Design and control of LCL filter with active damping for grid-connected

2015 International Conference on Electrical Drives D and Power Electronics (EDPE)

The High Tatras, 21-23 Sept. 2015

Design and Coontrol of LCL Filter with Active Damping for f Grid-Connected Invverter 1

Marek Pastor, 2Jaroslav Dudrik

1,2

Deppt. of Electrical Engineering and Mechatronics Facuulty of Electrical Engineering and Informatics Technical University of Košice, Letna 9, 042 00 Košice, Slovakia 1 [email protected], [email protected]

Abstract—The paper describes design an nd control of LCL filter with active damping. The LCL filter is i used in a single phase grid connected inverter. The performan nce of two different active damping methods is compared to paassive damping by simulation. Keywords—converter control, filtering, dc/acc converter

I. INTRODUCTION Grid connected pulse width modulatedd (PWM) voltage source converters require inductive filter for f its operations. These converters are used in many applications such as active power filters, PWM rectifiers or PWM inveerters. To decrease the weight and volume of the filter it is desirable to use higher-order filter. Usually an LCL filter iss used [2-14]. The LCL filter has a drawback of possible resonaance if excited at a resonant frequency. This resonance inntroduces system instability and increases THD of current. To suppress the oscillations a damping technique is used. Thhere are two ways of damping the oscillations in LCL filter: passive p and active damping. Both of them have its advantages and disadvantages and are still analyzed and designed. Passive damping [1] uses damping resistors which introduces additionnal system losses. An active damping is used to remove these extra losses but keep system stability. Active damping of the LCL filter is M rectifiers [5-7], studied in active power filters [2-4], PWM PWM inverters [8-12] and in general grid interacting converters [13-15]. This paper analyzes various damping i with LCL techniques for single.phase grid connected inverter filter.

Fig.1. LCL filter topology and its dynaamical model (RS and RG are parasitic resistances).

The voltage with a frequenccy equal to a resonant frequency defined by (1) causes a resonaance in the output current of the LCL filter. Any resonance in the system is undesirable. However, the resonance of thhe grid current excited by the inverter voltage causes the incrrease in the THD of the current supplied to the grid. f0 I

GVS

=

1 2π

LS + LG LS LG C

(1)

The example of the harm monic spectrum of LCL filter output current is shown in Fig. F 2. The resonance peak is clearly visible.

II. LCL FILTER A. LCL Filter Topology There are several filter`s topologies that can be used as the output filter for the grid-connected voltagge-source inverter (VSI). All of them must provide inductancee load for the VSI and suppress the higher-order frequencies prroduced by PWM. Usually higher order filters, such as LCL filter f (Fig. 1), are used. The LCL filter is a third order filter with w attenuation of 60 dB/dec. The advantage of high attenuatioon of a third order system has a drawback of resonance. The LC CL filter has three resonant frequencies. Connecting the LCL filter f to the output of a PWM modulated inverter causes driviing the LCL filter input with a spectrum of various high frequenncy voltages.

Fig. 2. Example of LCL filter output current c spectrum.

978-1-4673-7376-0/15/$311.00 ©2015 IEEE EDPE 2015

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2015 International Conference on Electrical Drives D and Power Electronics (EDPE) B. Passive Resonance Damping L filter. The soThere are two ways how to damp the LCL called passive damping employs extra resisttor added in series with a filter capacitor (Fig. 3). The value of the resistor is usually chosen as one third of the capacitoor reactance at the resonant frequency: RC =

1 1 3 2π f 0 I

Fig. 5. Simplified control structure of PR current control with active damping by notch filter

(2)

C GVS

fi is a notch (negative peak) The suitable type of the filter filter. The simple notch filter consists c of the LC resonant tank (Fig.6).

The damping resistor will change the trransfer function of the whole system (controller, PWM inverter and LCL filter) as is shown in Fig. 4. The resonant peak is signiificantly reduced.

a) LCL filter with damping resistor

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b) dynamiical model

Fig. 3. LCL filter with passive damping resistor.

a) notch filter topoplogy

b) notch filtter frequency characteristics

Fig. 6. Notch filter.

The transfer function of a notch n filter is defined by (3). Fnotch =

Ln Cn s 2 + 1 LnCn s 2 + Rn Cn s + 1

(3)

Ln = 1 mH H

(4)

1 1 3 2π f 0 I

(5)

where:

Fig. 4. LCL with various damping resistor values.

RC =

The advantage of passive dampingg consist in its robustness. However there are also dissadvantages. The damping resistor has losses which decrease the t overall system efficiency. The second main disadvantagge is decrease of higher frequency damping (Fig. 4). If the reesonant frequency of the LCL filter is not too far from the switching frequency, this decrease is minimal.

Rn =

C. Active Resonance Damping – Notch Filteer The frequency characteristics of the system can be T proper transfer changed also by modifying the controller. The function of the controller can damp the oscilllations of the LCL filter. The main idea is to remove undesiredd frequencies from the inverter output voltage by modifying the modulation signal of the PWM. This approach is called an activve damping.

