1426 PIERS Proceedings, Marrakesh, MOROCCO, March 2023, 2011

Comparison of Different Filter Types for Grid Connected Inverter

Jiri Lettl, Jan Bauer, and Libor LinhartDepartment of Electric Drives and Traction, Faculty of Electrical Engineering

Czech Technical University in Prague, Technicka 2, 166 27 Prague 6, Czech Republic

Abstract The acquisition of the electrical energy from renewable sources is very trendy inthese days. That is also why the applications for renewable energy generation undergo rapiddevelopment. As the greatest weakness of renewable sources can be assumed the instability anddependence of energy amount, that they deliver. In order to stabilize the energy output andto give it some defined shape and value, the power converter must be connected to the outputof the solar panel. For this purpose of application is the most suitable choice voltage sourceinverter (VSI). In order to suppress or reduce negative effects the filter is connected between theconverter and the network. The filter must be designed precisely, because it must have sufficientattenuation at the inverters switching frequency and it must not bring oscillations to the wholesystem.

This paper deals with design and simulation of such a filter type. Simulation models of thesystems inverter-filter were made.

1. INTRODUCTION

The amount of the energy from renewable energy sources, as solar energy or wind turbine energy,that is delivered to supply network, significantly rises. That is why the grid friendly interfacebetween the supply grid and the energy source is needed. The quality of generated energy iscrucial, because non-sinusoidal currents delivered to the grid can cause additional non-sinusoidalvoltage drop across the line impedances and therefore increase of the voltage distortions deliveredto the load.

Next problem is that the energy supplied by these sources does not have constant value, butfluctuates according to the surrounding conditions (intensity of sun rays, water flow, etc.). Thesesources are supplemented by additional converters as voltage source inverters (VSI). This converteris then controlled by a modern sophisticated control algorithm such as PWM which ensures nearlysinusoidal current generation. This solution is illustrated in Fig. 1. The power from some renewableenergy source is delivered to the DC-link and the output of the inverter is filtered in order to obtainlow current distortion.

2. FILTER TOPOLOGIES

The output filter reduces the harmonics in generated current caused by semiconductor switching.There are several types of filters. The simplest variant is filter inductor connected to the invertersoutput. But also combinations with capacitors like LC or LCL can be used. These possibletopologies are shown in Fig. 2.

Inverter

C1

DC linkLi Lg

Cf

RsdS1

S2S4

S3

L-C-L filter

UCfUDC

Controller

IoICf

SOLAR

ARRAY

DISTRIBUTION

NETWORK

Figure 1: Block diagram of the VSI.

Progress In Electromagnetics Research Symposium Proceedings,Marrakesh,Morocco,Mar. 2023, 2011 1427

VSI VSI VSI

(a) (b) (c)

Figure 2: Basic filter topologies.

2.1. L-filterThe L-filter (Fig. 2(a)) is the first order filter with attenuation 20 dB/decade over the whole fre-quency range. Therefore the application of this filter type is suitable for converters with highswitching frequency, where the attenuation is sufficient. On the other side inductance greatly de-creases dynamics of the whole system converter-filter. Transfer function of the L-filter is depictedin Fig. 3 as a black dashed line.2.2. LC-filterThe LC-filter is depicted in Fig. 2(b). It is second order filter and it has better damping behavioursthan L-filter. This simple configuration is easy to design and it works mostly without problems.The second order filter provides 12 dB per octave of attenuation after the cut-off frequency f0, ithas no gain before f0, but it presents a peaking at the resonant frequency f0. Transfer function ofthe LC-filter is

F (s) =1

1 + s LF + s2 LF CF (1)It is depicted in Fig. 3 by red colour. In order to suppress the negative behaviours near cut-offfrequency the damping circuit is added to the filter. The damping can be either series or parallel.The damping circuit selection influences the transfer function of the filter (Eq. (2) resp. Eq. (3)).The influence is depicted in Fig. 3.

F (s) =1 + s RPD CPD

1 + s RPD CPD + s2 LF (CF + CPD) + s3 LF CF RPD CPD (2)

F (s) =RSD + s (LF + LSD)

RSD + s (LF + LSD) + s2 LF CF RSD + s3 LF CF LSD (3)

The own design of the filter is a compromise between the value of the capacity and inductance.The high capacity has positive effects on the voltage quality. On the other hand higher inductancevalue is required to achieve demanded cut-off frequency of the filter. Connecting system with thiskind of filter to the supply grid, the resonant frequency of the filter becomes dependent on the gridimpedance and therefore this filter is not suitable, too.2.3. LCL-filterThe attenuation of the LCL-filter is 60 dB/decade for frequencies above resonant frequency, there-fore lower switching frequency for the converter can be used. It also provides better decouplingbetween the filter and the grid impedance and lower current ripple across the grid inductor. There-fore LCL-filter fits to our application. Transfer function of the LCL-filter is depicted in Fig. 3.

