Download Adaptive Phase-locked Loop Technology based on The Least Error

Adaptive Phase-locked Loop Technology based on The Least
Error Squares Filtering
Li Xianyun，Zhong Chongmin, Qi Qiulin, Zhang Dong
(Nanjing Institute of Technology)
Frequency and amplitude of the PV voltage is
Abstract:
Grid voltage fault (voltage sags, frequency jump,
detected by PLL, PLL (frequency) Phase-locked loop
harmonic, disturbance, etc.) for phase and amplitude of
can be divided into digital phase-locked loop and
phase-locked loop testing a large impact on the
software phase-locked loop; According to the phase
quickness and accuracy，In this paper, based on the
number, it is usually divided into single phase lock loop
least error squares filter and adaptive filter, raising a
and three-phase phase-locked loop; According to the
rapid and accurate grid synchronization technology,
structure, it can be divided into open loop phase-locked
which can extract of fundamental component of PCC
loop and closed loop phase-locked loop. paper [1-3]
voltage, realize the separation of positive and negative
proposed a single coordinate system synchronization
sequence power. Results using MATLAB/Simulink
software phase locked loop with low-pass filter, it is
simulation, and compared with the traditional phase
simple to implement, in the case of three phase grid
locked loop technique，show that the technology can
voltage drop, it can quickly and accurately detect the
restrain harmonic influence on phase-locked loop at the
phase and frequency of the grid voltage, but in the case
same time satisfy the quickness and accuracy
of unbalanced drop, positive sequence component
Key words：
detected by it containing a large amount of second
1
least error squares harmonic phase-locked loop
harmonic, the impact of the grid voltage. When the grid
Introduction
voltage asymmetry failure occurs, the grid would
With the rapid development of new energy,
capacity of solar photovoltaic power plant is rapid
increase and the proportion of photovoltaic power
generation in the grid is great growing. the stable,
reliable operation of PV grid-connected inverter has
become an important safeguard for the safe operation
of the power grid, the key is low voltage ride through
technology. Grid synchronization technology can
detect the magnitude of the grid voltage and track the
changes of frequency and phase angle. Phase angle
information and amplitude information needed by low
voltage ride through of photovoltaic grid inverters is
provided
by
Grid
synchronization
technology.
Furthermore, it provide reference for the closed loop
control to implement active control and reactive power
control. But Grid voltage fault is usually asymmetric
fault, it will produce negative sequence component and
affect the detection of the phase angle, which required
more at grid synchronization technology.
produce positive and negative sequence components.
In order to achieve positive and negative sequence
separated and improve accuracy of phase-locked,
paper[3] proposed the Dual synchronous coordinate
decoupling software phase-locked loop, the positive
and negative sequence component were decoupled by
the phase locked loop of, respectively, in the case of
Three-phase unbalanced voltage drop it can accurately
detect phase and frequency of the grid voltage, but the
calculation process of phase-locked loop is complex,
and it contains a first-order filter its dynamic
performance was affected to some extent. Paper [4-6]
put forward a phase-locked loop based on second order
generalized
integral,
second
order
generalized
integrator can be achieved an input signal phase angle
shift 900, thereby completing the separation of positive
and negative sequence in the condition of asymmetric
fault voltage, it also can to filter out higher harmonics
of the input signal, the technology can fast and accurate
lock phase lock phase not only in an ideal state but also
In the case of asymmetry fall. But inhibition of low
In the ideal state, voltage of PV grid-connected
harmonic is not obvious. Paper[7] proposed a
inverter containing only fundamental, but under normal
frequency phase-locked based on crossover frequency
circumstances voltage will be affected by turbulence
decoupling adaptive complex filter, which can separate
and contain amount of harmonics, in low voltage
positive and negative sequence by using complex filter
distribution network there is generally considered 5th,
when grid occurs asymmetrical falling, but the complex
7th , 11th and 13th harmonics. Equation of These three-
filter has failed in rapid detection.
phase voltage contained harmonics can be followed:
In addition, the paper [10, 11] proposed an
synchronous technology based on adaptive filter, it can
realize a great dynamic performance, the paper [12, 13]
proposed (least error squares) filter, which can extract
fundamental component from voltage source contained
harmonics, and study [12] apply LES in digital
impedance protection, Study [14] proposed phaselocked loop based on the synchronous rotating
coordinate system, and improvement of the LES filter
Combination of symmetrical components of phaselocked loop, which accurately extract the fundamental


