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2016 China International Conference on Electricity Distribution (CICED 2016)
Xi’an, 10-13 Aug, 2016
A Modified Grid Voltage Feedforward Method to Improve
the Stability-Robustness of the Grid-Connected Voltage
Source Converter under Weak Grid Conditions
Heng Wu
NR Electric Co., Ltd
Abstract—The grid voltage feedforward method
is widely used in the control scheme of the
grid-connected voltage source converter (GC-VSC)
because it can improve the quality of the injected grid
current as well as improving the dynamic performance
of the system during grid voltage variation. However,
when the grid is weak, this feedforward method may
amplify the high-frequency injected grid current
harmonics or even result in instability of the system.
To solve this problem, a low-pass filter which is
incorporated in the grid voltage feedforward path is
proposed
in
this
paper.
Therefore,
the
stability-robustness of the system is improved,
meanwhile, the advantage of the grid voltage
feedforward method is also remained. Finally, the
simulation and real industrial application results are
given to demonstrate the effectiveness of this control
method.
Index Terms—Grid-connected Voltage Source
Converter (GC-VSC), weak grid, grid voltage
feedforward, low-pass filter
I. INTRODUCTION
Nowadays,
the
power-electronic
based
grid-connected voltage source converters (GC-VSC),
such as grid-connected inverters, static var generators
(SVG), etc, are wildly used in the power grid [1]. It is
required that these GC-VSCs should inject high
quality ac current into the grid. However, the GC-VSC
usually exhibits low harmonic impedance presented to
the grid, which means the injected grid current from
the GC-VSC is more sensitive to the grid voltage
distortion [2]. To solve this problem, The grid voltage
feedforward method is usually adopted in the control
scheme of GC-VSC because it can almost eliminate
the effect of grid voltage distortion to the injected grid
current, and it can improve the dynamic performance
of the system during grid voltage variation as well [3].
However, recent literatures have pointed out that when
the GC-VSC is connected to the weak grid (which
features low short-circuit capability and unneglectable
grid impedance), this feedforward method may
amplify the high-frequency injected grid current
harmonics or even result in instability of the system
[4][5]. Therefore, how to increase the quality of the
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injected
grid
current
as
well
as
keep
stability-robustness of the system under weak grid
conditions is still a question.
The rest of the paper is organized as follows.
Section II analyzes the stability of the GC-VSC with
grid voltage feedforward under weak grid conditions.
Section III proposes a method which incorporates a
low-pass filter in the grid voltage feedforward path to
improve the stability-robustness of the system, the
simulation and real industrial application results of
10kV/10MVar SVG in Xinjiang Uygur Autonomous
region are presented in Section IV, and Section V
concludes the paper.
II. STABILITY ANALYSIS of THE GC-VSC WITH
GRID VOLTAGE FEEDFOWARD UNDER WEAK
GRID CONDITIONS
Fig. 1 shows the generic structure of the digitally
controlled GC-VSC with grid voltage feedforwad
(for simplicity, the power control loop is not
considered here). The GC-VSC is connected to the
grid at the point of common coupling (PCC)
through an output filter Lf. Vin is the input dc
voltage, and vAB is the output voltage of the inverter
bridge, For simplification, the grid at the PCC (vPCC)
is modeled by its Thevenin equivalent circuit,
consisting of an ideal voltage source vg in series with a
grid impedance Zg .
S1
S3
A
Vin
S2
Lf
+
vAB
–
B
Zg
ig
vPCC
+
vg
–
S4
S1~S4
Gate Driver
PWM Modulator
Hi
Gff(s)
vm
+
Gdelay(s)
Gi(s)
–
+ iref
+
Fig. 1. Generic structure of the digitally controlled GC-VSC with grid
voltage feedforwad
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2016 China International Conference on Electricity Distribution (CICED 2016)
vPCC
Gff(s)
iref (s) +
–
Gi(s)
+
+
Gdelay(s)
vm
KPWM
vAB
+ –
1
sLf
ig(s)
Hi
Fig. 2. Control scheme of the GC-VSC
The corresponding control scheme of the
GC-VSC is shown in Fig. 2, where iref is the current
reference, Hi is the sensor gain of the injected grid
current ig and Gi(s) is the current regulator. KPWM is
the transfer function of the inverter bridge, expressed
as KPWM=Vin/Vtri, where Vin is the input voltage and Vtri
is the amplitude of the triangular carrier. Gdelay(s)
represents the computation delay and pulse-width
modulation (PWM) delay introduced by digital control
system, and it has been pointed out that the delay time
is approximately equal to 1.5Ts [6], where Ts is the
sampling period of the digital controller, therefore, we
have
Gdelay (s)  e1.5sTs
(1)
The grid voltage feedfoward control is adopted
by feedforwarding vPCC to the output of the current
controller with transfer function Gff(s).
