that the observer structure is symmetric in the synchronous d-q reference frame. This can contribute to the simple implementation of the observer, because similar gains can be repeated in the d-q reference frame, as shown in Fig. 6. The symmetric structure can be achieved with (21) when the conditions of (15), (18), and (20) are assumed:

1 4 2 3 2 3p p , p p , q q= = − = − . (21)

By the settings of (15) and (21), the equations of (13) and (14) are simplified into (22) and (23), respectively. That is, the internal transfer functions in the d-axis become similar to those in the q-axis.

3 2 2 2t t 1 p 2 2 1 2

2 2p 1 2 p 2

ˆA F p s {2ω (q p ) p p }s

ˆ ˆ4ω p q s 4ω q

= = + − + +

+ + (22-a)

Page 4: Observer PLL

Copyright (c) 2013 IEEE. Personal use is permitted. For any other purposes, permission must be obtained from the IEEE by emailing [email protected].

This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication.

t tB E (p= − = −

t t 2 2C H p q= =

t tD G {q= − = −4 3

t 1

p 1 2

P s 2p s

ˆ4ω p q s

= +

+ +

The obserrespect to pfrequencies inharmonic disfrequency, it wto be proporti

n1 1 p nˆω k ω , ω=

where pω̂ is e

used for the dFor (21) an

and (23) resul

1 4 1 1p p (ζ k= =2p p 2ˆ ˆ4ω 4ω (q+ −

p 1 2 1ˆ4ω p q 2k k=2 2 2 2p 2 1 2ˆ ˆ4ω q k k ω=

If p1 in (25This resultantinto (29) by th

2

1 2 2 1

1 1 2 2

ζ k ζ k

ζ k ζ k

+ +

Because epositive, (29)

2 1 1(ζ ζ )(k k− −

When the gain settings oOne of two fwork. When (31) must be sk1 is equal to

22 pˆ(p /ω 2)− =

22 pˆ(p /ω 2)− =

It is imponumber in (31different undsame. Howevequal to k2. increase the d

21(1 ζ ) 0 − ≥ →

In a generwould occur Therefore, in the observer g

3 22 p 1ˆp s 2ω p s+ +2

2 p 1 2ˆs +2ω p q s +3 2

2 1 2q s p q s 2+ +2p p

2 2p 2

ˆ ˆ{4ω 4ω (q

ˆ4ω q

+ +

rver gains in predeterminedn (19) by thetortions commwould be convional to the gri

n2 2 pˆk ω=

estimated grid

design since (7nd (24), the colts in

2 2 pˆζ k )ω+ 2 2

2 1 2p ) p p− + + =

2 1 2 2 1 ˆk (ζ k ζ k )ω+4pω̂ .

5) is inserted int q2 must thenhe substitution

1= .

each value inis further sim

2k ) 0= .

observer poleof (15) and (2factors in (30)(26) is considsatisfied if ζ1 k2:

21 2(k k ) (1 ζ− −

2 21 1 2k (ζ ζ )− ⋅ −

ortant to reme1) and (32). Aer (33)’s con

ver, ζ1 must bTherefore, th

degree of freed

1 1 ζ 1→ − ≤ ≤ .

ral second orif the damp

(33), the damgains in (21) a

2p 2ˆ4ω q s)+

2 2p 2ˆ4ω q

p 2 2 2ˆ2ω q (q p− +2

2 2 1q p ) p p− + +

(23) can thed damping e coefficient cmonly occur venient to set tid frequency:

d frequency. ω

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.

ment of the Ob

(12) and (ge is expressed

d t t q

d t t q

v D /P v

v C /P v

− ⋅

+ ⋅.

ution of (36)eneral second o

functions in (ing common f

2p

2p p

ˆ(kω )

ˆ ˆkω s (kω )ρ+2

p

p

ˆk ω s

ˆ)kω s (kω

ρρ ρ+ +

g of k and ρ tions of obser

of k and ρ.xis pertaining s are placed aen, the rematting ρ, which

osed setting inrver shown infer functions i

adjusting them can be und

not clear wver is with onlthe unified ed on the fact t

m. Since the sthe response

sed observer acco

bserver

(22), the esd by

.

