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Adaptive synchronization of utility in abnormal voltage conditions

Adaptive synchronization of utility in abnormal voltage

conditions

Zheng Zeng a ,?,Rongxiang Zhao a ,1,Zhipeng Lv b ,2,Huan Yang a ,3

a College of Electrical Engineering,Zhejiang University,Hangzhou 310027,Zhejiang Province,China b

China Electric Power Research Institute,Haidian District,Beijing 100192,China

a r t i c l e i n f o Article history:

Received 8May 2013

Received in revised form 16March 2014Accepted 18March 2014

Available online 16April 2014

Keywords:

Abnormal utility

Imbalanced and distorted utility voltage Voltage interruption

Positive-,negative-sequence fundamental and harmonic components synchronization Adaptive iteration

a b s t r a c t

Synchronization is a key issue of an inverter-dominated distributed generator to enhance its uninter-rupted operation ability in abnormal utility voltage conditions.In this paper,an adaptive-?lter-oriented algorithm is proposed to fast and effectively synchronize the positive-and negative-sequence fundamen-tal,even the desired harmonic components of utility voltage.The proposed method consists of two parts.One part is a robust digital phase-locked loop associated with a Sliding-Goertzel-Transform-based ?lter to track the frequency of utility.The other part is an adaptive module to separate the desired synchronous voltage components from the abnormal utility voltage.Firstly,the mathematical model of the proposed algorithm is established and explained in detail.Then,some useful analysis on the tradeoff between the stability and the convergence of the adaptive module is investigated.Finally,the simulated results by using MATLAB and experimental results performed on a 32-bit ?xed-point DSP platform have veri?ed the validation and feasibility of the proposed method,in the cases of distorted and imbalanced utility voltage,frequency step,one-phase or three-phase voltage drops to zero.

Introduction

Recently,the distribution generation systems (DGSs)and mi-cro-grids integrated with renewable energy sources (RESs)have been paid common attention,due to the emergency demands of smart grid,low emission,and green power [1–5].To face the hugely increasing penetration of RESs and to reduce the in?uences of RESs on the utility,the uninterrupted operation abilities of inverter-dominated distributed generators (DGs)in abnormal voltage conditions are focused special concerns [6–8].Besides,the harmonic voltage ride-through of DGs is becoming a hot topic [9–12].In general,to achieve the uninterrupted operation of DGs in abnormal utility voltage conditions,how to robustly,fast,and effectively synchronize the desired positive-and negative-sequence fundamental,as well as harmonic voltage components for the controller is a key issue.

Although some literatures have carried out some efforts on the synchronization of DGs in abnormal utility voltage conditions,some of their drawbacks are avoidable and much more attention should be paid.An enhanced phase-locked loop (PLL)based on the decoupling of negative-sequence fundamental component in double synchronous rotating dq frame is presented in [13].In [14],an advanced algorithm is presented to immunize the dis-torted utility voltage.Moreover,a synchronization approach using variable sampling period ?lter is introduced in [15]to separate the negative-sequence from the abnormal utility voltage.However,these approaches cannot identify the harmonic voltage compo-nents for the synchronization control of harmonic voltage ride-through (HVRT).To synchronize the harmonic voltage of utility,a synchronization approach associated with adaptive notch ?lter is described in [16].Nevertheless,the decoupling network will be very complicated if many terms of harmonic are taken into consideration.In [17,18],space vector Fourier transformation and generalized time-delay canceling are employed to fast and accu-rately detect the desired fundamental and harmonic synchroniza-tion components.In [19,20],an advanced algorithm based on multi-complex-coef?cient ?lter is documented to synchronize the positive-,negative-sequence fundamental and harmonic components of utility voltage in abnormal utility condition.To well reject the disturbances from the severely distorted and unbalanced utility voltage,in [21–28],some SOGI-based enhanced PLL algo-rithms associated with adaptive frequency detectors are well documented.Besides,some other algorithms based on adaptive pre-?lter,notch ?lter,etc.are also introduced in [29–32].

In this paper,an adaptive-?lter-oriented algorithm is proposed to synchronize the desired utility voltage components in abnormal

https://www.sodocs.net/doc/0e1480519.html,/10.1016/j.ijepes.2014.03.013

?Corresponding author.Tel.:+86135********.