According to Fig. 2, the injected grid current ig can
be derived as
v
ig  s   is  s   PCC
(2)
Zo  s 
where is(s) and Zo(s) are the Norton equivalent
current source and output impedance, respectively,
expressed as
is  s  
1 T s
iref  s 
Hi 1  T  s 
Zo  Zoc / / Zoff 
Zoc Zoff
Zoc  Zoff
(3)
(4)
where T(s) is the loop gain of the current loop,
which can be derived as
T s 
H i Gi  s  Gdelay  s  K PWM
sL f
(5)
The closed loop output impedance of the
GC-VSC can be regarded as the paralleled
impedance of the impedance introduced by current
loop (Zoc) and the impedance introduced by grid
voltage feedforward (Zoff) [5], as shown in Eq. (4),
these impedance can be derived as
Z oc  s   sL f 1  T  s  
(6)
Z off  s  
 sL f 1  T  s  
Gdelay  s  G ff  s  K PWM
(7)
According to (2), the GC-VSC can be modeled by
its Norton equivalent circuit, consisting of an ideal
current source is(s) in parallel with an output
impedance Zo(s). Likewise, the grid can be modeled by
its Thevenin equivalent circuit, consisting of an ideal
voltage source vg(s) in series with the grid impedance
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Zg(s). Fig. 3 shows the equivalent circuit of the grid
connection system, from which, the injected grid
current ig can be derived as
Zo  s 
1
ig  s  
is  s  
vg  s  (8)
Zo  s   Z g  s 
Zo  s   Z g  s 
According to (8), in order to suppress the grid
current distortion induced by vg(s), the magnitude of
Zo(s)+ Zg(s) should be large enough. Since Zg(s) is
determined by the power grid, only Zo(s) can be
shaped to achieve this target.
PCC
is
Zo
ig + Zg
vPCC
vg
–
Inverter
PCC
Grid
Fig. 3. Equivalent circuit of the GC-VSC connected to the grid
As Zo(s) is paralleled impedance of Zoc(s) and Zoff(s),
if Zoff(s)=−Zoc(s), the paralleled impedance Zo(s) would
be infinite and the influence of vg(s) to ig(s) will be
entirely eliminated. Based on this requirement, it can
be solved that
1
G ff  s  
(9)
Gdelay  s  K PWM
However, 1/Gdelay(s) features the unity gain with a
pure phase-leading, the prediction component cannot
be realized physically. Therefore, the implementation
function can only be closely approximated as [5]
1
G ff  s  
(10)
K PWM
Substituting (10) into (4), (6)and (7)， the output
impedance Zo(s) can be derived as
1
Zo  s  
Z oc  s   K ap  s  Z oc  s 
(11)
1  Gdelay  s 
where Kap(s) is the amplification factor introduced by
the feedforward control, and its frequency response
plot is shown in Fig. 4. From Fig.4, it can be seen that
grid voltage feedforward can greatly increase the
output impedance within low frequency ranges, which
is helpful to increase the harmonic-rejection ability of
the system, but it fails to do so in the high frequency
ranges due to the computation delay and PWM delay
Gdelay(s). Moreover, because of Gdelay(s), the grid
voltage feedforward introduces a severe phase-lag to
the output impedance, which greatly weakens the
stability-robustness of the system, which has also been
pointed out in [5].
