2016 China International Conference on Electricity Distribution (CICED 2016)
Xi’an, 10-13 Aug, 2016
Study of the Interaction between Photovoltaic Inverter and
Power Quality Harmonic and Its Suppression Method
Zhang Shifeng1, Chang Xiao1, Yang Yunlei1, Lei Da1, Feng Lei1, Hao Zhiguo2
1. Electric Power Research Institute, State Grid Shanxi Electric Power Company
2. Xi’an Jiaotong University
Abstract—In the process of photovoltaic (PV)
produce large amounts of high-order and low-order
generator was connected to the grid, in order not to
harmonics when connected to the grid through an
affect the power quality of grid, the current harmonic
inverter, thus may cause serious resonance problems
component from PV inverter needs to meet the
due to the accordance of equivalent output impedance
relevant interconnection standards. This topic putof system and inverter [6-8].
forwards a method based on impedance analysis,
Current research on photovoltaic inverter harmonics
which analyses the harmonic interaction between the
are mostly concentrated in the generation mechanism
photovoltaic (PV) grid-connected inverter and power
and harmonic content feature as well as the
grid containing background harmonic. The basic
suppression method [9-10]. However, the mechanism
reason of harmonic resonance problem caused by
and process of its interaction with connected grid has
grid-connected PV system is duo to the existence of
not been fully revealed. The inverter as an important
impedance intersection at the point of common
interface devices connecting the PV plant and power
connection (PoC), which is determined by the
grid, its controls performance become a direct factor
equivalent output impedance of the inverter and the
affecting the quality of output current. When there is
equivalent impedance of the grid. At that intersection
existing an intersection of the equivalent output
point, the sum of the impedance reduced to the
impedance of the inverter and the equivalent
minimum value and the current amplitude significantly
impedance of the grid at the point of common
increased, which leads to the harmonic resonance
connection, the sum of the impedance reduced to the
phenomenon. To analyze this problem, this paper
minimum value and the current amplitude significantly
established the NORTON equivalent model of the
increased that is the so-called harmonic resonance
inverter, developed the expression for the equivalent
phenomenon.
output impedance of the inverter, and analyzed the
This paper mainly based on the equivalent output of
reasonable range of the equivalent inverter output
the PV inverter, taking the single-phase grid connected
impedance based on the maximum limit of
inverter as an example, through the Norton equivalent
photovoltaic (PV) grid harmonic voltage, current and
circuit conversion and then analyze the harmonic
harmonic resonance conditions. On this basis, the PI
generation principle of the impedance network. The
control and the quasi PR control methods were used
simulation results and test data of MATLAB given in
respectively to adjust the equivalent output impedance
this paper are used to verify the effectiveness of the
of inverter. Based on the simulation experiment, the
proposed analytical method.
equivalent output impedance was effectively
II. ANALYSIS OF HARMONIC RESONANCE
suppressed, and the harmonic resonance phenomenon
was avoided.
PRINCIPLE
Index Terms—Grid-connected photovoltaic inverter,
This paper conduct research based on the topology of
Harmonic component, Interaction, Impedance analysis
LCL filter of the single-phase photovoltaic inverter,
I. I NTRODUCTION
whose circuit diagram is depicted as Fig.1.
Grid-connected
AS the energy and environmental issues increasingly
Filter
Inverter
prominent, the photovoltaic power generation
technology improved and its cost reduced, the
Grid
proportion of photovoltaic capacity in power system
becomes higher and higher. With more photovoltaic
PV Array
power stations connected to grid, the overall modeling,
PWM
analysis of grid-connected characteristic and research
Control
of power quality harmonic for PV system get
Strategy
particularly important [1-5].
In the numerous research fields of photovoltaic (PV),
Fig.1. Circuit diagram of the grid-connected inverter
the analysis of generation mechanism of harmonic and
Since the output current of PV array injected into the
its interaction with connected grid is significantly
grid is controlled by the grid-connected inverter
meaningful but attracted few attention. PV will
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2016 China International Conference on Electricity Distribution (CICED 2016)
structure, therefore, the inverter system can be
regarded as a controlled current source. The NORTON
equivalent model of grid-connected PV system is
simplified as Fig.2. Here, sign of i0&Z0 are
respectively represent current source and equivalent
output impedance of inverter, so does the grid system
can be expressed as the series form of equivalent
grid voltage vg and equivalent impedance Zg.