makes the order system:

35) are then dfactors:

2pω̂ )

.

can be undersrver poles are All poles ato (31) and (3at a distance aining two ph is the relati

n this paper, thn (9) can be din (37) and (3e observer reerstood with

what the unify (35), (37), a

effect, the folthat the derive

superposition to three-phas

ording to k and ρ

stimated posi

transfer func

derived as (37

stood from Fidepicted with

are located on33). When k i

k−times thepoles are plive distance to

he operation odescribed with38). This featuesponses since

simple modefied effect ofand (38). llowing methoed system in (principle holdse voltage at

.

(34)

itive-

(35)

ctions

(36)

) and

(37)

(38)

ig. 2, h the n the is set grid

laced o the

of the h the ure is e the eling. f the

od is (8) is ds in each

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frequency can[14], the three

ah h

bh h

ch h

v (t) V s

v (t) V s

v (t) V s

= −

= − = −where ‘h’ can

Through Pvoltage can be

hdh

qh h

Vv (t)

v (t) V

=

If the Laplestablished be

tdh qh

ωv (s) v

s=

Based on three-phase vcan be derived

d+ t

q+ t

v̂ (s) (C /

v̂ (s) (D /

= =

The Bode replacing s widesign of the of Tq. It becoin frequency d

As shown serves as lowframe while oIn particular, pole placemeestimated freqcommon propresults from negative-sequ

Although estimation errband is more the grid freqnegative-sequthe estimatedwithin the freestimated freqthe magnitudeto be mitigate

II

The observPLL. By virtube readily acPLL to increa

n be separatele-phase voltag

p

p

p

sin(hω t)

sin(hω t 120 )

sin(hω t 120 )

− °

+ °

n be any real vPark’s transfore derived as

p

p

sin((h 1)ω t)

cos((h 1)ω t)

− −

ace transformetween the d- a

(s) .

(35) and (41oltage at the ad as

t t tt

tt t t

s/P D /P )

ω

ω/P C /P )

s

− ⋅

⋅ +

plot of Td anith jωt as showobserver, the

omes evident hdomain. in Fig. 3, the

w-pass filters offering the bthe bandwidth

ent, and the stquency. The lperty of obserthe proposed

uence voltage. both filtering

ror of the gridcritical. Then

quency error uence voltage d frequency inequency errorquency deviatee of negative-

ed by the obser

II. PLL BASE

ver proposed ue of this conchieved with ase its bandwid

y considered. ge can be gene

)

)

value. rmation in (3)

h t

h t

V sin(ω t)

V cos(ω t)

=

m is applied to and q-axis vol

1), the frequearbitrary frequ

dh d

qh q

v (s) T (s)

v (s) T (s)

⋅ =

⋅ =

nd Tq in (42)wn in Fig. 3. DBode plot of Thow the prop

e proposed obsin the synchr

band-stop funch of low-pass top band is lolow-pass functrver while thed modeling o

g functions ad frequency, thn, it has been d

as shown inwas considere

n (37) and (38r of 20%. As es from the gr-sequence volrver by up to o

ED ON THE OBS

in section II nstruction, filtless effort indth and contrib

Considering eralized into

), the generali

)

.

(40), equationltages:

ency responseuency, denoted

dh

qh

v (s)

v (s)

⋅.

can be obtaiDue to the symTd is the same

posed observer

server fundamronous d-q rection simultanfiltering is setocated at doution originatee band-stop fof (7) to rej

are affected he movement discussed in ten Fig. 4. Whed in (42) (ωt

8) has been ca result, even

rid frequency bltage is still exone tenth.

