Research Journal of Applied Sciences, Engineering and Technology 4(20): 4028-4033, 2012
ISSN: 2040-7467
© Maxwell Scientific Organization, 2012
Submitted: December 23, 2011
Accepted: April 23, 2012
Published: October 15, 2012
Research on the Decoupling Control of Wind Power Grid-connected Converter
Jian Guo, Yong Yang and Ligang Song
College of Mechanical and Electrical, Harbin Engineering University, Harbin 150001, PR China
Abstract: In this study, we provide a method to independent control the active current and the idle current
which are output by the inverter, the power factors are achieved to be adjusted. Moreover, the angle of grid
needs to be inspected by the vector control in real time so that the Software Phase-Locked Loop which has a
powerful ability in phase locking under the rotating reference frame is adopted to get the accurate electric
angles. In addition, a grid-connected experiment of the gird-side inverter is also conducted and the unit power
factors of the inverter get connected by this method.
Keywords: Current decoupling control, direct-drive wind turbine, grid-connected converter, software phase
lock loop
INTRODUCTION
Nowadays wind energy has proved to be one of the
most competitive and efficient renewable energy sources
and as a result its use is indeed continuously increasing.
For direct driving wind power generators, converter
system is responsible for converting mechanical energy of
wind turbines into electrical energy and transmitting it to
power grid. This part is the core of the whole system. And
it has direct influence on the performance, efficiency and
power quality of the whole system. So it is important to
research converter system suitable for direct driving wind
power generators in the domain of wind power technology
all the time (Xiao, 2010). Zhang and Zhang (2003) have
a research of the PWM rectifier and its control. ElAmawy and Mirbod (1988) provide an efficient softwarecontrolled PLL for low-frequency applications. Bertocco
et al. (2000) study the robust and accurate real-time
estimation of sensors signal parameters by a dsp
approach. Vikram and Blasko (1997) analyse the
operation of a phase locked loop system under distorted
utility conditions. Chen (2008) study the research on fullscale grid-connected power conversion technology for
direct-driven wind generation system. Guo et al. (2008)
have a research of a research on the control system of
wind power grid-connected inverter.
Two sides converter of total power converter system
are interlinked in theory and structure. Through research
on control method of grid-side converter, it can provide
the thought to design the total power converter system.
First, according to the establishment the mathematic
model of converter system, the decoupling control
strategy of grid voltage feed forward is analyzed and
determined. And then the power factor is controlled
effectively. Due to the shortage of traditional Phase Locke
Loop (PLL), the software PLL of coordinate
transformation is used. It can ensure that the grid phase is
accurately locked at the condition of grid with harmonic
waveform. At last, the grid-connected experiment of
converter is done. The results are also analyzed. And the
effectiveness of control method is proved.
In this study, the mathematic equation of converter
output current is achieved. Through decoupling control
mode of current, independent control of active current and
reactive current of output are realized. The influence that
voltage fluctuation of power grid has on system is
decreased by adding feed forward of power grid voltage.
The frequency and phase of power grid are completely
locked by using software PLL of reactive power theory.
And software PLL is of good dynamic and static
characteristics. It can be applied to decoupling control of
grid-connected converter with higher lock requirements.
The effectiveness and correctness of control strategy of
converter are proved sufficiently.
METHODOLOGY
To establish the mathematic model of converter: The
topological structure of three-phase voltage PWM
converter is shown in Fig. 1.
Fig. 1: The topological structure of three-phase PWM converter
Corresponding Author: Jian Guo, College of Mechanical and Electrical, Harbin Engineering University, Harbin 150001, PR
China
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Res. J. Appl. Sci. Eng. Technol., 4(20): 4028-4033, 2012
Clark transform is written as follows:
b
q
ß
d
θ
⎡
⎢
⎡ xα ⎤
⎢ ⎥ 2 ⎢⎢
⎢ xβ ⎥ = 3 ⎢
⎢x ⎥
⎢
⎣ 0⎦
⎢
⎣
E
ω
a,a
1
2
⎡ x d ⎤ ⎡ cosθ
⎢x ⎥ = ⎢
⎣ q ⎦ ⎣ − sin θ
Fig. 2: The relationship among each coordinate system
The switch function of converter is used to describe
the system. To define Sk (k = a, b, c) as switch function of
switching tube, when the up bridge arm is conducted and
the down bridge arm is turned off, Sk = 1. Otherwise
Sk = 0.