Z0
Zin
+
i0
ig
Zg
+
PoC
v0
Z0
vg
Fig.2. NORTON equivalent circuit of PV system
Through the above predigestion, then can easily
analyze harmonic resonance phenomenon. Picture a)
shows that at a certain frequency, the grid frequency of
harmonic voltage vgh caused by distortion is equal to
the series resonant frequency of impedance network
that will lead to great harmonic currents inject into
entire system network. In same case, if the frequency
of output harmonic current ioh due to the presence of
non-linear factors is equal to the grid parallel
resonance frequency, there will be a great harmonic
voltage appearing in the entire power system.
Zgh
igh
Zoh
RLf
vgh
a) Series resonance
Lf
ig
+
++
--
Ginvv*
+
Cf
vg
uC
iCf
v*
ig
*
++ ig
GI(s)
ioh
voh
Fig.5. Average model of grid connected inverter
Zoh
Zgh
b) Parallel resonance
Here GI(s) is the transfer function for filter current
regulator, v*is the modulating signal and Ginv means
pulse width modulation signal gain of inverter bridge
that can be described as equation (1).
Fig.3. Principle of harmonic resonance
Ginv 
III. EQUIVANLENT OUTPUT IMPEDENCE
MODELING OF GRID-CONNECTED INVERTER
+
PWM
Control
strategy
Vdc
Vcm
(1)
Where Vdc and Vcm separately represent the DC bus
voltage and carrier amplitude.
Combining the Fig.5. and mathematical model of LCL
grid connected inverter, the closed loop control
structure of the grid connected inverter revealed as
Fig.6. is easily available .
-
ig*
G(s)
-
+
GC(s)
v*
vinv
Ginv
+
-
iL
1
ZLf +
uC - vg
iCf
ZCf
- ig
+
1
Zg
Fig.6. Block diagram of closed loop control system
for single phase grid connected inverter
Fig.4 Structure diagram of LCL single-phase
grid-connected inverter system
To simplify the analysis process, for the three-phase
grid-connected inverter system, usually using
single-phase grid-connected inverter system to analyze
CICED2016 Session x
Lg
Rg
iL
+
+
voh
harmonic interaction problems. Generally it is of wide
adaptability to exert research on modeling of inverter
output impedance based on LCL single dual-loop
control system of the capacitive current feedback.
Fig.4 shows the structure diagram of LCL single-phase
grid connected inverter system, in which Vdc and uc
represents the DC bus voltage and filter capacitor
voltage, iL is the output current of the inverter bridge
while ig is the grid-connected current of the inverter.
In above circuit the PWM trigger signal is issued
through the comparison of modulation waveforms and
triangle carrier waveforms. Although the switching
state of the power switch is not continuous, but
according to the state-space averaging method, in a
switching cycle, when the switching frequency
(triangular carrier frequency) is much larger than
modulation wave, it is reasonable to use mean value of
the variable to replace the instantaneous value.
Therefore, the continuous state space average model of
grid-connected inverter system can be established as
Fig.5.
igh
+
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The equivalent output impedance model of the grid
connected inverter shown as Fig.7 is established by the
Norton equivalent circuit shown in figure Fig.2, which
is displayed in figure Fig.6. Applied The Norton
theorem to the control structure of the inverter, and
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2016 China International Conference on Electricity Distribution (CICED 2016)
make the output of the Norton equivalent circuit short
circuit, then obtain the short-circuit current, that is, the
output current source of the inverter i0. After that,
make sure that all the circuit independent source is
zero, and calculate the equivalent impedance of the
output end, that is, the equivalent impedance Z0 of the
inverter. Which expression is depicted as follows:
Z Cf Z Lf  Z Cf GinvG ( s )
u ( s)

Z 0 ( s)  C
(2)
i g 0
Z Cf  Z Lf  GinvG ( s )
 i g ( s)
Where ZCf =1/(sCf)，ZLf =RLf +sLf 。According to
Norton's theorem, the transfer function between the
output current of the grid connected inverter and the
current reference signal ig* is as follows:
Gi ( s ) 
iL (s)
i g ( s )
uC  0

G ( s )G inv
Z Lf  G ( s )Ginv
(3)
vg
ig*
uC
iL
Gi(s)
Z0(s)
+
-
+
-
Xi’an, 10-13 Aug, 2016
TABLE II. Distortion limit of power network
harmonic voltage U%h
Odd harmonics
Nun-multiple
of three
H
Voltage
harmonic
limits
(%)
Multiple of three
H
harmonic
Because the power electronic inverter is the interface
element of the distributed generation system and the
grid system, so the design of the inverter is largely
determined by the limitation of the harmonic content
of the output current. The requirement of current
distortion limit of photovoltaic grid-connected system
is given in GB/T 19939-2005 standard, as shown in
TABLE I. When photovoltaic power generation
inverter system is connected with the actual grid
system, it is hoped that the output harmonic current of
the inverter is within the limits of grid connected
current.