SERVER

is attached ttering harmon

n PLL, whichbutes to the hi

(1) and

(39)

zed d-q

(40)

n (41) is

(41)

e to the d by ωt,

(42)

ined by mmetric e as that r works

mentally eference neously. t by the

uble the s in the

function ect the

by the of stop

erms of hen the = 2ωp),

changed n if the by 20%, xpected

to SRF-nics can

allows igher

Fig

Fig

Fig

phshoAi

thehabe dirdrafredisass

dθ̂

pθ̂

g. 3. Frequency re

g. 4. Deterioration

g. 5. Entire PLL s

hase-angle tracown in Fig. 5ided PreprocesThe estimate

e observer gas been used asensitive to d

rectly deliverawback, ωe1

equency. The scussed with sumed, (44) ca

d p pˆθ θ θ≈ = −

pp ip

2pp i

k s k

s k s k

+=

+ +

esponse of the ob

n of band-stop fun

structure.

cking dynami and is referressing phase loed frequency iins accordings the estimatedistortions becrs scaled ang

in Fig. 5 ieffectivenesthe followi

an be derived

pip

θ

server to three-ph

nction by grid fre

ics. The entireed to as Synchcked loop (SOin PLL must

g to (34). Usued frequency. Hcause kpp, the

gle errors to s used as ths of this moing equationsfrom Fig. 5:

hase voltage.

equency error.

e PLL structuhronous Obse

OAP-PLL). be fed back t

ually, ωe2 in FHowever, ωe2

proportional it. To refine

he estimated odification cas. When (43

ure is erver-

to set Fig. 5

2 may gain,

e this grid

an be 3) is

(43)

(44)

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A

where kpp andPLL, respectiv

From Fig.

ipe1 d

k kˆω θs

= ≈

If pθ̂ in (44

ipe1 2

pp

k sω

s k s≈

+

ωe1 is a lousing this freq

less sensitive function in (4system, the Pof the second

pp pll npllk 2ζ ω ,=

where ζpll anfrequency of P

The gain stogether, so ais larger than is set to four pole of the dynamics inte

Meanwhileboth sides ospecifically imof obtaining according to design seemimplementatiodiscussed earand band-stop

IV. SIM

A. Evaluatio

The perforaspects: the mitigating abbeen examinecontaminated frequency wa

In particulas compared because its imgain settings a

d kip are propovely. 5 with (43), ω

ipp p

k ˆ(θ θ )s

− .

4) is inserted i

p 2ip

θk s

=+ +

ow-pass filterquency as pω̂

to distortions46) takes the I gains can beorder system:

2ip npllk ω=

nd ωnpll are PLL, respectivsettings of theall the gains ar

that of (44). Etimes greater observer is n

ended in (44) we, based on thf (10) by ‘s,mplemented, a

Fig. 6, the(15), (34), an

ms to be raon of the prlier, this singl

p functions sim

MULATION AND

on of SOAP-P

rmance of SOtracking err

bility against ded under grid f

by harmonics changed. ar, the effectivto DSOGI-FL

mplementationare known [10

ortional and in

ωe1 is derived a

into (45), it ca

ipp

pp ip

k s k+.

ed value of a, the observer

s. In addition,form of the g

e set accordin:

the dampingvely. e observer andre set where thEmpirically, ththan that of (

not larger thawould be distu

he equation ob,’ the proposas shown in F

e observer gand (36). Even ather complicroposed obsele observer camultaneously.

D EXPERIMENT

PLL

OAP-PLL can or on grid distortions. Eafaults where thcs and unbal

veness of SOALL. This methn is relatively 0].

ntegral (PI) ga

as

an be rearrang

actual frequenr performance

because the tgeneral secon

ng to the settin

g ratio and

d PLL have the bandwidth he bandwidth (44). If the doan that of PLurbed. btained from dsed observer Fig. 6. In the ains have bethough the o

cated, the perver is simpan offer the lo

TAL RESULTS

be discussedparameters aach performanhe grid voltaglances, and th

AP-PLL is dihod has been ssimple, and e

ains for

(45)

ed into

(46)

ncy. By e can be

transfer nd order ng rules

(47)

natural

to come of (37) of (37)

ominant LL, the

dividing can be process een set

observer practical ple. As ow-pass

d in two and the nce has es were he grid

scussed selected essential

Fig

Fig

B.

