Design of LCL filters for the back to back converter in a doubly fed induction generator

A back-to-back PWM converter in DFIG, consisting of grid side converter GSC and rotor side converter RSC, guarantees its good performance.. Though an LC filter can get higher harmonics a

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1

Abstract Wind power generator based on Doubly Fed

Induction Generator (DFIG) incorporates a back-to-back PWM converter Filters are used to eliminate the harmonics produced

by the PWM converter However, very few papers have detailed the design procedure of the filters for a DFIG based wind power generator A systematic procedure to design the LCL filters for DFIG back-to-back converter is proposed in this paper Both filters for the grid side converter and the rotor side converter are designed Simulations in PSCAD/EMTDC verify the effectiveness

of the design procedure

Index Terms LCL filter, doubly fed induction generator

(DFIG), back-to-back converter

I INTRODUCTION

Doubly fed induction generators (DFIG) are widely used in wind power systems A back-to-back PWM converter in DFIG, consisting of grid side converter (GSC) and rotor side converter (RSC), guarantees its good performance As there are power electronic devices, harmonics produced by the converters will be a problem Harmonics in the rotor currents cause undesirable fluctuations of generating active and reactive powers, and harmonics in the stator currents deteriorate the utility power quality In order to comply with corresponding standards [1], it is necessary to equip the converters with low-pass filters

Traditionally, an L filter or LC filter is be implemented to eliminate high-frequency harmonics However, since the capacitance of the PWM converter in a DFIG is large, the switching frequency is not very high Thus, to attenuate harmonics in comparatively low frequencies, large inductance

is required, which will result in large size and weight of the filter Though an LC filter can get higher harmonics attenuation than an L filter, it is not suitable for using in grid connected converter due to its low output impedance An LCL filter can provide higher harmonic attenuation than that of the

L filter, which is a better choice in DFIG application

However, resonance may occur if the LCL filter has not been

This work was supported in part by the National Natural Science Foundation of China (50937002) and the National Basic Research Program of China (2009CB219701, 2012CB215106)

P Zhan, W Lin and J Wen (contact author) are with State Key Labora-tory of Advanced Electromagnetic Engineering and Technology (Huazhong University of Science and Technology), Wuhan 430074, Hubei Province, China) (E-mails: zhanpeng_hust@163.com, weixinglin@foxmail.com, jinyu.wen@hust.edu.cn)

M Yao and N Li are with the Alstom Grid China Technology Center,

well designed [2]

There have been reports on using LCL filters to the GSC [3-5] and reports on designing LC filter for the RSC [6] In [3],

an LCL filter for inverter of wind power was introduced, and the characteristics of the LCL filter compared with the L filter were investigated Paper [4] investigated the damping of resonance oscillations for grid side converter with LCL filter for doubly-fed wind power system Paper [5] gave an optimized design rule of the LCL filter for inverter of a wind turbine As to LCL filter for rotor side converter, in [6], a second-order output LC filter was inserted between the inverter and the rotor circuit of a DFIG Taking the rotor leakage inductance into consideration, it is an LCL filter essentially However, no design details were provided Very few paper exists on designing LCL filters for both the GSC and the RSC to date

This paper designs a Y connected LCL filter for GSC and a delta connected LCL filter for RSC of a 2.5MW DFIG, and the design procedures are proposed as well Simulation and analysis results validate the effectiveness of the designed filters in attenuating harmonics

II LCL FILTER PRINCIPLE ANALYSIS

A Characteristic analysis of LCL filter

Fig 1 presents the schematic diagram of an LCL filter

which is inserted between a PWM converter and the grid

Where, UO is terminal voltage of PWM converter, US is grid

voltage, L1 is the converter side inductor, R1 is the equivalent

resistance of L1, L2 is the grid side inductor, R2 is the

equivalent resistance of L2, C3 is the capacitor, R3 is the

damping resistor in series with C3

Fig 1 LCL filter equivalent circuit diagram

Ignoring R1 and R2, the LCL filter can be viewed as L2 and

C3 paralleled, then, together they are in series with L1 The

transfer function between the input voltage UO and the output

Peng Zhan, Student Member, IEEE, Weixing Lin, Student Member, IEEE, Jinyu Wen*, Member, IEEE,

Meiqi Yao, Naihu Li, Member, IEEE

Design of LCL Filters for the Back-to-back Converter in a Doubly Fed Induction Generator

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current I2 is:

3

3

1 ( )

R C s

H s

+

=

While for an L filter, the transfer function becomes:

1 ( )

H s sL

Equation (1) is of third order It is expected that the LCL

filter gets higher harmonics attenuation at high frequency than

the L filter with a first order transfer function

The filter parameters L1, L2, C3, and R3 greatly influence

the performance of the LCL filter Poorly designed parameters

will not reach the expected attenuation effect or even cause distortion increase due to oscillation effects [2] The following section will describe how to design these parameters following a step-by-step procedure