To guarantee stability-robustness against grid
impedance variations, the GC-VSC must satisfy the
following criterions [7]:
1) the current-controlled GC-VSC is stable when
operating under an ideal grid with assumption of
Zg(s)= 0;
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2016 China International Conference on Electricity Distribution (CICED 2016)
2) the impedance ratio Zg(s)/Zo(s) satisfies the
Nyquist criterion.
The first criterion can be easily satisfied with
properly design of the current regulator. For the
second criterion, if Zg(s) and Zo(s) intersect at fi, the
phase margin (PM) must be a positive one, i.e., PM >
0. Here, PM is expressed as
PM  180  Z g  f i   Z o  f i  
(12)
Therefore, to improve stability-robustness, it is also
necessary to boost the phase of Zo(s) to acquire
sufficient PM. However, as pointed out above, grid
voltage feedforward control introduces a severe
phase-lag to the output impedance in the high
frequency ranges, which greatly weakens the
stability-robustness of the system, as shown in Fig. 4,
this is a problem must to be solved.
K zp  j 2 f   
|Kzp(j2πf)|(dB)
80
60
40
20
0
−20
180
90
0
−90
−180
1
10
102
f(Hz)
103
104
iref (s) +
–
Gi(s)
+
+
Gdelay(s)
vm
KPWM
vPCC
vAB
+ –
Fig. 5. Control scheme of the GC-VSC with a low pass filter
incorporated in its feed forward path
1
(14)
2 T
Obviously, lower value of fL means better
attenuation ability of the low pass filter.
Based on Fig. 5, together with Eq. (11), the output
impedance of the GC-VSC with the low pass filter
adopted in the feedforward path can be derived as:
1
Z o _ LPF  s  
Z s
Gdelay  s  oc
(15)
1
Ts  1
Based on Eq. (15), it is clear that:
1) In the low frequency ranges, Ts+1≈1, therefore
Zo_LPF(s)≈Zo(s), which means the advantage of the grid
voltage feedforward control is still remained.
2) In the high frequency ranges, Gdelay(s)/(Ts+1) ≈0,
therefore Zo_LPF(s)≈Zoc(s), which means the effect of
the grid voltage feedforward control is greatly reduced
in the high frequency ranges, as a result, the
stability-robustness of the system is increased.
fL 
How can we improve the stability-robustness of the
system as well as remaining the advantage of grid
voltage feedforward control? As mentioned before, the
grid voltage feedforward control can greatly increase
the output impedance within low frequency ranges,
which is helpful to increase the harmonic-rejection
ability, but it also introduces a severe phase-lag to the
output impedance in the high frequency ranges, which
weakens the stability-robustness of the system.
Therefore, it is reasonable to adopt the grid voltage
feedforward control in the low frequency ranges while
eliminating its effect in the high frequency ranges, to
achieve this, a simple and straightforward idea is
proposed in this paper which incorporates a first order
low-pass filter in the grid voltage feedforward path, as
shown in Fig. 5, the transfer function of the first order
low pass filter is expressed as
1
GLPF  s  
(13)
Ts  1
Its corner frequency fL is defined as:
Paper No xxx
Magnitude(dB)
Zoc
Zo
Zo_LPF
Zg
100
50
0
50
180
Phase(deg)
THE GRID VOLTAGE FEEDFORWARD PATH
TO IMPROVE THE STABILITY-ROBUSTNESS
OF THE GC-VSC
ig(s)
1
sLf
Hi
150
III. INCORPORATE A LOW-PASS FILTER IN
Session x
Gff(s)
GLPF(s)
Fig. 4. Frequency response of Kzp
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90
0
−90
−180
−270
1
10
103
102
f(Hz)
104
Fig. 6. Frequency response of Zoc, Zo, Zo_LPF, Zg
Fig. 6 shows the frequency response of output
impedance of the GC-VSC without grid voltage
feedforward (Zoc), with grid voltage feedforward (Zo),
with grid voltage feedforward and low pass filter
(Zo_LPF), and grid impedance (Zg) (the parameters are
listed in Table I). From Fig. 6, it can be seen that the
GC-VSC can keep stable without feedforward control,
however, the magnitude of its output impedance is
relatively
low,
implying
weak
harmonic-rejection-ability. On the other hand, the
magnitude of the output impedance is greatly
increased when the feedforward control is adopted,
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2016 China International Conference on Electricity Distribution (CICED 2016)
however, a large phase-delay is also introduced, which
leads to poor stability-robustness. Obviously, the grid
voltage feedforward control with the low pass filter is
a tradeoff between the abovementioned two methods,
it guarantees the stability robustness of the system as
well as increasing its harmonic-rejection-ability due to
the relatively high output impedance, therefore, it is
suitable to be used in the control scheme of the
GC-VSC in the weak grid condition.
