International Journal of Advanced Network, Monitoring and Controls          Volume 03, No.03, 2018 

DOI: 10.21307/ijanmc-2019-003                       23 

Research on Multi - Resonant LCL Harmonic Suppression Strategy 

Jingwen Chen, Xin Zhou and Hongshe Dang* 

School of electrical and information engineering 

Shaanxi University of Science and Technology 

Shaanxi 710021, China 

*Address correspondence to this author at xuefu Road,  

Xi'an, China, 710021;  

e-mail: 2452744621@qq.com 

 

Abstract—Aiming at the resonance problem in the process of 

grid connection of LCL filter microgrid inverter, a 

multi-resonance LCL harmonic suppression strategy is 

proposed. On the basis of analyzing the principle and 

establishing the mathematical model in detail, the realization 

process of the multi-resonance constant power compound 

control strategy is studied emphatically. Through the 

simulation, the validity of the control strategy is verified, The 

results show that the scheme stabilizes the output power and 

reduces the total harmonic distortion of the grid-connected 

inverter to 0.12%, and the corresponding phase current 

distortion rate drops to 0.02%.The suppression effect is 

obvious, it is an effective harmonic suppression method. 

Keywords-Microgrid Inverter;Harmonic;Multi Resonance 

Control;Constant Power Control 

I. INTRODUCTION 

With the depletion of traditional energy sources, the new 

energy power generation system with microgrid as the 

carrier has been developed rapidly because of its flexible, 

decentralized, small, close to users and the use of clean 

energy. Due to the energy structure of the micro grid mainly 

clean energy such as wind power, photovoltaic power 

generation, the distributed energy will generally need 

electricity to the grid through power electronic converter 

device to realize grid connected. Therefore, a lot of power 

electronic devices access to power grid harmonics, caused 

the converter power factor lower and parallel resonant circuit 

or series resonance, decrease active reactive power 

measurement accuracy, reduce the quality of power supply a 

series of problems, give the user the safe and security, 

economic operation of power system brings great harm. so 

harmonic suppression is very important. 

Current research of harmonic suppression methods, 

mainly has: the harmonic suppression method based on 

active filter [1] [2] [3]; the micro-grid harmonic suppression 

based on virtual impedance [4]; LCL type Grid-connected 

inverter harmonic suppression [5] [6] [7] [8] and so on. 

Compared to L-filter, LCL-type filter has a third-order 

low-pass filter characteristics,( LCL filter with third order 

low pass filter properties), so for the same harmonic standard 

and lower switching frequency, we can use a relatively small 

filter inductor design, effectively reduce the system 

size(volume) and reduce losses, but the same will bring 

resonance problems. In this paper, a harmonic control 

strategy of micro-grid inverter based on PI control, 

multi-resonance control and LCL constant power control is 

proposed, which is used in the process of grid-connected 

control of micro-grid inverter to further reduce and net 

voltage of the total harmonic distortion rate, get better power 

of the grid. 

II. MATERIAL AND METHODS 

A. Principle block diagram of multi resonance LCL 

harmonic suppression strategy  

Figure 1 is LCL multi-resonant constant power grid 

control system block diagram. Where ref
P

ref
Q

 are the 



International Journal of Advanced Network, Monitoring and Controls          Volume 03, No.03, 2018 

24 

actual active and reactive power reference values, abc
v

、

abc
i

are the actual values of the grid voltage and current, d
v

、

q
v

and d
i
、 q

i
 are the voltage components of the dq axis, 

dref
i

and qref
i

 are the capacitor current reference Value, 

cd
i

、 cq
i

、 cdref
i

、 cqref
i

are the capacitance current 

detection value on the dq axis components and capacitance 

current reference value. 

The figure includes PQ control module, current loop 

multi-resonance control module,  and PWM modulation 

module etc.   Micro-network inverter grid output voltage

abc
v

and current detection values oabc
i

,after    coordinate 

transformation to get   、  and   、  ,will be sent to the 

PQ controller; PQ controller according the active and 

reactive setpoint ref
P

 and ref
Q

to calculate the current 

reference values      and      and then compare with the 

current detection value of the     components   and   . 