B Constraints on LCL filter design

With the free variables in equation (1), the solution of the

LCL filter parameters is not exclusive, which brings difficulty

in the filter design However, according to the desired ripple attenuation ratio and other requirements [2], constraints on the

values of L1, L2, C3, and R3 can be deduced

1) The total value of inductance should limit current

ripple of I1 to 15%-25% of rated current [3] In Fig 1, the

current I1 depends on the impedance of L1 (denoted as XL1)

and the parallel impedance of L2 and C3 (denoted as XL2C3)

The impedance of C3 (denoted as XC3) at switching frequency,

should be much smaller than the impedance of L2 at switching

frequency (denoted as XL2) to ensure that most of the high

frequency currents flow through C3 branch, so the parallel

impedance is dominated by XC3 Because XC3 is small, I1 is

mainly determined by XL1, which requires large L1 value to limit current ripple The maximum current ripple in a PWM switching period is estimated as

dc rip max

PWM 1

8

U i

Where Udc is the converter dc-link voltage, fPWM is the

switching frequency Thus to reach a desired current ripple irip,

L1 is designed following:

dc rip PWM

1

8

U

i f

However, in order to improve the ability of current tracking

and avoid large ac voltage drop, L1 cannot be too large [7] L1

is also limited by

1

m

B

/ 3

I

L

ω

−

Where Um is the peak phase voltage of gird, Im is the peak

current of grid, ωB is the angular frequency of grid voltage

Low impedance of XC3 means large capacitor value of C3, which will result in large reactive power For converters

directly connected to the grid, the reactive power by C3 is generally less than 5% of rated power with the power factor

limit Thus, C3 is designed following:

rated

5%

3 2

P C

f U

π

Where Prated is the rated power of the converter, fB is the

grid frequency, Urated is the RMS value of converter output phase voltage

2) Select the desired current ripple reduction σ with respect to the ripple on the converter side to design the

inductance of L2 Thus in total the L2C2 part reduces the grid current ripple to a very low level

2

=

i f

σ

Where ig(fPWM) and iC(fPWM) are grid current ripple and converter current ripple at the switching frequency

3) To avoid resonance problems in the lower and upper

parts of the harmonic spectrum, ωres should be in a range between ten times the grid frequency and one-half of the switching frequency, i.e.,

For a Y connected LCL filter, the resonant frequency ωres is expressed as

res

1 2 3

L L C

For a delta connected LCL filter, ωres is

res

3

L L C

After designing L1, L2, and C3, the resonant frequency should be verified If the limit is not satisfied, the parameters would be changed accordingly

4) Without damping resistor R3, equation (1) becomes

3

1 ( )

H s

=

Transfer function in (8) has a pair of poles located at the imaginary axis The imaginary poles will cause oscillation to the system, which requires the filter to be damped to avoid resonance problems

Damping resistors are widely used to increase the stability

of the system due to its simplicity and reliability Studies have shown that the greater the damping resistor, the better resonant inhibition [3, 8] However, larger damping resistor

will cause larger power losses Generally, R3 is set at one-third the impedance of capacitor at resonant frequency [2],

3

1 3

R

C

ω

III LCLFILTERS DESIGNFORBACK-TO-BACK

CONVERTEROFDFIG

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A System configuration

Fig 2 Configuration of a DFIG system with two LCL filters

Fig 2 shows the overall configuration of a DFIG system

with a Y connected LCL filter on GSC side and a delta connected LCL filter on RSC side respectively The DFIG is

rated at 2.5MW with a 690V voltage (line to line, 50Hz) The stator rotor turns ratio is 0.3, and other parameters are listed in the Appendix The converter dc-link capacitor is 20,000uF, the dc-link reference voltage is set at 1,200V, and the switching frequency is 1,950Hz for both the converters

With the control of the back-to-back converter, DFIG realizes maximum wind power tracking control and decoupled

P-Q control [9] The controllers are typically designed in a dq

rotating frame using proportional-plus-integral (PI) based

control strategies The appearance of the LCL filter brings a

little change to the rotating frame as well as the controller design In [10], state feedback control was used to guarantee

the stability of a PWM inverter with an LCL filter However,

the approach increased complexity in the control algorithm

In fact, PI control parameters are generally designed only considering the low frequency components As the fundamental component of the output currents of both GSC and RSC is at low frequency, and the capacitor branch presents low pass characteristics for the high frequency components, the capacitor branch can be neglected while determining the control parameters Thus the PI controllers for

the converter with LCL filters can be designed by only

adapting the parameters of the PI controllers that is already

used for the converter with L filter configuration

B Y connected LCL filter design for GSC

Taking the constraints proposed in Section II into consideration, the systematic procedure to design the filter on GSC side is as follows