Considering point O as reference point of zero
potential, for the AC side, based on KVL, there is:
dia
⎧
⎪ ea = Ria + L dt + (v dc sa + v N 0 )
⎪
dib
⎪
+ (v dc sb + v N 0 )
⎨ eb = Rib + L
dt
⎪
dic
⎪
⎪ ec = Ric + L dt + (v dc sc + v N 0 )
⎩
1
2
3
2
1
2
1 ⎤
2 ⎥⎡x ⎤
⎥ a
3⎥⎢ ⎥
−
x
2 ⎥⎢ b ⎥
⎢
1 ⎥ ⎣ x c ⎥⎦
2 ⎥⎦
−
(5)
ea+eb+ec = 0, ia+ib+ic = 0
⎧ dv dc 3
⎪ C dt = 2 (id S d + iq S q ) − i L
⎪
⎪ did
− ωLiq + Rid = ed − v dc S d
⎨L
⎪ dt
⎪ diq
+ ωLi d + Riq = eq − v dc S q
⎪L
⎩ dt
(2)
(3)
Based on KCL, for DC side, there is:
dv dc
v − eL
= idc − i L = ia sa + ib sb + ic sc − dc
dt
RL
(6)
(7)
For the three-phase equilibrium power grid voltage of
reverse phase, there are e" = Em sin(Tt), eb = Em
sin(Tt+2B/3) and ec = Emsin(Tt!2B/3). In accordance
with the choice of coordinate system, axis q of rotation
coordinate system (d, q) is coincided with
electrodynamics potential vector E of power grid all the
time. And axis d component of power grid
electrodynamics potential is satisfied with ed = 0.
Active power P = e"i"+ebib+ecic = 3(edid+eqiq)/2 is AC
side. Similarly, reactive power is Q = 3(ediq+eqid)2.
When three-phase voltage is equilibrium, ed = 0. So:
According to (1) and (2), then:
sa + sb + sc
vdc
3
sin θ ⎤ ⎡ xα ⎤
⎢ ⎥
cosθ ⎥⎦ ⎣ x β ⎦
In the light of the above twice coordinate
transformation, the mathematic model of grid side
converter in the rotation coordinate system is written as
follows:
(1)
For node O, there is:
C
0
−
Park transform is written as follows:
c
vN0 = −
1
⎧
⎪⎪ P =
⎨
⎪Q =
⎪⎩
(4)
Based on Clark transform and Park transform, twophase coordinate system (", $) and two-phase rotate
coordinate system are ruled respectively as follows. At the
initial state, rotate coordinate system (d, q) is coinciding
with rest coordinate system (", $). Initial included angle
between axis d and axis " 2 = 0º. Moving coordinate
system (d, q) is synchronous rotation at angular frequency
T of power grid. Then the included angle between axis d
and axis " 2 = -Idt is showed in Fig. 2.
3
ei
2 qq
3
ei
2 qd
(8)
Assume that the power grid is stable. It is thus clear
that active power and reactive power are determined,
respectively by current iq and id of rotation coordinate
system at steady state. If active current iq and reactive
current id are independent controlled effectively, the
output active power and reactive power of converter are
decoupling controlled completely (Zhang and Zhang,
2003).
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Res. J. Appl. Sci. Eng. Technol., 4(20): 4028-4033, 2012
Fig. 3: The control block diagram of SPLL
Software phase lock loop: In the decoupling control of
converter, the controlled variable is needed to transform
coordinate system. At the process of Park transformation,
the included angle between axis d and axis " is required.
And it can be calculated through detecting angle of power
grid. This function is realized by PLL. Generally, there
are several methods described as follows.