And after the ratio multi-resonant regulator       in the 

current loop control module, the reference values       , 

       of the capacitive current are obtained, then compared 

with the capacitance current detection value αβ component 

   and    . And then adjusted by the proportional regulator 

G_1 (S), the control PWM circuit drives the inverter, so that 

the inverter output active power and reactive power constant. 

In order to meet the requirements of system stability, the 

current loop control module in Figure 1 solves the resonance 

problem caused by LCL, and achieves the purpose of 

suppressing low frequency harmonics and improves the 

system accuracy. 

 

Figure 1. Principle block diagram of multi resonance LCL harmonic 

suppression strategy 

B. Multi - resonant LCL Grid - connected Control 

Mathematical Model 

Figure 1 constitutes a third-order LCL-type filter, where 

1
L

is the inductance, 1
R

is its internal resistance and the 

equivalent resistance between the upper and lower legs of 

each phase, 2
R

 is the internal resistance of 2
L

. In the case 

of three-phase grid voltage symmetry, the mathematical 

model is as follows: 



 
 

 
 

     

1 2

1 1 1 2 2 2

dc k NO s

di t di t
L R i t L R i t

dt dt

U t S t U U t

  

  




 
   1 2

c
du t

C i t i t
dt

 



 

 
   

, ,

dc

dc dc k k

k a b c

du t
i t C i t S t

dt 
  





 
 

 
, ,3

dc

NO k

k a b c

u t
U t S t



  




International Journal of Advanced Network, Monitoring and Controls          Volume 03, No.03, 2018 

25 

Where k
S

is the switching function of the power 

switching device, when 
0

k
S 

, the upper arm is turned on 

and the lower arm is turned off; When 
1

k
S 

, the upper 

arm off, the lower arm conduction. Corresponding to the 

relationship between α and β stationary coordinate system is 

as follows:  



1
1 1 1

1

1 1 1

2
2 2 2

2

2 2 2

1 2

1 2

ca

c

c

c

c

c

di
L u u R i

dt

di
L u u R i

dt

di
L u e R i

dt

di
L u e R i

dt

i i i

i i i


 



  


  



  

  

  

  

  

  

  

 

 


1
i
 、 1

i
 、 2

i
 、 2

i
  are the α and β components of the 

input and output currents in the αβ coordinate system; c
i
 、

c
i
 、 c

u
 、 c

u
 are the α and β components of the 

capacitive current and voltage in the αβ coordinate system;

e
  and 

e
  are the α and β components of the grid voltage 

in the αβ coordinate system. 

C. A block diagram of current loop control 

LCL-type filter in the better suppression of 

high-frequency harmonics at the same time, because of its 

own structure for a third-order system, easy to produce 

resonance, the frequency near the narrow band and too high 

gain, will lead to the system and the load Parameter changes 

are very sensitive, affecting the stability of the system to 

bring a series of impact and harm to the grid. In order to 

reduce its sensitivity and high gain characteristics, to achieve 

the AC signal without static tracking, this paper on the basis 

of the use of active damping introduced into the capacitor 

current loop regulation to suppress high frequency 

interference, and the external loop current using proportional 

resonance control , Constructs a transfer function that 

performs AC compensation on the reference input signal. So 

that in a specific bandwidth in the same frequency response 

characteristics, to meet the system stability requirements, so 

that the output at the resonant frequency at high gain, the 

other frequency segment attenuation. Thus reducing the 

resonance, improve the stability of the system and control 

accuracy. 

The control block diagram is showas follows: 

 

 

Figure 2. Block diagram of current loop control 

As shown in Figure 2 where      selected proportional 

resonance regulator,      selected proportional regulator. 

After the current is transformed by the coordinate, the 

voltage and current   、    and   、    in the two 

stationary coordinates are obtained and sent to the PQ 

calculation module to obtain the reference current      、

     ,and then compared with   and   obtained the deviation 

by the proportionmulti-resonant regulator       in the 

current loop control module  ,  get the capacitor current 

reference value       and       , And it is compared with the 

capacitance current detection value αβ component    and 

   , after adjusting the proportional regulator      , then 

control PWM circuit drives the inverter, so that the inverter 

output active power and reactive power constant. 