1) According to (4), in order to obtain a 20% current

ripple of I1g, a minimum value of 0.65mH is required for

inductance L1g L1g should be less than 2.2mH according to (5)

Here, 1.0mH is adopted for L1g

2) The maximum value of capacitor C3g is 167μF under the 5% power factor limit, but capacitor value cannot be too

low to avoid too high a value of grid side inductance L2g Here

C3g is set at 100μF If other constraints cannot be met, it will

be increased up to the maximum value

3) Selecting a current ripple attenuation of 10% with respect to the ripple on the converter side, a value of

L2g=0.73mH is calculated using (7) Thus in total the L2gC3g

part reduces the grid current ripple to 2%

The consequent resonant frequency is 775Hz, which is in

the range between 10fB (500Hz) and 1/2fPWM (975Hz)

4) The impedance of the filter capacitor at the resonant

frequency is 2.05Ω, so the damping value R3g is chosen as one-third, i.e., 0.68Ω

TABLE I LCL filter parameters on GSC side

1.0e-3H 0.73e-3H 0.68Ω 100μF

In summary, the LCL filter parameters on GSC side are list

in TABLE I

Substituting L1g, L2g, C3g and R3g into (1), the transfer function becomes:

5

6.8 10 1 ( )

7.3 10 1.18 10 1.73 10

s

H s

−

=

-225 -180 -135 -90

Bode Diagram

Frequency (Hz)

-100 -50 0 50

Frequency (Hz): 1950 Magnitude (dB): -37.2

Fig 3 Bode plot of LCL filter on GSC side

The bold lines in Fig 3 are the bode plot of the LCL filter

on GSC side It can be seen that the filter has satisfactory filtering performance with the gain of -37.2dB for 1950Hz signal, and higher frequency harmonics get higher attenuation

The slender lines shows the bode plot of an L filter with a

7.2mH inductance It can be concluded that in order to get the

same attenuation as the LCL filter, a much larger inductance value is required for the L filter

C Delta connected LCL filter design for RSC

The frequency of RSC current varies in accordance with the rotor speed to keep stator frequency constant Assume the DFIG in our study operates at a maximum speed of 1.2pu on high wind speed conditions Thus a 0.2pu slip frequency exists and consequently the rotor current frequency is 10Hz (in negative sequence)

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r

Lσ I2r

r

E

r

R

Cr

U

1r

L

2r

L

3r

C

2c

I

Fig 4 Equivalent circuit of DFIG rotor side with the LCL filter

Fig 4 shows the equivalent circuit of DFIG rotor side with

the LCL filter Lrσ and Rr is the rotor leakage inductance and

the rotor resistor respectively Er is the induced electromotive

force Neglecting Rr, some differences exist in designing the

LCL filter on RSC side due to the existing Lrσ The detailed designing procedures are:

1) In order to obtain a 20% current ripple of I1r, a

minimum value of 0.36mH is required for inductance L1r

according to (4) To enhance the ability of current tracking, L1r

is set at 0.5mH, a little larger than the required value, which is also less than 4.6mH according to (5)

2) The filter is delta connected on RSC side With less

capacitance, the delta connected LCL filter can achieve the same harmonics attenuation as Y connected LCL filter [11]

The maximum value of capacitor is 633μF under the 5%

power factor limit Here C3r is set at 300μF In order reach a current ripple attenuation of 10% with respect to the ripple on

the converter side, a value of L2r=0.05mH is calculated using

(7) However, the existing rotor leakage inductance Lrσ is 0.106pu, which is 0.71mH when converted to rotor side

Because Lrσ is much larger than the required value, it will play

the role of L2r Thus L2r can be omitted Thus with the LrσC3r

part, a current ripple attenuation of more than 10% with respect to the ripple on the converter side can be reached It

must be pointed out that if Lrσ is smaller than the required value, an extra inductance should be added to rotor side

3) The consequent resonant frequency is 310Hz, which is

also in the range between 10fB (100Hz) and 1/2fPWM (975Hz)

4) The damping value R3g is set at 0.57Ω in delta connection, one-third of the impedance of the capacitor at the resonant frequency, 1.71Ω

The parameters are list in TABLE II

TABLE II LCL filter parameters on RSC side

Transforming the value C3r and R3r in delta connection into the Y connection, and then substituting the parameters into (1), the transfer function becomes:

4

1.7 10 1 ( )