 sin(t   a ) 
U a 


U   U sin(t  2   )  
1
b
 b


3
U c 


2
 c ) 
sin(t 
3


(1)


 sin (6n  1)t  


6 n 1 


2
 
2

U 6 n 1 sin (6n  1)t 
 6 n 1  
3

n 1
 
 
2

sin (6n  1)t  3  6 n 1  




component form harmonic grid and separate the
Where Ua, Ub, Uc are A phase, B phase and C
positive and negative sequence components, improving
phase of three-phase grid; 6n ± 1 represents the
the speed and accuracy of the phase locked loop
harmonic order; U represents the grid voltage
detection algorithm to reduce the impact of harmonics
amplitude of each harmonic order; x for the initial
on the phase detection.
In this paper, in order to suppress the grid voltage
phase of each order grid voltage;  is the angular
frequency of the fundamental component. Whereby the
low-order harmonics influence to the phase-locked
grid voltage is the sum of the fundamental, 5th, 7th,
loop,
11th and 13th harmonics.
combine
the
LES
filter
with
adaptive
synchronization technology, propose new software
phase-locked
error
information and amplitude information of voltage,
squares- second order generalized integrator frequency
fundamental component needs to be raised from the
locked-loop) to suppress the harmonics. Using Matlab
grid voltage distortion , for example, in Phase A, At
/ Simulink for voltage frequency hopping, and
t=t0+t, A-phase grid voltage as follows:
u (t )  U1 sin(t  1 ) 
asymmetrical
loop
drop
LES-SOGI-FLL
and
low-order
(least
In order to obtain accurate phase angle
harmonics
2
U
simulation. The results show that the phase locked loop
can suppress lower order harmonics to reduce the
influence to the phase-locked loop, an asymmetry
failure to accurately separate the positive and negative
sequence components, compared to the traditional
method, the accuracy and the dynamic of LES-SOGIFLL has been further improved. This new method
provides the necessary phase information and
amplitude information to low voltage ride through of
PV inverter.
1 Least error squares
1.1 Principle of least error squares
6 n 1
sin[(6n  1)t  6 n 1 ]
(2)
n 1
Expanding triangular conversion, equation (2) can
be obtained
u (t1 )  U1 cos 1 sin t  U1 sin 1 cos t 
2
U
6 n 1
cos 6 n 1 sin(6n  1)t 
U
6 n 1
sin 6 n 1 cos(6n  1)t
n 1
2
(3)
n 1
By decomposition transform of t=t0+t, available,
it can get formula (4):
u (t1 )  U1 cos(t  1 )sin t0 
U1 sin(t  1 ) cos t0 
2
U
6 n 1
n 1
2
U
6 n 1
cos[(6n  1)t  6 n 1 ]sin(6n  1)t0 
(4)
sin[(6n  1)t  6 n 1 ]cos(6n  1)t0
 u (t1 )   a11
 u (t )   a
 2    21

 
u (t )   a
 10   101
By observing the formula (4), extracted out of
the initial phase angle of the vector containing partially
consisting of the following:
U  u(t1 ) u(t2 )
X   x1
T
sin(13t  1 ) (5)
x2
 a11
A

 a101
Part containing the phase angle frequency can be
composed of the following vector:
a1  U1 sin t0 U1 cos t0
U13 cos13t0 
a102
a110   x1 
a210   x2 
 