The first way is the method of crossing zero
comparative phase lock (El-Amawy and Mirbod, 1988).
The square signal of zero crossing point in sine voltage is
caught. The catching timer is clear at rising edge of square
signal. When the current angle of power grid needs to be
known, the current value of catching timer is read out.
Through calculating the current angle of power grid is
achieved. If there is harmonic interference in power grid
and DC shifting in sine voltage, the effectiveness of this
method is obviously decreased and its dynamic property
is worse.
The second way is the inverse trigonometric function
method (Bertocco et al., 2000). To detect the voltage
value of two-phase or three-phase power grid, the angle of
power grid can be calculated by using arc tangent after
Clark transformation. Inverse trigonometric function
belongs to floating point calculation and it will expend
plentiful computation time. It is not advisable for instant
close of loop control of converter.
The third way is software PLL based on rotation
coordinate system transformation (Vikram and Blasko,
1997). Its control block diagram is showed in Fig. 3.
Taking a couple of line voltage of power grid sample,
with regard to three-phase equilibrium power grid of
reverse phase sequence, (9) is obtained in two-phase
fixed-coordinate system (", $) and is written as follows:
1
⎡
⎡ eα ⎤ 2 ⎢ 1 − 2
⎢e ⎥ = ⎢
3
⎣ β ⎦ 3 ⎢0
⎢⎣
2
1 ⎤ ⎡ E sin θ
⎤
m
⎥
⎡ sin θ ⎤
2 ⎥⎢
o
⎥ E sin(θ + 120 ) ⎥ = E m ⎢
⎥
3⎥⎢ m
⎣ cosθ ⎦
⎢ E sin(θ − 120 o ) ⎥
−
⎦
2 ⎥⎦ ⎣ m
−
(9)
The Park transformation of (9) is achieved by using
output angle 2* of PLL and is written as follows:
⎡ ed ⎤ ⎡ cosθ * − sin θ *⎤ ⎡ eα ⎤
⎡ sin(θ − θ *) ⎤
⎢e ⎥ = ⎢
⎥ ⎢ e ⎥ = E m ⎢ cos(θ − θ *) ⎥
sin
θ
*
cos
θ
*
⎣
⎦⎣ β ⎦
⎦
⎣ q⎦ ⎣
(10)
If phase lock is succeeded, 2 = 2* and ed = 0. The
difference value between ed and given 0 is represented as
the deviation between output angle of PLL and angle of
power grid. If output angle 2* is less than angle 2 of
power grid, feedback quantity ed>0. The deviation of
negative feedback is adjusted by PI and then deviation of
angular velocity )T<0 is obtained. After )T and basic
angular velocity of power grid T0(T0 = 100B) of
superposition, the output angular velocity T*>T0 is got.
The angular difference is gradually reduced between
output angle of PLL and power grid. At last, angle 2*of
power grid is gained through integration.
At the conditions of power grid imbalance and
harmonic wave in power grid, the power grid is
decomposed into positive-sequence component, zerosequence component and negative-sequence component.
After coordinate system transformation, zero-sequence
component becomes zero and it can be ignored. The
positive-sequence component of fundamental wave is
transformed into direct current. The negative-sequence
component and higher harmonic are both transformed into
high-frequency components. There are two integral
elements in PLL. So it itself is of good low pass filtering
function. And high-frequency component can be filtered
without adding other filters. The positive-sequence
component of fundamental wave can be locked by PLL
and is not influenced by higher harmonic of power grid.
Control strategy: The three-phase converter generally
uses the double closed-loop control which consists of
voltage outer-loop and the current inner-loop, the current
vector following the direction of the voltage vector of
power grid and the output of closed-loop is transformed
into pulse control signal through PWM adjustment. The
function of voltage outer-loop is mainly to stabilize
voltage of DC side. At the same time the output of voltage
loop is represented as the given of current loop. The major
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Res. J. Appl. Sci. Eng. Technol., 4(20): 4028-4033, 2012
function of current inner-loop is realized to be connected
to grid at unity power factor. At this time, the reactive
current given is zero. At the condition of reactive power
compensation, the output of reactive power is realized by
giving reactive current.