TABLE I. Distortion limit of grid-connected
harmonic currents I%h
Odd harmonics
Distortion limit
3th-9th
＜4.0%
11th-15th
＜2.0%
17th-21th
＜1.5%
23th-33th
＜0.6%
Here, taking EN 50160 as an example, the harmonic
voltage of the power network is limited, as shown in
TABLE II.
Voltage
limits
(%)
6
3
5
2
2
5
9
1.5
4
1
11
3.5
15
0.5
6-24
0.5
13
3
21
0.5
17
2
19-25
1.5
Based on above indicators, the minimum amplitude
limit of the equivalent output impedance of the
inverter in a certain frequency range is studied, and its
expression is listed as equation (4)
Z %h 
LIMIT FOR GRID-CONNECTED INVERTER
H
harmonic
7
1
Zg
IV. ANALYSIS OF EQUIVALENT OUTPUT IMPEDANCE
Voltage
limits
(%)
5
ig
Fig.7. Output impedance model of single phase
grid-connected inverter
Even harmonic
U 1U % h
I1 I %h
(4)
Here U%h is each harmonic content limit of the
harmonic voltage content in table 5-4 in TABLE II,
and I%h is the relevant harmonic currents limit of the
harmonic current content in TABLE I . U1 is the
fundamental voltage of the power network, and the I1
is the rated fundamental current of the grid- connected
inverter system. Besides, |Z%h| indicates the minimum
expected value of the output impedance of the inverter
under the h sub harmonic. According to the
corresponding theory, when the equivalent output
impedance of the inverter is bigger than |Z%h|, the
output current of the inverter is satisfied with the limit
value of the harmonic current in TABLE I, otherwise it
is not satisfied.
V. SIMULATION AND RESULTS
TABLE III. System parameter
Parameter
Symbol
Value
Rated fundamental voltage of grid
U1
230V
Rated fundamental current of inverter
I1
7A
Resistance of network side
Rg
0.4Ω
Reactance of network side
Lg
0.8mA
DC bus voltage
Vdc
400V
Filter capacitor
Cf
5μF
Filter inductor
Lf
2mH
Filter resistance
RLf
0.1Ω
Amplitude of carrier wave
Vcm
7.5V
According to the GB/T 19939-2005 standard and the
EN 50160 standard, the lower the voltage harmonic
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2016 China International Conference on Electricity Distribution (CICED 2016)
幅值/Ω
corresponding sub harmonic impedance value. Here
KP=1 ， KI=50rad/s ， KI5=KI7=KI11=25rad/s ，
ω1=314rad/s，ωc=10rad/s.
Apply the quasi PR controller expression to the
formula (2) of equivalent output impedance of the
inverter, and calculate the equivalent output
impedance of the inverter|Z0| by adding quasi PR
control value, then compare with the lowest magnitude
limit index |Z%| which is shown in Fig.10.
幅值/Ω
component of the power system is better (the harmonic
content is not more than 8%). In order to study the
problem, select the grid voltage with 28% total
harmonic distortion rate (THD), including the 20% of
5th harmonic, the 10% of 7, 11, 17 and 19 harmonics.
Table III is the parameter table for single phase grid
connected inverter control system.
A. G (s) adopts PI controller to adjust, where, KP=1,
KI=10000.
At rated voltage U1=230V, rated current I1=7A, make
use of the formula (2) to obtain the Potter diagram of
harmonic impedance Z0 of the inverter and harmonic
impedance limit indicator |Z%|, as shown in Fig. 8.