 
a 1010   x10 
(12)
Among them,
n 1
x  cos(t  1 ) sin(t  1 )
a12
a22
u(t10 ) ,
T
x10  ,
T
a110 


a1010 
(6)
Namely U=AX, X=A-1U is obtained by matrix
Grid voltage can be get by formula (5), (6) dot:
(7)
u (t )  a1 x1  a2 x1   a10 x10
operations, Based on matrix X calculation can get
When t0=0,that is t=t. compared the x2 element
of formula (5) with the fundamental component of
If the initial sampling time is determined, and the
sampling interval is determined, then the matrix A
formula (2), it can be seen that the second element of x
composed by factor of 10 equations was uniquely
is equal to fundamental component of the grid voltage:
(8)
u1 (t )  x2
determined. In the sampling, the initial sampling time
2.2 The implementation of LES
interval specified, subsequent sampling time is also
Through
the
section
on
can be set to t1=0, then in the case of the sampling
the
uniquely determined. In the power system, there is a
fundamental component of the inverter can be
certain frequency error tolerance. When the deviation
separated by solving type (4). In order to obtain phase
of frequency less than 0.2Hz, it can be tolerated by the
angle information of the inverter voltage, put initial
system; With the development of digital chip
phase Angle of each order power grid voltage as an
technology, the digital chip performance has been
unknown quantity, the equation containing an unknown
greatly improved, to avoid excessive occupation of
amount of 10, which requires 10 equations consisting
chip resources, taking into account the grid frequency
of solving equations. In order to obtain the equations
deviation, the sampling interval of control system is
requires input voltage signal for 10 consecutive
0.1ms, the sampling frequency is 10kHz. The initial
samples. Assuming the sampling time t1, at time t1, the
grid voltage sampling time and sampling interval is
inverter voltage can be expressed as:
determined, then the coefficient matrix A is also
u (t1 )  a11 x1  a12 x2 
deduction,
various order inverter voltage harmonic component.
 a110 x10
(9)
PV grid-connected inverter voltage at time t2 (t2=t1+t,
of which the t for sampling interval) by the following
equation:
(10)
u (t2 )  a21 x1  a22 x2   a210 x10
By analogy, the grid voltage at time t10 (t10=t1+10t)
expression by the following equation:
(11)
u (t10 )  a101 x1  a102 x1   a1010 x10
By equation (8), (9) and (10) can get the following
equations:
uniquely determined:
sin t1

 sin  (t  t )
1
A

sin  (t  9t )

1
cos t1
cos  (t1  t )
cos  (t1  9t )
cos13t1

cos13 (t1  t )  (13)


cos13 (t1  9t ) 
And then through the matrix calculation extracted
fundamental component of the inverter.
2 Adaptive Synchronization
2.1 adaptive filter
When power grid occur asymmetry fall, grid
voltage produces negative sequence component, and
occurs power grid frequency disturbance, This brings
the traditional phase-locked loop a great deal of
influence, In order to obtain a more accurate grid
x

frequency, extract positive and negative sequence
component of grid voltage, Paper[10] proposed an
adaptive notch filter. Dynamic characteristics of the
adaptive filter is described by the following equation:


u
x

Fig. 2
module of frequency locked loop
As can be seen from the above analysis, the
x   x  2 e(t )
2
   x e(t )
(14)
e(t )  u (t )  x
adaptive filter synchronous technology uses a closedloop control, the adaptive filter center frequency along
The u(t) represents the input of grid voltage, 
represents adaptive filter estimated frequency,
with the optimization algorithm automatically adjusted
adjustable parameter ζ and γ determines the estimated
determines the depth of the notch, affect the stability of
accuracy and convergence rate of the adaptive filter.
the system, γ determines the speed of the filter
For the voltage grid u(t)=A sin(t+), The only
periodic trajectories of Adaptive filter as follows:
adaptation, in particular, it also determines the rate of
 x    A /  cos(t   ) 
O   x    A sin(t   ) 
  