E-mail addresses:zengerzheng@https://www.sodocs.net/doc/0e1480519.html, (Z.Zeng),rongxiang@https://www.sodocs.net/doc/0e1480519.html, (R.Zhao),dkylzp@https://www.sodocs.net/doc/0e1480519.html, (Z.Lv),yanghuan@https://www.sodocs.net/doc/0e1480519.html, (H.Yang).1

Tel.:+86139********.2

Tel.:+86186********.3

Tel.:+86135********.

utility conditions.It can support the uninterrupted operation of DGs in some severe circumstances,like utility failure and distorted utility.The remainder of this paper is organized as follows.In

Section ‘Mathematical model of the adaptive synchronization algo-rithm’,the mathematical model of the adaptive and recursive algo-rithm is comprehensively indicated.Besides,the stability and convergence of the algorithm is also investigated analytically.Sim-ulated results on the presented synchronization algorithm are gi-ven in Section ‘Simulation results’.And,the validations of the proposed algorithm are veri?ed by the experimental results performed

on a 32-bit ?xed point DSP in Section ‘Experimental validations’.Final-ly,some conclusions are drawn in Section ‘Conclusions’.

Mathematical model of the adaptive synchronization algorithm According to the method of symmetrical components,the utility

voltage u abc =[u a ,u b ,u c ]T can be decomposed as positive-,negative-,and zero-sequence components [33],which can be expressed as

u abc

?X p

u pabc tX n

u nabc tX

u nabc

e1T

where the positive-,negative-,and zero-sequence voltage,u pabc ,u nabc ,and u nabc can be,respectively,written as

u pabc ?U p sin ep x t tu p T

U p sin ep x t tu p à2p =3TU p sin ep x t tu p t2p =3T2

643

u nabc ?U n sin en x t tu n TU n sin en x t tu n à2p =3TU n sin en x t tu n t2p =3T

264375u zabc ?U z sin ez x t tu z TU z sin ez x t tu z TU z sin ez x t tu z T2643

where x is the fundamental angular frequency of utility;U p (U n or

U z )and u p (u n or u z )represent the amplitude and phase angle of p th-(n th-or z th-)order of positive-(negative-and zero-)sequence components,respectively,while p 2{6m +1,m 2Z },n 2{6m à1,m 2Z }and z 2{3m ,m 2Z }.According to the Clarke transformation as expressed as

T abc =a b 0

????23

r 1

à1=2à1=20???3p =2à???3p =21=???2p 1=???2p 1=???2p 2

75e2T

whose inverse transformation satis?es T a b 0=abc ?T à1abc =a b 0?T T

abc =a b 0,the utility voltage u abc can be transformed into stationary a b 0frame u a b 0=[u a ,u b ,u 0]T ,namely

It can be seen from (3)that the positive-and negative-sequence components will not appear in the zero-sequence components u 0.Thus,to detect the desired positive-and negative-sequence components for synchronization,the zero-sequence can be ignored in (3).Furthermore,supposing that p =àn ,Eq.(3)can be rewritten as

For convenience,in the following parts,the synchronization of positive-and negative-sequence fundamental components (p =àn =1),as well as ?fth-order harmonic component (p =àn =à5)of utility voltage is taken for example.For the consid-eration of much more harmonic terms,some similar results can be achieved.According to (4),the estimated utility voltage ~u

??~u a ;~u b T can be written as ~u

a ~u

j 11j 12

j 21j 22

!sin ex t Tcos ex t T

!th

h 12

h 21

h 22

!sin e5x t Tcos e5x t T

e5T

Eq.(5)can be rewritten,in the matrix form,as

?KX 1tHX 5e6T

where ~u

??~u a ;~u b T is the objective vector,X 1=[sin(x t ),cos(x t )]T and X 5=[sin(5x t ),cos(5x t )]T are the state-variable vectors,coef?-cient matrixes K and H can be,respectively,expressed as

K ?