Xi’an, 10-13 Aug, 2016
频率/Hz
Fig.10. Amplitude frequency characteristic curve of Output
impedance limit by applying quasi PR control
Fig.8. Amplitude frequency characteristic curve of Output
impedance limit
幅值/Ω
Comparison of the two curves it can be drawn, in the
case of greater than 11 harmonic frequency, the
equivalent value |Z0| of the grid connected inverter
output impedance is always lower than the amplitude
of the |Z%|. Therefore, the inverter output harmonic
current will not meet the harmonic current limit values
in Table I. According to the EN 50160 standard to
carry out simulation experiment for the photovoltaic
power generation system that is of 5th to 19th odd
harmonic component (excluding 3n times harmonic,
n=2, 3, 4). And from the simulation results can be seen,
the inverter output current harmonic spectrum in 11,
13, 17 and 19th slightly higher than table I harmonic
current limit value, namely inverter output current
harmonics will not meet Table I in the harmonic
current limit value.
Grid-connected current standard
As expected, the amplitude of the equivalent output
impedance of the inverter |Z0| increases sharply at a
certain frequency after adding a quasi PR control
method as shown in Fig.10. Special attention should
be paid to some frequency of harmonic compensation,
the equivalent output impedance of the inverter |Z0| is
also more than the harmonic impedance of the
minimum limit value of |Z%h| (such as 13,17,19
harmonics). In the same simulation model as Fig.9,
adding quasi PR control method, it can be found that
the equivalent output impedance of the inverter
increases in value and some uncompensated harmonic
current content is also lower than the standard limit
under a certain frequency. The simulation result is
depicted as Fig.11
幅值/Ω
频率/Hz
Grid-connected current standard
频率/Hz
Fig.11. Output harmonic current spectrum of grid-connected
inverter system by applying quasi PR control
频率/Hz
Fig.9. Output harmonic current spectrum of grid-connected
inverter system with background harmonics
B. G (s) is adjusted by the quasi PR controller, and the
5,7,11 sub harmonic is added to the quasi PR
resonance control (n=5, 7, 11), which is compensated
for the specific harmonics to improve the
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C. G (s) is respectively adjusted by PI controller and
the quasi PR controller.
Observe the current waveform of the grid connected
inverter system, and reveal it in Fig.12 and in Fig.13.
Seen from Fig.12, the output current of the grid
connected inverter system still exist certain content of
harmonic current component after using PI controller.
However, compared with the current waveform shown
in Fig.13 using quasi PR control, it can be known that
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2016 China International Conference on Electricity Distribution (CICED 2016)
value appears and that is the cause of harmonic
resonance. In order to avoid or reduce the harmonic
resonance, it shall make impedance intersection point
(the resonant frequency) above 40th harmonic and
then the harmonic sources will have lower amplitude.
幅值/Ω
电流/kA
the harmonic content of the output current of the grid
connected inverter system is significantly reduced
after the adjustment of quasi PR controller. Therefore,
the quasi PR control has better control characteristics.
Xi’an, 10-13 Aug, 2016
时间/S
Fig.12. Output current waveform of grid-connected
inverter system by applying PI control
频率/Hz
电流/kA
Fig.15. Amplitude frequency characteristic curve of |Z0+Zin|
by applying quasi PR control
时间/S
Fig.13. Output current waveform of grid-connected
inverter system by applying quasi PR control
D. Analysis of the harmonic resonance at the
intersection point of the equivalent output impedance
of inverter and the power network impedance.
At present, the grid connected harmonic resonance
problem is a problem deserving attention. As shown in
Fig3. (a), the harmonic voltage voh can be expressed as
a function of the power grid harmonic voltage vgh:
voh 
Z oh
v gh
Z oh  Z gh
(5)
幅值/Ω
If the value of Zoh and Zgh is very small or close to zero,
at this time, a small disturbance of grid connected
inverter harmonic current injecting into the grid
harmonic voltage vgh, will lead to voh a great harmonic
voltage disturbances. Similar to this, if a small
disturbance of harmonic current ioh is injected into the
output current of inverter, it will also cause the
resonant circuit in Fig.3. (b) appears a large harmonic
igh..