  

convergence speed can be obtained by increased
(15)
so that the output signal is more accurate. Parameter ζ
convergence of the frequency error, and faster
parameter γ. By adjusting the parameters δ and γ can
make adaptive synchronization technology has the
Adaptive notch filter (ANF) structure can be obtained
ability to quickly and accurately detect the phase angle
by the formula (13) ,as shown below
and amplitude information of the voltage information.
u

e
2

x




x

Fig. 1
1.2 double adaptive filter synchronous
technique
Double adaptive filter synchronous technique is
the technology to extract symmetrical component of
grid voltage based on adaptive filter. When gird occurs
asymmetric fault, the grid will produce positive and
Structure 0f the trapper
As can be seen, Adaptive notch filter has two
negative sequence components. The positive and
output signal, one signal is fundamental x , the other is
a fundamental shift signal 90 ° phase θx. the amplitude
negative sequence component transformation from
of the fundamental can be calculated by These two
two-phase static coordinate system according to Clark
signals, the relationship is
A=((θX)2+X2)1/2.
Through
static three-phase coordinate system transformation to
can get the following expression
the calculation of the grid voltage amplitude can judge
whether the drop occurred. If the value of A is less than
the rated voltage, indicating grid voltage drop occurs,
When the drop amplitude reaches the standard of Low
voltage ride through, grid-connected inverters need to
execute reactive power control, injecting reactive
current, supporting voltage recovery.


v
 T  vabc
(16)


v
 T  vabc
(17)
Through calculation can get
1 1

v
 T   v ; T    



 2 q
q 
1 
(20)
q
1 
(21)
that frequency tracking is associated with the error
1 1