j 11j 12j 21j 22 !;H ?h 11h 12

h 21h 22

According to (4)–(6),the coef?cient matrixes contain the infor-mation of fundamental and harmonic components of utility volt-age.Therefore,if the coef?cient matrixes can be well identi?ed,the desired voltage components for synchronization can be ob-tained.In the following part,the procedure of the algorithm to esti-mate the coef?cient matrixes will be demonstrated step-by-step according to the adaptive ?lter theory [34,35].Taking the mathe-matical expectation of the error between the actual and the esti-mated utility voltage,named as J ,as the minimum objective of the recursive algorithm,it can be derived that

u a b 0

?T abc =a b 0u abc ????6p 2P p U p sin ep x t tu p TtP n U n sin en x t tu n TàP p U p cos ep x t tu p TàP n U n cos en x t tu n T???2p P

z U z sin ez x t tu z T

2643

????6p U p P p

sin ep x t Tcos u p tcos ep x t Tsin u p h i tU n P n sin en x t Tcos u n tcos en x t Tsin u n ? àU p P p cos ep x t Tcos u p àsin ep x t Tsin u p h i àU n P n cos en x t Tcos u n àsin en x t Tsin u n ? ???2p U z P

z sin ez x t Tcos u z tcos ez x t Tsin u z ?

26664

37775e3T

u a u b

???

6p X p ?àn eU p cos u p àU n cos u n Tsin ep x t TteU p sin u p tU n sin u n Tcos ep x t TeU p sin u p àU n sin u n Tsin ep x t TàeU p cos u p tU n cos u n Tcos ep x t T"#?

X p

j p 11j p 12j p 21j p 22 !sin ep x t Tcos ep x t T !&'e4T

Z.Zeng et al./Electrical Power and Energy Systems 61(2014)152–162153

J ?E eu à~u TT eu à~u Th i

?E eu àKX 1àHX 5TT

eu àKX 1àHX 5T

h i

?E u T u ??tE KX 1tHX 5eTT

KX 1tHX 5eTh i à2E u T KX 1tHX 5eT

???E u T u ??tE X T 1K T KX 1h i t2E X T 1K T HX 5h i tE X T 5H T

HX 5

h i à2E u T KX 1??à2E u T HX 5

???r 2

tE X T 1K T KX 1h i tE X T 5H T HX 5h i à2E u T KX 1??à2E u T HX 5

??e7T

where E [u T u ]=r 2is the variance of the utility voltage.It should be noted that some simpli?cation can be satis?ed based on the orthog-onal feature of trigonometric function,namely

E X T 1K T

HX 5h i

?0e8T

E X 1X T 1h

?1T R t tT t sin 2

ex s Td s R t tT t

sin ex s Tcos ex s Td s R t tT t cos ex s Tsin ex s Td s R t tT

t cos 2ex s Td s "#?1T T =2

00T =2 !?1=2001=2

e9TE

X 5X T 5

?1R t tT

sin 2

e5x s Td s R t tT

sin e5x s Tcos e5x s Td s

t tT t

cos e5x s Tsin e5x s Td s R t tT

cos 2

e5x s Td s 2

1T T =20

0T =2"

#?1=200T =2

e10T

where T =2p /x is the utility period.According to the partial

derivative

@J =@K ?2K E X 1X T 1

h i à2E uX T 1h i ?K à2E uX T 1h i @J =@H ?2H E X 5X T 5h i à2E uX T 5h i ?H à2E uX T

h i

<:e11T

and the optimal theory,J can reach its minimum value when o J /o K =o J /o H =0.In such condition,the estimated optimal coef?cient matrixes can be derived as

e K ?2E uX T 1

h i

e H ?2E uX T 5

h i

8><>:e12T

It is worth nothing that Eq.(12)is in accordance with the Wie-ner–Hof equation of adaptive ?lter theory [35].The coef?cient ma-trixes can be obtained based on the recursive iteration using

gradient descent approach,which can be expressed as

K i ?K i à1tl eà@J =@K i à1TH i ?H i à1tl eà@J =@H i à1T

(

ei !1Te13T

where l is the adaptive learning ratio,K 0and H 0are the initial coef-?cient matrixes for the recursive iteration.