IV. SIMULATION AND REAL INDUSTRIAL
APPLICATION RESULTS
The ideas described earlier have been verified with
simulations. The parameters of the GC-VSC used in
the simulations are given in Table I.
Xi’an, 10-13 Aug, 2016
As the analysis presented in Section II and III, grid
voltage feedforward control introduces a severe
phase-lag to the output impedance in the high
frequency ranges, which greatly weakens the
stability-robustness of the system. In fact, the phase
margin is only 6.5 ° when the grid voltage
feedforward control is adopted (as shown in Fig. 6).
Obviously, it is not enough to keep the stability of the
system, as a result, high frequency harmonic current
appears in the injected grid current, as shown in Fig.
8(b). However, when the low pass filter is
incorporated in its feedforward path, the phase margin
is increased to 35.7°(as shown in Fig. 6)， which
reflects strong stability-robustness, and the system can
work well with this control method, as shown in Fig.
8(c).
TABLE I. PARAMETERS OF THE GC-VSC
Parameters
Value
Parameters
Value
Input voltage Vin
360 V
Line frequency fline
50 Hz
Grid voltage Vg
(RMS)
220 V
Switching frequency fs
20 kHz
Rated Power
6 kVA
Inverter-side inductor L1
4 mH
The PI regulator is used for the injected grid current
regulator in this paper, which is expressed as
k
Gi  s   k p  i
(16)
s
The parameters of the PI regulator is carefully tuned
to ensure the stability of the system when Zg=0 (which
satisfies the first stability criterion presented in Section
II), finally, kp=1.075, ki=2027 is chosen to meet this
stability requirement.
Fig. 7 shows the simulation results when the
GC-VSC is connected to the stiff grid (which means
Zg=0) with different control method: a) without grid
voltage feedforward, b) with grid voltage feedforward,
c) with grid voltage feedforward and low pass filter, as
pointed out in Section II, in stiff grid, the GC-VSC
only needs to meet the first stability criterion to ensure
its stability, which has already been guaranteed, and
the grid voltage feedforward control won’t affect its
stability as well. As a result, the GC-VSC is stable and
works well in the stiff grid with different control
method.
Fig. 8 shows the simulation results when the
GC-VSC is connected to the weak grid (which means
the grid impedance Zg is unneglectable, here we
choose Zg=2.6mH, which corresponds to a typical
short-circuit ratio of 10) with different control method:
a) without grid voltage feedforward, b) with grid
voltage feedforward, c) with grid voltage feedforward
and low pass filter, as pointed out in Section II, in
weak grid, the GC-VSC needs to meet both two
stability criterions to ensure its stability, although the
first criterion is always guaranteed, whether the second
criterion can be satisfied should be carefully examined.
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vg: [200 V/div]
ig: [40 A/div]
Time: [10 ms/div]
(a)
vg: [200 V/div]
ig: [40 A/div]
Time: [10 ms/div]
(b)
vg: [200 V/div]
ig: [40 A/div]
Time: [10 ms/div]
(c)
Fig. 7. Simulation results of the GC-VSC connected to the stiff grid
(Zg=0): a) without grid voltage feedforward, b) with grid voltage
feedforward, c) with grid voltage feedforward and low pass filter
vg: [200 V/div]
ig: [40 A/div]
Time: [10 ms/div]
(a)
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2016 China International Conference on Electricity Distribution (CICED 2016)
Xi’an, 10-13 Aug, 2016
to the weak grid. a) the low pass filter with high corner frequency. b) the
vg: [200 V/div]
low pass filter with low corner frequency.