froidenothe

1V

5V

fauf

whord‘no

allthe

eargasim(48ρ

of PLspetim

phaftoscsyn

g. 6. Block diagra

g. 7. Grid fault un

Simulation

The fault conom the literatueal grid is sel

ormal voltage e fault conditio

0.5 30 ,+ = ∠ − °

5 70.2 0 ,V− += ∠ °

ult norf 5Hz− = −

here the subscder, and the nor’. When the nor

l the conditione fault wavefoInitially, the

rlier work [10ins of SOAP-P

milar to those8). The specifi

pll1, k 1.7, ζ= =

The gains of Fig. 6, and t

LL of Fig. 5 ecific values,

me under the cDue to the st

hase angle andter the fault, cillations disnchronization

am of the propose

nder conditions of

Results

nditions for simure [12]. Whlected as the is denoted as

ons are given

1V 0.25 11− = ∠

110.2 0 ,V+ −= ∠ °

z

cript number onormal conditi

rmal grid is asns in (48), (49)orms are show

gains of DSO0]. For a fair cPLL had to beof DSOGI-FL

fic values of th

l npll1, ω 2π= =

ρ and k are dithe gains of ζ

through the SOAP-PLL h

condition spectep variations d frequency pas captured

appear, both s as if there

ed observer.

f (48), (49), and (

mulation testshen the voltag

base voltage, s 1∠0°. Basedas follows:

10°

0.2 0− = ∠ °

of a voltage reion is indicate

ssumed to be 2), and (50) aren in Fig. 7.

OGI-FLL wercomparison ofe set such thatLL under the hose gains wer

20⋅ .

irectly inserteζpll and ωnpll a

PI gains in has presentedified in (48), ain (48), the e

present oscillain Fig. 8. Hmethods sh

are no unba

(50).

s have been quge amplitude

the phasor od on this con

epresents harmed by the subs

220Vrms-60Hze applied after

re set accordinf performancest its dynamics unbalance fau

re

d into the obsare reflected in

(47). With d the same setas shown in Fistimation erroations for a w

However, afterhows perfect alance distort

uoted at an

of the ncept,

(48)

(49)

(50)

monic script

z, and fault,

ng to s, the were

ult of

(51)

erver n the these ttling ig. 8. ors of while r the grid

tions,

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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication.

which confirmcomparable w

The perforDSOGI-FLL discrete time in fault condFLL was baimplemented implementatiotested under tsimulation res

As shown DSOGI-FLL PLL consists Even though timproved by [12], this extcode lines forDSOGI-FLL due to harmon

The other the steady-staTo discuss thiin Fig. 10. following tran

2

ˆkωD(s)

ˆs kω=

+

2

ˆkωQ(s)

ˆs kω=

+

where the subreference framsignal of inpuharmonics.

When a sydomain, its orcomputationacircles in Figspecify thesedistortion (ZT

H

HZTD (ω

H) =

where ‘H’ symoriginal systetransformed sfrequency of cimplementatio

The meandomain systemZTD correspoof each system

10 H20log | ZTD

ms that the unwith that of DSrmance of SO

when each domain, or th

ditions. The dased on [21]

with backwons under 10 the fault condsult is presente

in Fig. 9, Sin harmonic of two filteri

the filtering peextending to m

tension can onr implementatpresents the

nics. conspicuous f

ate error of 2.is phenomenoTo estimate

nsfer functions

p α2

p p α

ω s v̂ˆs ω v

=+

2p α

2p p α

ω̂ v̂ˆω s ω v

q=+

bscript ‘α’ refme. Q(s) in put while both

ystem is transfriginal proper

al delay of z-

gs. 6 and 10, me types of TD) is introduc

sωΤz

s

(e )

H ( ω)

j

j

mbolizes the em in the ssystem in theconcern and Ton.