To ensure the good performance of the recursive iteration,its stability should be con?rmed ?rstly.Taking the matrix K for in-stance,according to (11)and (13),it yields that

K i ?K i à1tl eà@J =@K i à1T

?K i à1àl f 2K i à1E ?X 1X T 1 à2E ?uX T

1 g

?K i à1àl ?2K i à1e1=2TI àe K ?e1àl TK i à1tl e K ?e1àl Ti

K 0t

X i à1k ?0

l e1àl Tk e K

e14T

where I is a second-order unitary matrix.According to (14),the relationship of {K 0,...,K i }can be expressed as

K i àK i à1?e1àl TeK i à1àK i à2T?e1àl Ti à1eK 1àK 0T

e15T

It can be found from (15)that the stable criterion of the recur-sive iteration can be written as

1àl j j <1

e16T

Namely,when the learning ratio meets 0

iteration algorithm is stable.In such condition,K i will be conver-gent to its steady-state value e K

when the number of iteration step i is big enough.Similar results can be achieved for H .However,to avoid the ?uctuation of the variables of coef?cient matrixes re-sulted from too big learning ratio,l should be a rather small value.To fast detect the desired synchronization components,the con-vergent speed of the algorithm should also be veri?ed.According to (14),when i is zero,the initial coef?cient matrix satis?es K i =K 0;on the contrary,when i ?1,the matrix will be convergent

to its steady value K i !e K

.De?ning the dynamic response time s is the number of iteration step i when K i is convergent to

K 0te1àe à1Tee K

àK 0T,it can be expressed as e1àl Ts

K 0t

s à1k ?0

l e1àl Tk e K

?K 0te1àe à1Tee K àK 0Te17T

Consequently,it can also derive that

e1àl Ts K 0?e à1K 0

X s à1

k ?0

l e1àl Tk e K ?e1àe à1Te K 8

<:e18T

In general,the learning ratio l is rather small and the dynamic response time s is much larger than 10.Therefore,for the term of K 0in (18),a simpli?cation can be approximately yielded as

e1àl Ts ?e à1)s eàl T%à1)s ?1=l es )10T

e19T

For the term of e K

in (18),it should be noted that X

i à1k ?0

x k ?x i x à1à

x à1

e20T

Namely,

s à1k ?0

l e1àl Tk

e K

?e1àe à1

Te K )l e1àl Ts àl

à1

àl

?1àe à1)e1àl Ts ?e à1)s %1=l

e21T

It can be observed that the same dynamic response time can be derived compared with (19)and (21).

It is worth nothing that the stability and convergence of the algorithm are highly related to the learning ratio l .And the learn-ing ratio is a tradeoff between the stability and convergence.Be-cause the big l results in fast convergence but will lower the stability of the algorithm according to (16),(19),and (21);on the contrary,similar results can also be obtained in the condition of big learning ratio l .

In summary,the analytical solutions on the stability and con-vergence of the algorithm are achieved in (16)and (19).In practice,the mathematical expectation E ?uX T 1 in (11)and (12)cannot be ob-tained ahead.Fortunately,the objective J can be estimated by the results of each iteration step,namely

e J ei T?12e 2ei T?12?u ei Tà~u ei T T ?u ei Tà~u ei T

n o e22T

As a result,(13)can be rewritten as

K i ?K i à1tl eà@e J =K i à1T?K i à1tl ?u ei à1Tà~u ei à1T X T 1ei à1T

H i ?H i à1tl eà@e J =H i à1T?H i à1tl ?u ei à1Tà~u ei à1T X T 5ei à1T

(

e23T

154Z.Zeng et al./Electrical Power and Energy Systems 61(2014)152–162

In the iteration process,the desired voltage components for synchronization can be derived from the coef?cient matrixes K and H .Taking K for instance,it can yield that

???

6p U 1sin u 1?j 12tj 21???6p U 1cos u 1?j 11àj 22???6p U à1sin u à1?j 12àj 21???

6p U à1cos u à1?àej 11tj 22T

8>>>><>>>>:e24T

Therefore,the positive-sequence fundamental voltage in sta-tionary a b frame can be expressed as

u 1a u 1b

???

6p 2U 1sin ex t tu 1T

àU 1cos ex t tu 1T

6p 2

U 1cos u 1sin ex t TtU 1sin u 1cos ex t T

U 1sin u 1sin ex t TàU 1cos u 1cos ex t T !

j 11àj 22j 12tj 21j 12tj 21j 22àj 11 !sin ex t Tcos ex t T

!e25T

Besides,the amplitude and phase angle of the positive-sequence fundamental component can be,respectively,written as

U 1????????????????????????????????????????????????????????????

eK t2j 12j 21à2j 11j 22T=6p u 1?tan ?ej 12tj 21Tej 11àj 22T

e26T

where K ?j 211tj 212tj 221tj 2

22.Similarly,the results of negative-sequence fundamental component in stationary a b frame can be ex-pressed as

u à1a u à1b

???