It is shown from (7) that dq component of AC side of
the converter has mutual coupling, which causes some
difficulty to design the controller. Therefore the
decoupling control is adopted (Chen, 2008). In addition,
there is voltage fluctuation of power grid in reality. So it
puts the power grid voltage as the feed-forward of the
control system in order to eliminate the negative effect on
it. The decoupling control method of power grid voltage
feed forward is obtained. When the PI adjuster is acted as
current adjuster, the input control voltage of PWM
converter is calculated as follows:
⎧
⎪ vq * =
⎪
⎨
⎪v * =
⎪⎩ q
(
reactive current value of output of converter are following
their given value respectively. The decoupling control of
current is realized (Song, 2011). In addition, it is showed
that voltage drop of both sides of filter of AC side is
determined by current-loop output value adjusted through
PI adjuster from (12). The output voltage of the variable
current bridge is Vx=VL+Ex. According to the maximal
withstand voltage value of switching element of converter
bridge, the maximal voltage drop of both ends of
inductance can be determined. The value of current loop
output is limited based on it.
Another requirement of the grid-connected converter
is to stabilize voltage of DC side. It is achieved depending
on PI adjusting of voltage outer-loop. Using PI adjuster,
equation of the voltage-loop is showed as follows:
K vI ⎞
⎛
U out = ⎜ Kvp +
⎟ (U *dc − U dc )
⎝
s ⎠
)
KiI ⎞
⎛
− ⎜ KiP +
⎟ i * − i − ωLid + eq − Riq
⎝
S ⎠ q q
(11)
KiI ⎞
⎛
− ⎜ KiP +
⎟ (i * − i ) − ωLiq + ed − Rid
⎝
S ⎠ d d
(13)
where,
KvP, KvI : The scale factor and integral factor of the
voltage-loop
: The given value of the DC
U*dc
where,
KiP ,KiI : The scale factor and integral factor of the current
inner-loop
i*q, i*d : The given of the active current and reactive
current
Substitution into model equation of system and
simplification, (12) is got and is written as follows:
⎧ diq ⎛
KiI ⎞
= ⎜ KiP +
⎟ i − i *q
⎪L
s ⎠ q
⎪ dt ⎝
⎨
⎪ L did = ⎛⎜ K + KiI ⎞⎟ (i − i * )
d
⎪⎩ dt ⎝ iP
s ⎠ d
(
)
(12)
So the control diagram of the grid side of converter
is shown in Fig. 4.
Because of the symmetry of two current loops, just
take the design of iq loop as an example, the deviation of
the voltage outer-loop is as the given value of the active
current i*q after being adjusted by PI adjuster. It forms the
small error signal with the feedback of the active current
iq after being adjusted by PI adjuster again. The
decoupling power grid voltage eq, voltage signal of gridconnected resistance and inductance and former signal
handled by PI adjuster are superposition. Then the
reference voltage signal vq is generated. According to the
reference voltage signal vq and vd, SVPWM produces the
three bridge arms control signal so as to achieve the
e q-Ri q
U dc
*
iq
PI
*
PI
V q*
ia
Udc
iq
WL
SVPW M
id
id
ic
WL
*
PI
V d*
e d-Rid
Fig. 4: The control block diagram of decoupling control of grid side of converter
4031
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Res. J. Appl. Sci. Eng. Technol., 4(20): 4028-4033, 2012
90
70
50
30
10
-30
-50
1
21
41
61
81
10
1
121
141
161
181
20
1
221
24
1
261
28
1
301
32
1
34
1
361
38
1
-10
-70
-90
Fig. 6: The curve of feedback quantity Ed of PLL at stable state
a) the phase lock effect at frequency 50 Hz
Fig. 7: The current waveform output of converter
b) the phase lock effect at frequency 45 Hz
Fig. 5: The phase lock effect at different frequency
purpose of controlling the output current (Guo et al.,
2010).