ning of ZTD m from the s-onds to the dim:

H 10(ω) | 20 log=

nbalance rejectSOGI-FLL. OAP-PLL was

method washe harmonics idigital implem

while SOAward Euler m

kHz samplingditions of (48)ed in Fig. 9. OAP-PLL obfiltering. Thi

ing stages: therformance ofmultiple SOGnly be done btion. In additiaverage error

feature is that7 ° in estimat

on, one of the e positive-seqs are importan

fers to the d-aparticular geneh D(s) and Q

formed from thrty can be dist-1, which is imay be includdistortions, tced:

system of inte-domain, and

e z-domain. ITs is the sampl

is the distort-domain systeifferences betw

sωΤz| H (e ) | 20j −

tion of SOAP

s different to s implementein (49) were in

mentation of DAP-PLL was method. Withgs, each meth), (49), and (5

bviously outpeis is because e observer anf DSOGI-FLL

GI-FLL (MSOGby increasing ion, the frequer of 0.79 Hz

t DSOGI-FLLting the phasedual SOGI is

quence voltagnt in Fig. 10:

axis in the staerates the qua(s) serve as f

he s-domain ttorted. Moreovindicated by ded for feedbathe z-transfor

erest, Hs referd Hz represen addition, ωling period for

ted degree ofem. The Bode ween the Bod

10 s0 log | H ( ω) |j

-PLL is

that of d in a ncluded DSOGI-

simply h these hod was 50). The

erforms SOAP-

nd PLL. L can be GI-FLL) source ency of mainly

L shows e angle. s shown ge, the

(52-a)

(52-b)

ationary adrature filtering

o the z-ver, the dashed

ack. To rmation

( 5 3 )

rs to the nts the

ω is the r digital

f the z-plot of

de plots

(54)

Figimp

Figdig

Fig

Z∠

DSfremawhAsthefre

DSPLPLvo

g. 8. Simulation replementations.

g. 9. Simulation regital implementati

g. 10. Second ord

HZTD (ω H) = ∠

The Bode pSOGI-FLL arequency is seagnitude and hich correspons shown in Fige frequency equency.

From Fig. 1SOGI-FLL anLL and DSOGLL can sepaoltages via Pa

esults under unba

esults under faultions.

er generalized int

sωΤz sH (e ) Hj − ∠

plots of critire depicted inet at 10 kHzphase must b

nd to unity, whg. 11, the ZTD

of concern

11, the reasond not in SOAP

GI-FLL are diffarate the poark’s transform

alance fault of (48

t conditions of (48

tegrator.

( ω)j .

cal ZTDs inn Fig. 11 whz. In the Bobe 0 dB and hen the z-tranDs deviate fro

approaches

n for the steP-PLL can be

fferent theoretisitive- and mation. By th

8) with analog

8), (49), and (50)

n SOAP-PLL here the samode plot of Z

0 °, respectinsformation is om the unity w

to the Ny

eady-state erroexplained. SO

ically since SOnegative-sequ

his separation

) with

(55)

and mpling

ZTD, ively, ideal. when

yquist

or in OAP-OAP-uence n, the

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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication.

negative-sequfrequency whband. In contnegative-sequwhere both vo

As shownexhibit the phfrequency, wDSOGI-FLL.parallel displadistortion of pstate error in sampling fre@5kHz). In cunity at the Dappears in SOvoltage wouldobserver funcfrequency as stop functionresult of Fig.are required f[22].

In additionthe fault test property of SOare not observrejects negatvariation.