p U à1sin eàx t tu à1TàU à1cos eàx t tu à1T

???6

p 2àU à1cos u à1sin ex t TtU à1sin u à1cos ex t T

àU à1sin u à1sin ex t TàU à1cos u à1cos ex t T"

?1j 11tj 22j 12àj 21j 21àj 12j 11tj 22"#sin ex t T

cos ex t T

"#e27T

And its amplitude and phase angle can be written as

U à1????????????????????????????????????????????????????????????K t2j 11j 22à2j 12j 21eT=6p u à1?tan ?ej 21àj 12T=ej 11tj 22T

e28T

Correspondingly,the results of ?fth-order harmonic can also be achieved.

Supposing that the coef?cient matrix in (27)can be recorded as

M ?

j 11tj 22j 12àj 21

j 21àj 12j 11tj 22

e29T

where its steady-state values including the accurate amplitude and phase information of utility voltage can be expressed as

f M ?

e j 11te j 22e j 12àe j 21e j

21àe j 12e j 11te j 22 !

e30T

According to (23)and (25),the schematic block diagram of the

adaptive iteration can be displayed as shown in Fig.1.

It can be found from Fig.1that the transfer function of such system can be derived as

G ez T?M ei TM ?0:5l X 1X T 11

1àz à1

1t0:5X 1X 111àz à1z

à1?

0:5l X 1X T 1

1àz à1t0:5l X 1X T 1z

à1e31T

It should be noted that,when the number of iteration step is big

enough,the estimated coef?cient matrix M (i )will approximate to the accurate one f M .Because,Eq.(31)meets

lim z !1

G ez T?lim

i !1M ei T

e32T

Additionally,the state variable z in discrete domain and the La-place operator in s domain have the relationship that z =1/(1àT d-s ),where T d is the sampling time of the algorithm.Therefore,Eq.

(31)can also be rewritten as

G es T?0:5l X 1X T 1

1àz à1t0:5X 1X 1z à1

z à1?1àT

d s

0:5l

X 1X T 1

e1à0:5X 1X 1TT d s t0:5X 1X 1

e33T

From (33),it can be seen that the transfer function G (s )is a typ-ical ?rst-order model and its response time can be expressed as

t s ?

10:5l X 1X T 1

T d àT d e34T

According to (9),the mathematical expectation of

E ?X 1X T 1 ?12

1001

,so the expectation of the dynamic response time t s is

E t s ? ?E

T d 0:5X 1X 1

àT d

#?4T d l 1001

àT d

e35T

That is to say,the response time of the iteration for the coef?-cient matrix M is 4T d /l àT d and is much longer than the one in (21),while the response time of iteration process for the matrix K is approximate T d /l according to (21).Notation that the response time also in?uenced by the vector X 1according to (34),and the fre-quency x of X 1is estimated by the following discussed phase-locked-loop (PLL)block.Thus,the response time of the algorithm will be in?uenced by the frequency detection block in the accuracy.However,the functionality of the algorithm can be con?rmed even the response time of the algorithm is in?uenced by the PLL block and the learning ratio.

It should be noted that the fundamental frequency of utility x may be not constant because of utility failure and some other con-ditions.Thus,it is necessary to introduce a module to adaptively track the frequency of utility.In this paper,a modi?ed PLL is em-ployed as shown in Fig.2(a).According to the relationship between the phasor of utility voltage u abc and the virtual current,i d =sin(x t )and i q =cos(x t ),the instantaneous active power in virtual i d ài q frame can be expressed as

P ?u a sin ex t Tteu c àu b Tcos ex t T=???

3p ?te P

e36T

where P is the active power component generated by fundamental

voltage,while e P

is generated by the harmonic,negative-,and zero-se-quence voltage components.With the aid of an low pass ?lter (LPF),the can be separated from P .In the steady-state condition,there is

?U 1cos u 1

e37T

Obviously,to control P ?0and con?rm the stability of the PLL,the phase of vector i dq =[i d ,i q ]T ,namely x t ,will lag p /2by the phase of fundamental voltage,as shown in Fig.2

(a).