v
 T   v ; T    



 2  q
between input power grid voltage u as with
q=ejπ/2 is lagging behind 900 phase-shift operator.
fundamental wave of output signal, at the same time
By formula (11), (12) in the case of grid asymmetry
also with the frequency of the power grid and the
falls, positive and negative sequence of two-phase
fundamental component shitted 90 °. The control
stationary coordinate system can be separated, then
structure shown in FIG. 2 obtained by analyzing:
transform
The second equation of formula (13), it is known
the
two-phase
stationary
coordinate
transformation to the three-phase stationary coordinate
by Clark inverse system, Thus Realizes the separation
of positive and negative sequence.
In the above analysis of the ANS-FLL, it can
quickly and accurately track the grid voltage phase
angle information and detect voltage amplitude
variation under asymmetric fault. When low harmonics
exist in the power grid, the ANS-FLL do not work well.
Before phase lock, fundamental component wound be
（a）comparison of angular frequency
extracted from the grid voltage containing harmonics.
So this paper proposes a synchronization techniques
based on LES filter and adaptive filter, low-order
harmonics of the low voltage distribution grid can be
significant restrained by new LES-SOGI-FLL, greatly
improving the detection accuracy and speed voltage
frequency and amplitude. The basic structure as shown
in Figure 3
（b）positive sequence of LES- SOGI
Fig. 3
3
Structure 0f LES-SOGI-FLL
Simulation
In MATLAB/Simulink simulation software to
build two kinds of phase-locked loop, the one phase-
（c）positive sequence of SOGI
Fig. 4
Frequency simulation Figure
locked loop for the traditional second-order generalized
See from Figure 4, when in the grid voltage
integral, the other for LES - SOGI - FLL, simulating in
frequency jump, change rate of the frequency more
the case of grid frequency change occurs, the
than 4%, By figure (a) of figure 4 can see in the cases
occurrence of asymmetric grid voltage drop and grid
of serious frequency variation, The traditional SOGI
containing harmonics, The basic condition is that the
phase-locked loop and LES-SOGI–FLL simulation
voltage amplitude is 220V, and the frequency of
curve basic coincidence, it can quickly locking grid
f=50Hz.,assumed to be a fault in the 0.1s.
angular velocity within 50ms, it indicates that the phase
Simulation conditions (1) voltage at 0.1s, the
locked loop is fast; By comparing (b), (c) of figure 4
frequency of the power grid voltage jump, frequency
can be seen that these two kinds of phase-locked loop
from the original 50HZ into 48HZ, and its two kinds of
can accurately and fast calculate the positive sequence
different phase-locked loop simulation waveforms
component of grid voltage under the condition of
shown in figure;
serious frequency changes.
Simulation condition (2) in the time of 0.1s, the
voltage occur asymmetric fall, in which the A phase
voltage drop is 0.5pu, that is, 110V. Two kinds of
different phase lock loop in the asymmetric fault
13th harmonics, Which contains a specific harmonic
simulation results are shown in figure 5;
amplitude of the fifth harmonic is 40V, amplitude of the
seventh harmonic is20V, the amplitude of the 11th
harmonic is 30V and amplitude of the 13th harmonic
is10V. Where THD = 0.061983, the simulation results
are as follows:
（a）comparison of angular frequency
（a）waveform of harmonic
（b）positive sequence of LES- SOGI
（b）comparison of angular frequency
（c）
positive sequence of SOGI
Fig. 5
Simulation of asymmetric voltage drop
The simulation results can be obtained in the
condition 2: When the grid asymmetric drop, SOGI
PLL and LES-SOGI–FLL are able to quickly detect the
angular frequency of the voltage, the accurate phase
locking time is less than 30ms and angular frequency
（c） negative sequence of SOGI
fluctuation is smaller, the two phase locked loop
angular frequency waveform coincide, This shows that
LES filter did not affect the quickness of SOGI. Form
the comparison of graph (b) and (c), two phase-locked
loop can accurate output amplitude of positive
sequence component, and the amplitude voltage
changes in the natural.
Simulation conditions (3) in the time of
0.1s ,power grid was injected into the 5th, 7th, 11th and
（d）positive sequence of SOGI
detecting voltage frequency and phase tracking, and
implement the positive and negative sequence
separation.
(3) Under the condition of the power grid voltage
with low harmonic, the phase-locked loop can fast
accurate output of positive sequence component and
phase Angle information, it also can suppress the
influence of harmonics
（e）positive sequence of FLL-SOGI
Fig. 6
simulation of contain harmonic
Therefore, the phase locked loop proposed in this
paper can meet the requirements of the low voltage ride
As can be seen from the figure (a), the grid
through of the grid, support the grid connected
contains many harmonic components, its THD value
operation of the power converter, and ensure the safe
reached 6.2%, SOGI-FLL can not be well eliminate the
operation of the power grid.
influence of harmonics on the angular frequency, By
5
figure (b) can get the traditional SOGI-FLL containing
[1] Li Ming, Wang Yue, Fang Wei, et al. Undocumented cross
obvious angular frequency fluctuations, The output of
signal generated virtual single phase locked loop DQ [J].
Chinese CSEE, 2011,31 (15): 70-76.
the LES-SOGI –FLL is smooth and stable, and can be
locked accurately in the 20ms in the case of such
serious distortion, From the graph (c) and (d) it can be
seen that the classical SOGI-FLL cannot be very good
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converter [M], Zhou Keliang, Wang Zheng, et al, translated.
positive sequence components affected by harmonics.
By figure (e) can get, positive sequence component
waveform output by LES–SOGI-FLL is smooth, and
no distortion, Show that the phase lock loop can
restrain the influence of harmonic to the positive
sequence component.
4
conclusion
In view of the actual, power grid containing a
small amount of low order harmonics and frequently
asymmetric fault, etc., this paper puts forward the
phase-locked loop based on combination of dual
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(1)LES-SOGI-FLL can fast track the amplitude
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(2) In the grid voltage occurrence frequency
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