VI I. CONCLUSION
ig: [40 A/div]
Time: [10 ms/div]
(b)
vg: [200 V/div]
This paper proposes a modified grid voltage
feedforward method which incorporates a low-pass
filter in its feedforward path to improve the
stability-robustness of the GC-VSC under weak grid
conditions, the simulation and real industry application
results are given to demonstrate the effectiveness of
this control method
REFERENCES
ig: [40 A/div]
Time: [10 ms/div]
(c)
Fig. 8. Simulation results of the GC-VSC connected to the weak grid
(Zg=2.6mH): a) without grid voltage feedforward, b) with grid voltage
feedforward, c) with grid voltage feedforward and low pass filter
Fig. 9 shows the operation waveform of a real
industrial application of a 10kV/10MVar SVG
connected to a weak grid (the project is located in
Xinjiang Uygur Autonomous region), although the low
pass filter was introduced in Fig. 9(a), its corner
frequency fL is high and its impact is not obvious, as a
result, we could still see high frequency oscillation
appears in the injected grid current, when we decrease
the corner frequency of the low pass filter, as shown in
Fig. 9(b), the system becomes stable and the current
quality is improved. However, we can still see the
harmonic current which is introduced by grid
harmonic voltage, how to increase the current quality
under weak grid conditions is beyond the scope of the
paper and can be left for future research. The real
industrial application results presented here further
demonstrate the effectiveness of the control method
proposed in this paper.
[1] F. Blaabjerg, R. Teodorescu, M. Liserre, and A. V. Timbus,
“Overview of control and grid synchronization for distributed power
generation systems,” IEEE Trans. Ind. Electron., vol. 53, no. 5, pp.
1398–1409, Oct. 2006.
[2] X. Wang, X. Ruan, S. Liu, and C. K. Tse, “Full feedforward of
grid voltage for grid-connected inverter with LCL filter to suppress
current distortion due to grid voltage harmonics,” IEEE Trans.
Power Electron., vol. 25, no. 12, pp. 3119–3127, Dec. 2010.
[3] W. Li, X. Ruan, D. Pan, and X. Wang, “Full-feedforward
schemes of grid voltages for a three-phase LCL-type grid-connected
inverter,” IEEE Trans. Ind. Electron., vol. 60, no. 6, pp. 2237–2250,
Jun. 2013.
[4] M. Xue, Y. Zhang, Y. Kang, Y Yi, S. Li, and F. Liu, “Full
feedforward of grid voltage for discrete state feedback controlled
grid-connected inverter with LCL filter,” IEEE Trans. Power
Electron., vol. 27, no. 10, pp. 4234–4247, Oct. 2012.
[5] D. Yang, X. Ruan, and H. Wu, “Impedance Shaping of the
Grid-Connected Inverter with LCL Filter to Improve Its Adaptability
to the Weak Grid Condition”. IEEE Trans. Power Electron., 2014,
29(11): 5795–5805.
[6] D. Pan, X. Ruan, C. Bao, W. Li, and X. Wang, “Capacitor current
feedback active damping with reduced computation delay for
improving robustness of LCL-Type grid-connected inverter,” IEEE
Trans. Power Electron.,vol. PP, no. 99, pp. 1−13, Aug. 2013.
[7] J. Sun, “Impedance-based stability criterion for grid-connected
inverters,” IEEE Trans. Power Electron., vol. 26, no. 11, pp.
3075–3078, Nov. 2011.
Heng Wu was born in Jiangsu Province,China, in 1990. He received
the B.S. degree in electrical engineering and automation and the
M.S. degree in power electronic engineering both from Nanjing
University of Aeronautics and Astronautics (NUAA), Nanjing,
China, in 2012 and 2015, respectively.
He is currently an electrical engineer at NR Electric Co., Ltd,
Nanjing, China. His current research interests include digital control
technique, renewable energy generation system and flexible AC
transmission system (FACTS). He has published 3 technical papers
in IEEE Transaction on Power Electronics and IEEE Transaction on
Industrial Electronics. He is also a reviewer of IEEE Transaction on
Power Electronics and IEEE Transaction on Industrial Electronics
(a)
(b)
Fig. 9. Real industrial application of a 10kV/10MVar SVG connected
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