Z.Zeng et al./Electrical Power and Energy Systems 61(2014)152–162155

To immunize the in?uence of e P

on the frequency detection,a LPF ?lter based on Sliding-Goertzel-Transform (SGT)is utilized to replace the traditional Butterworth ?lter [15],which can consider-ably cancel the tradeoff of traditional LPF like Butterworth ?lter be-tween bandwidth and response time.The con?guration of the SGT ?lter is shown in Fig.2(b),where the order of the ?lter N S =f s /f 0is the ratio between sampling frequency and fundamental frequency.In summary,the adaptive algorithm to synchronize the desired

fundamental and harmonic voltage components of utility voltage can be demonstrated in Fig.2(c).It should be noted that presented the algorithm is valid and can be employed in three-wire and four-wire utility.It can be found that the schematic diagram in Fig.2(a)is utilized to indicate that the instantaneous power of the three-wire or three–four wire system can be calculated by the utility voltage in naturally abc frame and virtual current in synchronous dq frame.Note that the virtual current in dq frame,i d and i q ,is gen-erated and balanced in fundamental line-frequency,as shown in Fig.2(c).On the other hand,the voltage u abc can be unbalanced for a four-wire utility application.Besides,due to the SGT-based low pass ?lter as shown in Fig.2(b),the ?uctuating components of instantaneous power P ,resulting in the unbalanced and dis-torted utility voltage,can be ?ltered out.Therefore,the in?uences of the unbalanced and distorted voltage for three-wire and four-wire utility application can be overcome.So,the proposed synchronization algorithm has good performances for three-wire and four-wire application even in some abnormal utility

conditions.

Table 1

Parameters of the synchronization algorithm.Sampling frequency 10kHz,so the sampling time T d =0.1ms

Utility Line-line voltage 380V,the based voltage U base =1000V for per unit,and line-frequency 50Hz SGT ?lter N s =100

PI controller Proportional gain K p =50,integral gain K i =20Learning ratio

l =0.05

156Z.Zeng et al./Electrical Power and Energy Systems 61(2014)152–162

Simulation results

To verify the performance of the proposed algorithm for funda-mental and harmonic synchronization,simulation analysis is car-ried out in MATLAB/Simulink and some results are obtained. Some important parameters for simulation study are listed in Table1.

Fig.3indicates the dynamic responses of the proposed algo-rithm when the utility voltage is distorted and unbalanced from 0.1s to0.2s.In such condition,per unit fundamental voltage of each phase is0.341,0.341,0.15,respectively,besides?fth-order harmonic voltage0.04665(15%)is embedded in each phase.As shown in Fig.3(a),the adaptive synchronous algorithm can effec-tively detect the desired positive-or negative-sequence fundamen-tal and?fth-harmonic voltage component.And the performances of the algorithm on frequency tracking and adaptive iteration are displayed in Fig.3(b).As expected,the response time of the adap-tive synchronization module is controlled by the learning ratio. Additionally,due to the good performance of the SGT?lter,the re-sponse time of the frequency detection module is also very short, and the frequency can be locked no more than40ms after the volt-age is distorted and unbalanced.Besides,it can be seen that there is an obvious dynamic process when the synchronization algorithm is enabled.Because the initial parameters of the algorithm,such as the coef?cients matrixes,are zeros,there must be a dynamic process to con?rm the parameters are in steady-state condition. Fortunately,on one hand,this start-up process is very short and last approximate20ms.On the other hand,for grid-connected inverters applications,the power generation functionality will not work until the synchronization successes.So the start-up pro-cess of the algorithm hardly affects the performances of the grid-connected inverter.

Fig.4demonstrates the performances of the proposed algo-rithm when the line-frequency of the utility steps from50Hz to 52Hz at0.1s and then restores50Hz at0.2s.Since the utility has no distortion or unbalance issues,there is no detected nega-tive-sequence fundamental or harmonic component.However, due to the changed phase feature in different line-frequency condi-tions,the terms of the coef?cient matrixes K and H are in?uenced. However,the dynamic responses of coef?cient matrixes are con-trolled by the learning ratio,so the settling time of the adaptive iteration module can be regulated and customized.Additionally, thanks to the good performances of the SGT?lter,the settling time of the frequency tracking block is approximate40ms.