C. Experime

To demonwas emulatedalgorithms w(DSP), TMSthrough voltaPLL were set

The most f[17], which isby grid-connephase-to-phasconsidered:

a

b

c

V 1

V 1 / 2

V 1 / 2

= = − −

= − +

where Vsag isvoltage sag. In

The magnphase of Vsag 40° . The morders were variation in (5

uence voltagehile the posititrast, DSOGI-uence voltagesoltages appearn in Fig. 11, thhase distortion

where the posi For AC signacements in tpositive-sequeDSOGI-FLL,quencies as

contrast, the ZDC band, wh

OAP-PLL. In od not be distoction is slighshown in Fig.

n in SOAP-PL. 9. Unlike Sfor digital imp

n, the conditionof Fig. 9 to

OAP-PLL. Beved often in Ftive-sequence

ental Results

strate the feasd using an AC were implemen

320F28335, aage sensors pe

according to (frequent fault s commonly rected convertese fault betw

sag

sag

V 3 / 2

V 3 / 2

j

j

+

s a complex n addition, all

nitude of Vsag

[19]. As an exmagnitudes of

set to about 50) was includ

e appears ave-sequence v-FLL deals ws in the stationr at the grid frehe ZTDs of D

ns of 2.2 and 3itive-sequencenals, these nothe time-domaence voltage c, and can be ishown in FTDs of SOAP

here the positiother words, torted in SOAPhtly distorted . 11, the effecLL can be co

SOAP-PLL, caplementation o

n of (50) has ao examine theecause the secFig. 9, the SOA

voltage ev

sibility of SOAprogrammabl

nted in a digand grid voltr 100 μs. All (51). is the single p

recognized as ers due to tra

ween b- and

number indic magnitudes a

g is determinxperiment, Vsa

harmonics at0.08 per unit

ded as well. Th

at double thvoltage is at

with the positivnary referenceequency. D(s) and Q(s) .2 degrees at t

e voltage apponzero phaseain. Then, thecan cause the intensified at ig. 11 (deno

P-PLL presentive-sequence the positive-seP-PLL. Althou

at double thctiveness of thorroborated wareful consideof DSOGI-FL

also been incle frequency-acond order distAP-PLL succe

ven after fre

AP-PLL, a grle source, MX

gital signal prtages were sthe gains for

phase-to-grounphase-to-pha

ansformers [1c-phases ha

cating the deare in per unit.

ed according ag was set to 0t 5th, 7th, ant, and the frehe grid voltage

he grid the DC ve- and e frame,

in (52) the grid

pears in s mean e phase steady-smaller

oted by t almost voltage

equence ugh the he grid

he band-with the erations

LL [20]-

luded in adaptive tortions essfully equency

rid fault X30. All rocessor sampled SOAP-

nd fault ase fault 9]. The

as been

( 5 6 )

gree of

to the 0.38∠nd 11th equency es

Figsam

Fig

arothe

stato oscgenset

haeffcobeneSOsituSOFLthePL

err

g. 11. Bode plots mplings.

g. 12. Grid fault fo

ound the faulte voltages recoInitially, the c

arting point ofcapture sever

cilloscope. Itnerate almostttings. Under the f

rmonics in thefect of the promparison withen eliminatedgative-sequen

OAP-PLL wheuations, the

OAP-PLL, 1.5LL. Furthermoe average devLL.

Because the rors were calcu

of ZTDs in SOAP

for experiment.

t occurrence aognized by thec-phase voltag

f the fault, wasral waveformt was assumet time-invarian

fault situatione frequency eoposed observh SRF-PLL, wd from SOAPnce distortionen compared RMS of freq

52 Hz for SRFore, the frequiation of 0.10

actual phase ulated with re

P-PLL and DSOG

are shown in Fe DSP board. ge, whose negs selected as th

ms from the lied that the nt faults acco

n, SOAP-PLLstimation show

ver can be mowhere only theP-PLL. As s

ns were evidwith SRF-PL

quency rippleF-PLL, and 0.4ency of DSO2 Hz when co

angle was noespect to the ph

GI-FLL under 10

Fig. 12, whic

gative peak wahe reference simited channeAC source c

ording to the

L has the fewn in Fig. 13

ore obvious vie observer parhown in Fig

dently rejectedLL. After trane was 0.1 Hz45 Hz for DSO

OGI-FLL preseompared to SO

ot accessed, ahase angle of

0 kHz

h are

as the signal els of could same

ewest . The ia the rt has . 13, d by nsient z for OGI-ented OAP-

angle

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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication.