D. PR control  

Since the PR regulator is equivalent to the PI modulator 

in the stationary coordinate system under the αβ coordinate, 



International Journal of Advanced Network, Monitoring and Controls          Volume 03, No.03, 2018 

26 

the PR regulator can also be used to design the PI regulator 

parameter. Figure 2 in the parallel current and reference 

current deviation, through the multi-resonant control get the 

capacitor current reference value cref
i

， cref
i

and the actual 

capacitance of the current deviation, and then through the 

proportional control, the resulting signal through the PWM 

modulation to achieve active damping control. The use of a 

proportional feedback control of the capacitor current, 

stabilize the capacitor voltage, and enhance the stability of 

the system. The parallel current and capacitive current 

transfer functions are as follows: 



 
 

 
2

4 3 2

1 2 2

ref

PWM PWM i

PWM PWM PWM i

I S
G S

I s

KK K s KK K

L L Cs KK L Cs Ls KK s KK K








   


The corresponding characteristic equation is: 



  4 3 21 2 2PWM

PWM PWM i

D S L L Cs KK L Cs Ls

KK s KK K

  

 


According to the Rouse stability criterion, the system 

stability condition is calculated as: 


 

2 1

1 2

1

0
PWM i

K L L

K L K L KK K L C






 

  


According to the stability criterion (formula 9) to set the 

parameters, so that when the grid to reach a stable state. 

III. MULTIPLE PR CONTROL 

A single PR regulator generates an infinite gain at a 

specific frequency. In order to ensure its stability and easy to 

achieve, using the approximate structure; its transfer function 

is as follows:The transfer function is as follows: 

       
  hwcs

s   wcs wh
                            (9) 

Where   is the scale factor,    is the frequency 

adjustment coefficient,   is the resonance coefficient, and 

   is the resonant frequency.  

In order to achieve the 5,7,11 harmonic current 

compensation need to re-connect three resonant controller. 

The transfer function of the current inner loop 

multi-resonance controller is: 

        
      

          
        

The minimum value of the resonant frequency in the 

LCL grid-connected inverter is: 

   
 

  
 

     

     
                               (11) 

Then the minimum value of K is: 

     
   

        


In order to ensure the stability of the control system, the 

cutoff frequency should be chosen to be less than   so the 

   in the multi-resonance PR control can be approximated 

by the cutoff frequency   : 

   
           

 


According to the scope of K and the specific control 

requirements, through the control system open-loop baud 

diagram for parameter adjustment. 

IV. DISCUSSION 

Based on the detailed analysis of the principle of 

multi-resonance constant power control, the simulation 

results of the mathematical model are as follows 



International Journal of Advanced Network, Monitoring and Controls          Volume 03, No.03, 2018 

27 

 

Figure 3. DC side voltage control after active, no power waveform 

As shown above, the active and reactive power of the 

output after LCL multi-resonant constant power control is 

constant, which ensures the stable operation of the system. 

 

Figure 4. By LCL multi-resonant constant power control before and 

after the voltage waveform 

From Fig. 4, we can find that the voltage and current 

waveforms before the LCL multi-resonant constant power 

control are unstable and distorted. After the control of the 

voltage and current waveform is improved, harmonic 

suppression effect is obvious. 

 

Figure 5. By LCL multi-resonant constant power control before and 

after the current waveform 

From the above figure can be found by the LCL 

multi-resonant constant power control after the current 

waveform has improved. 

In order to analyze the filtering effect by LCL 

multiresolution constant power control, the voltage distortion 

rate, the total voltage distortion rate and the current distortion 

rate of the respective voltage waveforms before and after the 

control are summarized as shown in Table 1 and 2 

respectively. 