Since the uninterrupted operation of grid-connected inverters in balanced and/or unbalanced utility voltage drops is a very pop-ular and common term in many regulations of utility,some much more attention also should be paid on this issue for the applica-tions of the proposed synchronization algorithm.Fig.5shows the performances of the algorithm in the interesting case that one phase of the utility voltage drops to zero.It can be found that the proposed algorithm can fast synchronize the desired positive-and negative-sequence fundamental and harmonic components within one period.Additionally,the severe disturbance of one-phase voltage interruption will affect the frequency detection, and the settling time is much longer than the cases mentioned be-fore.Besides,the settling time for the terms of coef?cient matrixes is within50ms.In summary,the proposed algorithm can adapt the interrupted one phase of utility voltage and can fast detect the ex-pected synchronization components for the control blocks of grid-connected inverters.

To further con?rm the performances of the proposed algorithm, the simulation results are depicted in Fig.6in the worst case that three-phase voltage of utility drops to zero.It can be seen that the proposed algorithm can fast detect the statuses of utility and effec-tively separate the required synchronization components no more than two cycles.

Although the proposed algorithm can work well in the abnor-mal utility conditions due to the aforementioned disturbances, the performances of the synchronization module are greatly decided by the learning ratio l.Therefore,some much more attention should also be paid on the value of l.Fig.7indicates

Z.Zeng et al./Electrical Power and Energy Systems61(2014)152–162157

the performance of the proposed synchronization algorithm when the line-frequency steps or one-phase is interrupted.It should be noted that the stability of the algorithm is directly determined by the learning ratio l.As mentioned in(16),the algorithm will be stable in the case of0

158Z.Zeng et al./Electrical Power and Energy Systems61(2014)152–162

Z.Zeng et al./Electrical Power and Energy Systems61(2014)152–162159

grid-connected inverter applications.Besides,dynamic response time s will be shortened when the learning ratio increases,but the settling time may be longer if the big l results to oscillation. As a result,a small learning ratio is a good choice as indicated be-fore.As shown in Fig.7,l=0.05may be a preferred value for the learning ratio,due to its fast convergence and good stability performances.

In order to bring a clear vision of the proposed method,a com-parison of some available approaches is demonstrated.To compare with the proposed adaptive?lter synchronization(AFS),three typ-ical well-known approaches are selected.The?rst chosen one is the very traditional Synchronous-Reference-Frame PLL(SRF-PLL). To overcome the drawback of SRF-PLL and separate the positive-/ negative-sequence elements from the unbalanced utility voltage, the second selected algorithm Double-Decoupling-Synchronous-Reference-Frame PLL(DDSRF-PLL)is regarded as a landmark approach.Then,the third selected approach is the recent common researched PLL with adaptive?lter which is also named as Dual Second Order Generalized Integrator resting on an FLL(DSOGI-FLL).As displayed in Fig.8,all the algorithms start at0s,and the voltage is asymmetrically dipped during0.1–0.2s.Then,the fre-quency jumps from50Hz to52Hz at0.2s and jumps to50Hz at 0.3s again.It can be concluded from Fig.8that the SRF cannot immunity the abnormal distorted and unbalanced utility voltage due to the nonlinear loads and unbalanced faults in distribution networks,although it can track the frequency stepping.The left three algorithms can ensure the negative-sequence estimation and can work in such bad conditions.It also should be noted that the proposed adaptive-?lter-based synchronization has advanta-ges of fast response and small overshoot features compared with DSOGI and DDSRF.Table2shows the compared performances of the four synchronization algorithms.

Table2

Performances of compared four synchronization algorithms.

Algorithm Settling time

(ms)Negative-sequence

detection

Harmonic detection

AFS40Yes Yes

DSOGI40Yes Yes

DSRF40Yes Need much more

decoupled terms

SRF20No No

Experimental results in the case of distorted and unbalanced utility voltage.(a)Performances of the algorithm on synchronization and(b)dynamic responses matrixes K and H .

Experimental results in the case of utility frequency step.(a)Performances of the algorithm on synchronization and(b)dynamic responses of coef?cient

160Z.Zeng et al./Electrical Power and Energy Systems61(2014)152–162

Experimental validations

To verify the validations and feasibility of the proposed algo-rithm,a32-bit?xed-point DSP TI TMS320F2812is employed to perform the aforementioned algorithm.The sampling frequency f s is10kHz,and the learning ratio is set as l=0.05.Besides,for common application,the uni?ed voltage is employed on the DSP control board,and the base value of the uni?ed voltage is chosen as U base=1000V.