3.2 10 2.1 10 1.2 10

s

H s

−

=

According to (14), the bode plot of the designed LCL filter

on RSC side is shown with the bold lines in Fig 5

As can be seem from Fig 5, a gain of -47.8dB is obtained for 1,950Hz harmonic, which shows the good performance of the filter on attenuating high frequency harmonics It can be found that this system is unstable because the resonant peak is

above 0dB In order to enhance the system stability, Rr3 is

increased The slender lines are the bode plot with Rr3 equals 1.14Ω (2 times of 0.57Ω) With the larger damping resistor,

the resonant peak is below 0dB, so the designed value of Rr3 is changed to 1.14Ω It can be seen that the greater the passive damping resistor, the better resonant inhibition, but larger losses will be caused

Fig 5 Bode plot of LCL filter on RSC side

IV SIMULATIONANDANALYSIS

The DFIG with the two LCL filters proposed is modeled

and simulated in PSCAD/EMTDC The phase A currents on

GSC side are shown in Fig 6(a) and Fig 6 (b), where ICA is

the converter output current and IgA is the current into the grid The currents are analyzed using FFT, and their spectrums are shown in Fig 6(c) and Fig 6 (d) It can be found that the lowest frequency current ripple of the currents is around 1,950Hz, 3,900Hz and 5,850Hz ect It’s obvious that

harmonics magnitude of ICA is much higher than IgA The Total Harmonics Distortion (THD) is used to evaluate the filtering performance THD is expressed as

2 2

( ) THD=

(1)

h

I h I

∞

=



(15)

Where I(1) is the RMS value of fundamental current and

I(h) is the RMS value of the hth harmonic current RMS values and the THDs of the currents are list in TABLE III

TABLE III Phase A current of GSC (RMS: kA) Overall

current(kA) Fundamental current(kA) Overall-harmonic currents(kA) THD

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It can be seen that current THD is significantly reduced from 11.05% on converter side to 1.70% on grid side, which

shows the effectiveness of the LCL filter

Fig 6 Phase A currents on GSC side and the spectrums

Taking into account the active power consumed by the damping resistor and the reactive power provided by the capacitor, the losses are 0.48% of rated power, and the power factor is 4.4% consequently

Phase A currents on RSC side with their spectrums are shown in Fig 7 IcA is the converter side current and IrA is rotor side current The analysis results are list in TABLE IV

TABLE IV Phase A currents on RSC side (RMS: kA) Overall

current

Fundamental current

Overall-harmonic currents THD

The fundamental current on rotor side is a little larger than that of the converter side because the power flows form rotor side to converter side due to supersynchronous operation The THD is 7.19% at converter terminal and it is reduced to 1.64%

on rotor side, and the loss is 0.22%, which also demonstrates the good performance of the LCL filter

Fig 7 Phase A currents on RSC side and the spectrum

V CONCLUSION

By analyzing the characteristic of the LCL filter, the constraints on designing the parameters of the LCL filter are provided Based on the constraints, two LCL filters, one in Y

connection and one in delta connection, are designed for the back-to-back converter of a 2.5MW DFIG The detailed design procedures are proposed as well PSCAD/EMTDC simulation and analysis results show that the THD of the current after filtering is 1.70% on GSC side and 1.64% on RSC side respectively, which verified the effectiveness of the designed filters in attenuating harmonics produced by the back-to-back converter

VI APPENDIX

DFIG parameters:

Stator resistance: 0.023pu Rotor resistance: 0.0396pu Stator leakage inductance: 0.104pu Rotor leakage inductance: 0.106pu Magnetizing inductance: 2.93pu

REFERENCES [1] "IEEE Recommended Practices and Requirements for Harmonic Control

in Electrical Power Systems," IEEE Std 519-1992, p 0_1, 1993-01-01

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[4] Z Xianping, "Damping Strategy of Grid-side Converter With New Topology Filter in Doubly-fed Wind Power System," vol 29, L Yaxi, Ed., 2009, pp 1-7

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pp 833-838

BIOGRAPHIES

Peng Zhan was born in 1987 He received the B.Eng in electrical

engineering from Huazhong University of Science and Technology (HUST), Wuhan, China in 2010 Currently he is pursuing a Mater degree at HUST His research interest is the wind power generation and the control schemes for

integrating wind power to the grid through HVDC

Weixing Lin was born in 1986 He received the B.Eng in electrical

engineering from Huazhong University of Science and Technology (HUST), Wuhan, China in 2008 Currently he is pursuing a Ph.D degree at HUST His research interest is control, technical and economic comparisons of different

schemes for integrating wind power to the grid

Jinyu Wen received the B.Eng and Ph.D degrees all in electrical

engineering from HUST, Wuhan, China, in 1992 and 1998, respectively He was a visiting student from 1996 to 1997 and research scholar from 2002 to

2003 all at the University of Liverpool UK In 2003 he entered the HUST and now is a professor at HUST His current research interests include smart grid, renewable energy, energy storage, FACTS, HVDC and power system operation and control