TABLE I. LCL MULTI-RESONANT CONSTANT POWER GRID-CONNECTED 

CONTROL BEFORE AND AFTER THE VOLTAGE HARMONIC CONTENT 

 
Voltage 

distortion rate 

current 

distortion rate 

Before filtering 76.03% 15.23% 

After filtering 0.12% 0.02% 

TABLE II. LCL MULTI-RESONANT CONSTANT POWER CONTROL BEFORE 

AND AFTER THE VOLTAGE AND CURRENT DISTORTION 

Number of 

harmonics 
5 7 11 

Before filtering 2.86% 0.93% 0.98% 

After filtering 0.08% 0.04% 0.01% 

From Table 1, it can be found that the contents of the 

harmonics before the filtering are reduced and have an 

inhibitory effect. 



International Journal of Advanced Network, Monitoring and Controls          Volume 03, No.03, 2018 

28 

Table 2 can be seen by LCL multi-resonant constant 

power control filter before the voltage distortion rate of 

76.03%, a phase current distortion rate of 15.23%, filtered 

voltage distortion rate reduced to 0.12%, the corresponding 

phase current distortion Small to 0.02 inhibitory effect is 

obvious. 

V. CONCLUSION 

In this paper, a harmonic suppression strategy for 

micro-grid inverter combined with LCL constant power 

control and multi-resonant PI control is proposed for the 

resonant problem of LCL filter microgrid inverters. It is 

found that the scheme stabilizes the output power LCL and 

reduces the total harmonic distortion rate of the grid inverter 

to 0.12% and the corresponding phase current distortion rate 

is reduced to 0.02%. The harmonic suppression effect is 

obvious. 

 

REFERENCES 

[1] Shang taohong. Study and parameter design of shunt hybrid active 
power filter [J] proceedings of the computer science, 2012, 29 (11): 
327-330. 

[2] Li Yan, Luo an, Fang Lu, Wang Wen. High voltage type hybrid 
active power filter [J]. Journal of electric technology, 2013, 28 (6): 
147-157 

[3] Wang Jidong, Qin Meicui. Micro grid harmonic suppression method 
[J]. Journal of Tianjin University APF based on the (Science and 
Technology Edition), 2015, 48 (7): 637-642 

[4] Li Li. Study on hierarchical control and power quality improvement 
of microgrid [D]. Beijing: North China Electric Power University, 
2015 

[5] Han Yongru, Xue Shilong, and Study on the control strategy of grid 
connected inverter based on LCL filter [J]. Shanghai: Maritime 
University, 2015, 1 (103-109): (in Chinese) 

[6] Huang Yafeng, Li Long, Yan Gangui large capacity PV inverter LCL 
filter parameter optimization design [J]. Beijing: North China Electric 
Power University, 2013, 41 (21): 104-110 

[7] Zhang Xing, Li Fei, and in the grid connected inverter LCL filter 
improved topology [J]. Hefei: HeFei University of Technology, 
2014,6:10-17 

[8] Xu Jinming, Xie Shaojun, L L filter grid connected inverter robust 
current control [J]. Nanjing: Nanjing University of Aeronautics and 
Astronautics, 2012,36 (19): 99-104 

[9] Yang Kun, Xie Chuan, Chen Guozhu. Current control of static 
reactive power generator based on frequency adaptive resonance 
controller [J]. Journal of electrical engineering, 2014, 29 (8): 
249-254. 

[10] Zhang Zhicheng, Liu Zhenlai, Guan Huchang. Island micro grid 
harmonic control method of [J]. power electronic technology, 2015, 
49 (12): 135-13 

Chen Jingwen (1978-), male (Han nationality), Inner Mongolia 
Chifeng people, associate professor, graduate tutor, research direction 
for micro-grid technology and application, E-mail: 
chenjw@sust.edu.cn 

Zhou Xin (1993-), female (Han), Xianyang, Shaanxi, Master, 
research direction for micro-grid harmonics, inter-harmonics of the 
study 

Dang hongshe(1962-), male (Han nationality), ShaanXiXianyang 
people, professor,  research direction for micro-gridtechnology and 
application, (Corresponding author: E-mail: 2452744621@qq.com) 

 

 

mailto:2452744621@qq.com