Firstly,the performances of the presented algorithm on har-monic and negative-sequence voltage detection for synchroniza-tion are con?rmed.Supposing a single-phase utility failure is occurred,the amplitude of the voltage is changed from311V to the one associated with U a=341V,U b=341V,U c=150V,and?fth harmonic voltage46.65V(15%)in each phase.The PLL can fast and effectively track the frequency and phase of utility with the aid of the SGT-based?lter.Fig.9(a)demonstrates the experimental re-sults of the algorithm to detect the synchronization components, like positive-,negative-sequence,and?fth-order harmonic compo-nents.The analytical convergence time of the algorithm is s%1/ l=20iteration steps or sampling points,which corresponds to 20T d=20/(10?103)s=2ms.Meanwhile,the convergence time

can also be measured from the dynamic response of the variables

of coef?cients matrixes,as indicated in Fig.9(b).According to the

aforementioned de?nition,the measured convergence time is

the time when k12is increased from its initial value0to the

(1àeà1)=63.4%of its steady-state value e j12,which is approxi-mately2ms.It is worth nothing that the experimental results

match the analytical results well.From Fig.9(b),it can also be ob-

served that the presented algorithm has good steady-state and

transient performances.

Fig.10depicts the responses of the algorithm when the utility

frequency steps.Since the response time of the SGT-based?lter

is approximate20ms,which can well ensure the frequency detec-

tion and con?rm the performances of recursive iteration module.

The response time of PLL module is no more than50ms,as can

be seen from Fig.10(a).Because the voltage synchronization mod-

ule is dependent on the frequency detection module,the response

time of frequency detection will be added to the one of recursive

iteration progress.Thus,the convergence time of the coef?cient

matrixes may be much longer than the2ms mentioned before,

as displayed in Fig.10(b).Fortunately,the response time may be

Experimental results in one-phase utility interruption condition.(a)Performance of the algorithm on synchronization components synchronization and(b)

of coef?cient matrixes K and H .

Experimental results in the case of three-phase utility interruption.(a)Performances of the algorithm on synchronization and(b)dynamic responses of

K and H.

Z.Zeng et al./Electrical Power and Energy Systems61(2014)152–162161

decreased due to the coupling of coef?cients of K and H in(23)and (25).It can be observed from Fig.10that,the dynamic response time of coef?cients are approximate the one of frequency detection.

As mentioned before,in utility fault conditions,to con?rm the uninterruptable operation of grid-tied inverters for wind and solar energy application,the presented synchronization algorithm should be able to adapt the one-phase short even three-phase short utility interruption.Fig.11indicates the measured results when one-phase voltage of the utility is drops to zero due to the utility fault.It can be seen that the proposed algorithm can fast and exactly synchronize the desired components.Besides,the worst condition is also considered,and the test case that three-phase utility voltage drops to zero is also veri?ed in Fig.12.It can be found that the synchronization algorithm can synchronize the positive-,negative-sequence fundamental and?fth-order har-monic well,and the dynamic response time is less than20ms. Conclusions

In this paper,a fast and effective algorithm is presented to syn-chronize the positive-,negative-sequence,and harmonic voltage components for the voltage and/or harmonic voltage ride-through control of DGs.Experimental results performed on a?xed-point DSP veri?ed the validations and feasibility of the proposed ap-proach.Some conclusions can be drawn as follows.Firstly,the sta-ble and convergence issues of the algorithm can be analytically con?rmed,although the learning ratio of the algorithm is a tradeoff of these issues.Small learning ratio can well con?rm the stability of the algorithm,but will result in long response time.On the con-trary,big learning ratio can achieve fast response but it lowers the stable performance of the algorithm.Secondly,the elements of coef?cient matrixes coupling with each other,and can effectively immunize the in?uence of the PLL module on response time.Final-ly,the experimental results indicate the good performance of the algorithm on steady-state and dynamic features.It can be of great signi?cance for the uninterrupted operation of DGs and the seam-less transfer of DGs between islanded and grid-tied modes in the abnormal utility voltage conditions.Additionally,it can also very useful for the controller of APF and/or DVR to generate the accurate synchronous signals.

Acknowledgements

Thanks for the?nancial supporting from National High Tech-nology Research and Development Program(‘‘863Program’’) (Grant2011AA050204),National Natural Science Foundation of China(Grant50907060),and China Postdoctoral Science Founda-tion(Grant20090451438).

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Adaptive synchronization of utility in abnormal voltage conditions

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