C GVS

( 2π f n )2 LnCn − 1 ( 2π f nCn )2

(6)

The frequency fn defines thhe notch filter bandwidth around the LCL filter resonant frequenncy f0IGVS. The advantage of the activve damping by notch filter is its sensorless concept. When com mpared to the passive damping, the system transfer function for higher frequencies is not influenced by inserting the notcch filter. However, the design of the notch filter depends on the LCL filter parameters.

There are several ways how to achieve thhe active damping. Probably the most straightforward is to rem move the resonant frequency from the inverter output voltage byy a filter (Fig. 5).

EDPE 2015

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2015 International Conference on Electrical Drives D and Power Electronics (EDPE)

The High Tatras, 21-23 Sept. 2015

D. Active Resonance Damping – Virtual Ressistor Another active damping method is usinng the concept of virtual resistor. The virtual resistor method is based on LCL filter capacitor current sensing and multiplyinng this current Fig. 9. PR controller.

FPR = K P +

2 K I ω PR s s 2 + 2ω PR s + ω g2

(7)

Fig. 7. Simplified control structure of PR current controol with active damping by virtual resistor.

The frequency ȦPR defines the PR controller bandwidth T design the PR controller it is around the grid frequency Ȧg. To necessary to know the transferr function from inverter voltage VS (manipulated variable) too grid current IG (controlled variable). The grid voltage VG is i a measured disturbance and is compensated in the PR conttroller. The grid current is a measured controlled variable.. The high frequency transfer function from VS to IG of the LC CL filter is:

by virtual damping resistor resistance. Thhe resulting virtual voltage is then subtracted from inverter PWM P modulating voltage (Fig. 7). The value of the virtual resistor can bee calculated using (2). As can be seen from Fig. 8, the virtuall resistor does not change the system frequency characterristic for higher frequencies than the f0IGVS resonant frequencyy.

IG = VS 1 3

s LS LG C + s

2

(8)

( LS CRG + RS CLG ) + s ( RS CRG + LS + LG ) + RS + RG

The PR controller controls the grid current IG with grid frequency and thus generates thhe manipulated variable VS with grid frequency. The transfer function (3) is simplified by omitting the high-frequency terrms: IG VS

Fig. 8. Frequency characteristics of LCL filter with actiive damping by virtual resistor.

1 s ( LS + LG ) + RS + RG

(9)

The LCL filter is therefore simplified to first order system with time constant of:

III. CONTROL SYSTEM DESIG GN A. LCL filter parameters The performance of three damping metthods is compared by simulation. The system consists of a siingle-phase PWM voltage source inverter with switching frequeency of 5 kHz and dc link voltage of 420 V. The inverter is connnected to the grid through the LCL filter with parameters show wn in Table I. TABLE I.

= LL

TLCL =

LS + LG RS + RG

(10)

K LCL =

1 RS + RG

(11)

And gain of:

LCL FILTER PARAMEETERS

LCL filter parameter Apparent power S Switching frequency fSW Current ripple of IS Resonant frequency f0IGVS Inductance LS Inductance LG Capacitance C

Value

Unit

1.2 5 20 2 3.6 1.8 5.3

kW kHz % kHz mH μH μF

The PR controller is designed to compensate the time constant TLCL. The proportional gain of the PR controller is set to (IJ is time constant of reqquired control dynamics of the whole controlled system): KP =

TLCL

τ K LCLL

(12)

The integral gain of PR controller is set to:

B. PR Controller The inverter is single-phase system. It iss thus beneficial to use proportional resonant (PR) controller (Fig. 9) with the transfer function:

KI =

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KP TLCL

(13)

2015 International Conference on Electrical Drives D and Power Electronics (EDPE) TABLE II.

PR CONTROLLER PARAM METERS

PR Controller parameters Time constant TLCL Gain KLCL Proportional gain KP Integral gain KI Frequency ȦPR Grid frequency ȦG

Value

Unit

13.5 2.5 5.4 400 1 314

ms S rad/s rad/s

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C. Virtual Resistance To create a damping in the t controlled system a virtual damping resistor with resistannce of 10 Ÿ was choosen. The Fig. 12 shows the frequency chharacteristics of undamped LCL filter and the LCL filter damped with notch filter.

IV. COMPARISON OF DAMPING METHODS E A. Passive damping method The damping resistor RC for the LCL filter specified in Table I calculated using (2) is 5 Ÿ. Fig. 100 shows frequency characteristics of undamped inverter with w LCL filter controlled by PR controller, and damped withh RC = 5 Ÿ.