Fig. 13. Frequenc

Fig. 14. Angle es

SOAP-PLL, θAfter transienθDSOGI, deviatin Fig. 14.

In this papextract positivoltage. This of PLL by uequation has bthe observer, suggested whand their com

In a functiospecifically srejecting unbparticular, theimplemented implementatiomethod has bresults. The distortions owithout steady

[1] A. E. EmanMeasuremeNonsinusoiInd. Appl.,

cy estimations in

stimations in expe

θSOAP, when nt situations, ted from that

V. C

per, an obserive-sequence extraction is sing the obsebeen newly deand the gain

hen considerinmbination with

onal aspect, thcrutinized in balances unde performancestructures un

on. As a resultbeen confirme

proposed mf the estimay-state errors.

RE

nuel, “Summary oent of Electric idal, Balanced, ovol. 40, no. 3, pp

experiment: time

eriment: time [10

considering ththe phase anof SOAP-PLL

CONCLUSION

rver has been voltage fromintended to re

erver as a preerived on gridsettings of theg the mitigatioPLL.

he proposed Pterms of filte

der polluted es have been dnder the consit, the effective

ed by simulatimethod exce

ated frequenc

EFERENCES

of IEEE StandardPower Quant

or Unbalanced Cp. 869-876, May/J

e [10 ms/div].

0 ms/div].

he simulationngle of DSOGL by 2.4 °, as

proposed to m the polluteeinforce the f

eprocessor. Thd voltage to coe observer havon of grid dist

PLL method hering harmongrid conditio

discussed in dideration of peness of the prion and experelled in mitcy and phase

d 1459: Definitiontities Under SiConditions,” IEEJune 2004.

n result. GI-FLL, s shown

clearly ed grid function he state onstruct ve been tortions

has been nics and ons. In digitally practical roposed rimental tigating e angle

ns for the inusoidal,

EE Trans.

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

[10

[11

[12

[13

[14

[15

[16

[17

[18

[19

[20

V. Kaura and Under Distorteno. 1, Jan./Feb

S.-K. Chung, Interface Inve431-438, May

S.-J. Lee, H. KPower ConvePower System1999, pp. 2167

R. K. Sinha, agrid connected81, Issue 1, pp

M. P. KazmiControl of GrDistortions,” IMay 2011.

F. Liccardo, PPhase PLL Tra1, pp. 221-231

F. Gonzalez-ESynchronous-RImprovement vol. 59, no. 6,

Y. F. Wang, Cascaded Delavol. 26, no. 7,

0] P. Rodriguez, Teodorescu anSynchronizatioConverters UElectron., vol.

1] P. Rodriguez, Boroyevich, “for Power Conno. 2, Mar. 20

2] P. Rodriguez, Blaabjerg, “SynchronizatioConditions,” I

3] X. Guo, W. WBased Phase-LPhase Grid-InIEEE Trans. In

4] E. Robles, S. “Variable-FreqLow-Pass FilteElectron., vol.

5] I. Carugati, S“Variable SamSystems,” IEEJan. 2012.

6] D. G. LuenbAutomatic Con

7] J. Keller and Inverter-BasedTech. Rep. NR

8] A. R. BergenSystems Analych. 12-1, pp. 4

9] A. Sannino, MTesting of ThPower Deliver

0] A. G. Yepes, and P. Fernanthe PerformanElectron., vol.

V. Blasko, “Opeed Utility Conditb. 1997.

“A Phase Tracrters,” IEEE Tra

y 2000.

Kim and S.-K. Suersion Systems

m,” in Conf. Rec. I7-2172.

and P. Sensarma, d applications,” Ep. 129-137, Jan. 2

ierkowski, M. Jrid-Connected PoIEEE Trans. Ind.