THE EXPERIMENTAL RESULTS
AND ANALYSIS
The experiment of software PLL: Use frequency
inverter to control the motor to output three-phase AC
with variable frequency. In order to improve voltage
waveform, three-phase isolation transformer is connected
to the frequency inverter. Three-phase transformer is
represented as power grid and the phase lock is studied.
To measure a couple of line voltage, the angle of power
grid is got through software PLL. The three-phase AC,
which is corresponding to modulation output angle of
SVPWM, is used for DSP. The voltage waveform is
observed by using another three-phase transformer. The
phase lock effects are achieved at different frequency and
shown in Fig. 5. In Fig. 5, the bigger amplitude is voltage
input and the smaller amplitude is voltage input.
From the above experimental results, it is showed
that frequency and phase of three-phase AC voltage input
are completely locked based on software PLL of reactive
power theory. It is of good dynamic and static
characteristics. It can be applied to decoupling control of
grid-connected converter with higher phase lock
requirement.
At the frequency of 50 Hz, when PLL is at the steady
state, feedback quantity Ed is observed and the feedback
curve is obtained shown in Fig. 6. From Fig. 6, feedback
quantity Ed is stabilized at zero all the time. And its
fluctuation range is about ±2%. It illustrates that the phase
lock is achieved and is at stable state.
The experiment of converter: The grid-connected
current waveform of grid-side converter is shown in
Fig. 7. In it, the bigger amplitude is the phase voltage
waveform of power grid and the smaller amplitude is the
current waveform output. The current waveform is
achieved through taking sample of the resistance after
being measured by the current hall sensor. From Fig. 7, it
is clearly shown that grid-connected current has the same
frequency as voltage of power grid. And their phase is
conversed. It is connected to grid at unity power factor.
In order to prove the control of the DC voltage outerloop, the step response curve of the voltage outer-loop is
obtained and shown in Fig. 8. It shows that the voltage
outer-loop is of typical characteristics of the first-order
system. And the transmit time is less than 50 ms. The
adjustment of DC voltage is finished at two or three
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Res. J. Appl. Sci. Eng. Technol., 4(20): 4028-4033, 2012
loop is less and its dynamic response is fast. The
effectiveness and correctness of control strategy of
converter are proved sufficiently.
ACKNOWLEDGMENT
This study is partially supported by the Fundamental
Research Funds for the Central Universities
(HEUCF110707).
REFERENCES
Fig. 8: The response curve of voltage loop
power grid periods in voltage out-loop. It is of good
dynamic response.
CONCLUSION
By means of analyzing the mathematic model of gridside converter, mathematic equation of converter output
current is achieved. Through decoupling control mode of
current, independent control of active current and reactive
current of output are realized. The influence that voltage
fluctuation of power grid has on system is decreased by
adding feed forward of power grid voltage. The frequency
and phase of power grid are completely locked by using
software PLL of reactive power theory. And software
PLL is of good dynamic and static characteristics. It can
be applied to decoupling control of grid-connected
converter with higher lock requirements. From the
analysis of experimental results, the frequency of gridconnected current is the same as the power grid voltage
and their phase is inversed. And it is connected to grid
with unity power factor. The static error of voltage outer
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2000. Robust and accurate real-time estimation of
sensors signal parameters by a DSP approach. IEEE
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Chen, Y., 2008. Research on Full-scale Grid-connected
Power Conversion Technology for Direct-driven
Wind Generation System. Doctoral Dissertation of
Beijing Jiaotong University, China.
El-Amawy, A.A. and A. Mirbod, 1988. An efficient
software-controlled PLL for low-frequency
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Guo, J., L.G. Song and Y. Yang, 2010. A research on the
control system of wind power grid-connected
inverter. 2010 International Conference on Materials
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551-556.
Song, L.G., 2011. To Control Wind Turbine Power with
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Vikram, K. and V. Blasko, 1997. Operation of a phase
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Xiao, C.Y., 2010. Experiences and Enlightenment of
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