VI. CONCLUSION
In this paper, the research of LCL type photovoltaic
grid connected inverter is carried out, which mainly
focuses on the research of the influence of inverter
control parameters on the grid connected system. In
order to reduce the harmonic components of the output
current of the inverter, this paper analyzed the
reasonable range of equivalent output impedance of
the inverter, and introduced the concept of limit index
of harmonic impedance based on the maximum value
of harmonic voltage and current as well as harmonic
resonance conditions. In order to avoid the serious
harmonic problem (i.e. harmonic resonance
phenomenon), the PI control and the quasi PR control
is used to adjust the equivalent output impedance of
the inverter. The simulation results show that the quasi
PR control has certain advantages compared with the
PI control. At the same time, the validity of the index
of harmonic impedance is verified.
REFERENCES
频率/Hz
Fig.14. Amplitude frequency characteristic curve of |Z0+Zin|
by applying PI control
When connected to grid, the equivalent output
impedance of the inverter and power grid will have
some intersection, where the minimum impedance
CICED2016 Session x
Fig.14 and Fig.15 depicts the amplitude frequency
characteristic curve of the equivalent output
impedance of the inverter and power grid after
applying PI control and quasi PR control. Seen from
the chart, the equivalent output impedance of the
inverter and the power grid have the intersection point
outside 40th harmonic, so harmonic content in inverter
output current amplitude is not obvious, as shown in
Fig.12 and Fig.13.
Paper No xxx
[1] Xie Ning, Luo An, Chen Yandong, et al. Dynamic Modeling and
Characteristic Analysis on Harmonics of Photovoltaic Power
Stations [J]. Proceeding of the CSEE, 2013, 33(36):10-17.
[2] Zhang Xing, Yu Changzhou, Liu Fang, et al. Modeling and
Resonance Analysis of Multi-paralleled Grid-tied Inverters in PV
Systems [J]. Proceeding of the CSEE, 2014, 34(3):336-345.
[3] Zhou Lin, Zhang Mi. Analysis of Resonance Phenomenon in
Large-scale Photovoltaic Power Plant [J]. Electric Power
Page /7
2016 China International Conference on Electricity Distribution (CICED 2016)
Xi’an, 10-13 Aug, 2016
Automation Equipment, 2014, 34(6):8-14.
[4] RoK,RahmanS. Two-loop Controller for Maximizing
Performance of A Grid-connected Photovoltaic-fuel Cell Hybrid
Power Plant [J] IEEE Transactions on Energy Conversion, 1998,
13(3): 276-281.
[5] Ma Jie, Zhang Jiancheng. Harmonics Measurement and
Analysis of Grid-connected PV System [J]. Power System and
Clean Energy, 2010, 26(11):112-115.
[6] Xie Ning, Luo An, Ma Fujin, et al. Harmonic Interaction
between Large-scale Photovoltaic Power Stations and Grid [J].
Proceeding of the CSEE, 2013, 33(34):9-16.
[7] SHIH F Y, CHEN D Y, WU Y P, et al. A Procedure for Designing
EMI Filters for AC Line Applications [J]. IEEE Transactions on
Power Electronics, 1996, 11(1):17-18.
[8] Wei Shaochong, Zhang Guangming, Ji Baojian, et al. A High
Efficiency Photovoltaic Grid-connected Micro-inverter with Low
Input Current Ripple [J]. Automation of Electric Power Systems,
2014, 38(8):91-97.
[9] Wu Dongchun, Kan Jiarong, Wu Yunya, et al.
High-frequency-link Inverter with Input Current Ripple Reduction
for Photovoltaic System [J]. Automation of Electric Power Systems,
2015, 39(18):101-107.
[10] Li Xiaozheng, Sun Jianpin, Zhen Xiaoya, et al. DC Injection
Suppression Technology Based on PR & PI Integrated Control for
Grid-connected PV System[J].Electric Power Automation
Equipment, 2013, 33(3):118-122.
Zhang Shifeng received the B.E. degree and M.E from North China
Electric Power University and Xi’an Jiaotong University, China, in
2012 and 2015, respectively. Currently, he is employed in Shanxi
Electric Power Research Institute as an electrical engineer. His fields
of interest include dynamic reactive power compensation
technology for wind farm and electrical energy quality. (E-mail:
[email protected]).
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