P. Marino, and Gacking System,”1, Jan 2011.

Espin, E. FigueReference-Framein a Polluted Utipp. 2718-2731, J

and Y. W. Li, ayed Signal Cancpp. 1987-1997, J

A. Luna, R. S. Mnd F. Blaabjerg,on System for

Under Adverse G. 27, no. 1, Jan. 20

J. Pou, J. Berga“Decoupled Doubnverters Control,”07.

A. Luna, I. Can“Multiresonant on of Power IEEE Trans. Ind.

Wu, and Z. Chen,Locked Loop andnterfaced ConverInd. Electron., vol

Ceballos, J. Pouquency Grid-Seqer Stage and a Ph. 25, no. 10, pp. 2

. Maestri, P. G. mpling Period FEE Trans. Power

berger, “An introntrol, vol. 16, no.

B. Kroposki, “Ud Distributed EnREL/TP-550-466

n and V. Vittal, ysis 2nd edition, K446-450.

M. H. J. Bollen,hree-Phase Voltary, vol. 20, no. 2,

F. D. Freijedo, ndez-Comesana, nce of Resonan. 25, no. 7, July 2

eration of a Phasetions,” IEEE Tra

cking System fons. Power Electr

ul, “A New PhaseConsidering Di

IEEE 34th IAS An

“A pre-filter baseElectric Power S

2011.

Jasinski, and G.ower Converters

Informatics, vol

G. Raimondo, “RIEEE Trans. Ind

eres, and G. Gae Phase-Locked Lility Grid,” IEEEJune 2012.

“Grid Synchronicellation,” IEEE TJuly 2011.

Munoz-Aguilar, I “A Stationary RThree-Phase G

Grid Conditions,”012.

as, J. I. Candelable Synchronous ” IEEE Trans. Po

ndela, R. Mujal, Freuqency-Locke

Converters UnElectron., vol. 58

, “Multiple-Compd Synchronizationrters in Distributl. 58, no. 4, pp. 1

u, J. L. Martin, Jquence Detector Bhase-Locked Loop2552-2563,Oct. 20

Donato, D. CarrFilter PLL for Dr Electron., vol. 2

oduction to obs. 6, pp. 596-602,

Understanding Fnergy Resources,”98, Jan. 2010.

“Symmetrical CKorea: Pearson E

and J. Svenssoage Source Conpp. 1633-1639, A

J. Doval-Gandoy“Effects of Discnt Controllers,” 010.

e Locked Loop Sans. Ind. Appl., vo

or Three Phase Uron., vol. 15, no.

e Detecting Methstorted Conditionnu. Meeting, Oc

ed PLL for three-Systems Research

Wrona, “DSP-Operating Unde. 7, no. 2, pp. 204

Robust and Fast Td. Electron., vol. 5

arcera, “An AdLoop for Power QE Trans. Ind. Elec

ization PLL BasTrans. Power Ele

. Etxeberria-OtadReference Frame

Grid-Connected ” IEEE Trans. P

, R. P. Burgos aReference Fram

ower Electron., v

R. Teodorescu aed Loop for nder Distorted 8, no. 1, Jan. 201

plex Coefficient-n Technique for Tted Utility Netw194-1204, April 2

J. Zaragoza, P. IbBased on a Quasip,” IEEE Trans. P010.

rica, and M. BenDistorted Three-27, no. 1, pp. 32

servers,” IEEE Dec. 1971.

Fault Characterist” NREL, Golden

Components” in PEduc. Korea Ltd,

n, “Voltage Tolenverters,” IEEE April 2005.

y, O. Lopez, J. Mcretization Metho

IEEE Trans. P

System ol. 33,

Utility 3, pp.

hod for ons in ct. 3-7,

-phase h, vol.

-Based r Grid 4-211,

Three-58, no.

daptive Quality ctron.,

sed on ectron.,

dui, R. e Grid Power Power

and D. e PLL ol. 22,

and F. Grid Grid

1.

Filter-Three-

works,” 2011.

banez, i-Ideal Power

nedetti, -Phase 1-330,

Trans.

tics of n, CO,

Power 2009,

erance Trans.

Malvar ods on Power

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