Fig. 12. LCL filter output current specctrum. CLUSIONS V. CONC

The paper presents usingg of the LCL filter in grid connected inverter and somee problems associated with it, mainly the phenomen of LCL filter f resonance. The problem of the LCL filter reconance is analyzed a on single.phase gridconnected VSI with PWM control. c The PR controller is designed to ensure the currrent control. Three different damping techniques are designned and verified by simulation. The passive damping has thee advatntage of robustness but aditional losses and decrease of higher-order frequencies mping resistor are undesirable. suppresion produced by a dam The active damping by notch filter enables to remove or reduce the power losses introduced by passive damping but this damping technique needds to be tuned for particual resonant frequency and is thuus less robust. However it can operate without aditional sennsor. The active damping by virtual resistance can mimicck the bahaviour of passive damping resistor. By sensinng the cpacitor current this technique is more robust butt at a cost of aditional current sensor.

Fig. 10. LCL filter output current spectrum.

B. Notch filter The simulated notch filter transfer functioon is: Fnotch =

6.36.10 −9 s 2 + 1 6.36.10 −9 s 2 + 4.664.10 −5 s + 1

(14)

To suppres the resonant frequency thee notch filter has narrow bandwith of 1 kHz. The Fig. 11 shoows the frequency characteristics of undamped system and thhe system damped with the notch filter.

ACKNOWLLEDGEMENT The authors wish to thank the t project VEGA 1/0464/15 for its support. The paper presents results of the project implementation: University Science Park TECHNICOM T for Innovation Applications Supported by Knowledge K Technology, ITMS: 26220220182, supported by the Research & Development Operational Programme fundedd by the ERDF." REFER RENCES [1] Fig. 11. LCL filter output current spectrum.

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C. Chen, Z. Wang, Y. Zhang, G. Li, Y. Wu, "A novel passive damping LCL-filter for active power filter," in Transportation Electrification Asia-Pacific (ITEC Asia-Pacificc), 2014 IEEE Conference and Expo , 2014-Sept. 3 2014 pp.1-5, Aug. 31 doi: 10.1109/ITEC-AP.2014.6940684

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Marek Pastor (M’15) was born in Košice (Slovakia) in 19885. He received electrical his master degree in engineering in 2010 andd PhD. in 2014 from Technical Universsity of Košice, Slovakia. He is currently an assistaant professor at Dept. of Electrical Enngineering and Mechatronics, faculty of Electrical Enngineering and Informatics at Technical University of Kosicce, Slovakia. His interest is in the area of power electronics.

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X. Lu, K. Sun, L. Huang, M. Lisserre, F. Blaabjerg, "An active damping method based on biquad digital filter for parallel grid-interfacing inverters with LCL filters," in Applied A Power Electronics Conference and Exposition (APEC), 2014 Tw wenty-Ninth Annual IEEE , pp.392-397, 16-20 March 2014, doi: 10.1109//APEC.2014.6803338 Ch. Bao, X. Ruan, X. Wang, W. W Li, D. Pan, K. Weng, "Design of injected grid current regulator and capacitor-current-feedback activedamping for LCL-type grid-connnected inverter," in Energy Conversion Congress and Exposition (ECCE E), 2012 IEEE , pp.579-586, 15-20 Sept. 2012, doi: 10.1109/ECCE.2012.66342769 Y. Shi, J. Su, "An active dampingg method based on PR control for LCLfilter-based grid-connected invverters," in Electrical Machines and Systems (ICEMS), 2014 17th Intternational Conference on , pp.944-948, 22-25 Oct. 2014, doi: 10.1109/IC CEMS.2014.7013604 M.L. Sowjanya, B.C. Babu, "Coomparative analysis of LCL filter with active and passive damping methods for grid-interactive inverter system," in Students' Technology gy Symposium (TechSym), 2014 IEEE , 2014-March 2 2014, doi: pp.350-355, Feb. 28 10.1109/TechSym.2014.68080744 W. Yao, Y. Yang, X. Zhang, F. F Blaabjerg, "Digital notch filter based active damping for LCL fillters," in Applied Power Electronics Conference and Exposition (APE EC), 2015 IEEE , pp.2399-2406, 15-19 March 2015, doi: 10.1109/APEC C.2015.7104684 R. Pena-Alzola, M. Liserre, F. Blaabjerg, B Y. Yang, "Robust design of LCL-filters for active dampinng in grid converters," in Industrial Electronics Society, IECON 20013 - 39th Annual Conference of the 10-13 Nov. 2013, doi: IEEE , pp.1248-1253, 10.1109/IECON.2013.6699311 s of discrete-time active damping M. Orellana, R. Grino, "On the stability methods for VSI converters withh a LCL input filter," in IECON 2012 38th Annual Conference on IEEE I Industrial Electronics Society , pp.2378-2383, 25-28 Oct. 2012, doi: d 10.1109/IECON.2012.6388871

Jaroslavv Dudrik received the M.S. and Ph.D. deegrees in electrical engineering from thhe Technical University of Košice, Slovakia, S in 1976 and 1987. He is currently full professor of Electrical Engineering at the Department of Eleectrical and Mechatronic Engineerring, Technical University of Košice, where w he is engaged in teaching and research. His primary innterest is power electronics. His field of research includes dc-to-dc d converters, high power soft switching converters, coonverters for renewable energy sources and control theory off converters.

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