The LCL filter has good current ripple attenuation even with small inductance values. Howeverit can bring also resonances and unstable states into the system. Therefore the filter must bedesigned precisely according to the parameters of the specific converter. In the technical literaturewe can find many articles on the design of the LCL filters [4, 5]. Important parameter of the filter isits cut-off frequency. The cut-off frequency of the filter must be minimally one half of the switchingfrequency of the converter, because the filter must have enough attenuation in the range of theconverters switching frequency. The cut-off frequency must have a sufficient distance from the gridfrequency, too. The cut-off frequency of the LCL filter can be calculated as

fres =12pi

Li + LgLiLgCf

(4)

The LCL filter will be vulnerable to oscillations too and it will magnify frequencies aroundits cut-off frequency. Therefore the filter is added with damping. The simplest way is to add

1428 PIERS Proceedings, Marrakesh, MOROCCO, March 2023, 2011

Figure 3: Filter transfer functions.

1sCf

1sLg

R

iI ig

ug

++

++

- -

Figure 4: Filter model in operator area. Figure 5: Effects of the damping circuit.

damping resistor. In general there are four possible places where the resistor can be placed series/parallel to the inverter side inductor or series/parallel to filter capacitor. The variant withresistor connected in series with the filter capacitor has been chosen. The value of the dampingresistor can be calculated as

Rsd =1

3resCf(5)

Transfer function of the filter with damping resistor is depicted in Fig. 3 by cyan colour. Thepeak near resonant frequency has nearly vanished. This is simple and reliable solution, but itincreases the heat losses in the system and it greatly decreases the efficiency of the filter. Thisproblem can be solved by active damping. The filter can be modelled as shown in Fig. 4.

The effect of the damping resistor is clear from Fig. 4. The resistor reduces the voltage acrossthe capacitor by a voltage proportional to the current that flows through it. This can be also donein the control loop. The current through Cf is measured and differentiated by the term sCfRsd.A real resistor is not used and the calculated value is subtracted from the demanded current. Inthis way the filter is actively damped with a virtual resistor without losses. The disadvantage ofthis method is that an additional current sensor is required and the differentiator may bring noiseproblems because it amplifies high frequency signals.

3. FILTER DESIGN AND SIMULATION RESULTS

For this filter were taken these limitations into account:

1) the cut-off frequency of the filter must be minimally 10 times greater then grid frequency andsimultaneously maximally one half of the converter switching frequency

2) The decrease of the power factor caused by the filter capacitance should be lower than 5%

Progress In Electromagnetics Research Symposium Proceedings,Marrakesh,Morocco,Mar. 2023, 2011 1429

Table 1: Parameters for calculating the filter components.

Grid Voltage (V) 230 Inverter Side Inductance Li (mH) 17.7Output Power of the Inverter (kVA) 1.5 Grid Side Inductance Lg (mH) 5.7

DC link Voltage (V) 400 Filter Capcitor Cf (F) 3.45Grid Frequency (Hz) 50 Damping resistor R () 11.3

Switching Frequency (Hz) 3000 Cut-off Frequency (Hz) 1300

Figure 6: Output of the inverter with filter.

The parameters of the designed filter as well as parameters required for the filter design aresummarized in Table 1.

The simulation results of the inverter with the designed filter with active damping connected toits output are in Fig. 6. Fig. 5 shows the effect of the damping resistor and active damping withthe virtual resistor.

4. CONCLUSIONS

The output current filter has been designed and simulated. The obtained results seem to bepromising. However, we will be able to evaluate the functionality of the filter after the wholesystem is realized and the filter will be connected to the output of the inverter.

ACKNOWLEDGMENT

This work was supported by the Grant Agency of the Czech Technical University in Prague, grantNo. SGS 10 800630. The research described in the paper was supervised by Prof. J. Lettl, Csc.

REFERENCES

1. Hinz, H., P. Mutschler, and M. Calais, Control of a single phase three level voltage sourceinverter for grid connected photovoltaic systems, PCIM, 1997.

2. Liserre, M., F. Blaabjerg, and S. Hansen, Design and control of an LCL-filter based three-phase active rectifier, Industry Applications Conference, 2001, Thirty-Sixth IAS Annual Meet-ing, Conference Record of the 2001 IEEE, Vol. 1, 2001.

3. Araujo, S. V., A. Engler, and B. Sahan, LCL filter design for grid-connected NPC invertersin offshore wind turbines, The 7th International Conference on Power Electronics, Daegu,Korea, 2007.

4. Dahono, P. A., A method to damp oscillations on the input LC filter of current-type ac-dc pwmconverters by using a virtual resistor, Telecommunications Energy Conference INTELEC03,2003.

5. Raoufi, M. and M. T. Lamchich, Average current mode control of a voltage source inverterconnected to the grid: Application to different filter cells, Journal of Electrical Engineering,2004.