This paper concentrates on the LCL filter with damping resistance intended to connect the shunt active power filter of an active DC-traction substation to the point of common coupling with the transmission grid. In order to find design conditions and conceive a design algorithm, attention is directed to the transfer functions related to currents and the associated frequency response. The mathematical foundation of the design method is based on the meeting the requirements related to the significant attenuation of the high-frequency switching current, concurrently with the unalterated flow of the current that needs to be compensated by active filtering. It is pointed out that there are practical limitations and a compromise must be made between the two requirements. To quantify the extent to which the harmonics to be compensated are influenced by imposing the magnitude response at both highest harmonic frequency to be compensated and switching frequency, a performance indicator is defined. As an additional design criterion, the damping power losses are taken into consideration. The validity and effectiveness of the proposed method are proved by simulation results and experimental tests on a laboratory test bench of small scale reproducing the specific conditions of a DC-traction substation with six-pulse diode rectifier.
1. DC-traction substations
2. LCL filter
3. Passive damping
5. Shunt active power filters
Fig. 1. Block diagram of the active DC-traction substation.
EXPECTED SIMULATION RESULTS:
Fig. 2. Voltages and currents in the TT’s primary in traction regime
Fig. 3. LCL filter input current.
Fig. 4. Current flowing through the capacitor of the interface filter.
Fig. 5. Harmonic spectra of the LCL filter input current (black bars) and output current (yellow bars) for harmonic order k[1, 37].
Fig. 6. Voltages and currents upstream of PCC during the operation in traction regime.
Fig. 7. Succesive traction (filtering) and braking (regeneration) regimes: (a)
phase voltage (blue line) and supply current (green line); (b) DC-capacitor
voltage (black line) and DC-line voltage (red line).
A new design method of an LCL filter with damping resistance intended to couple the three-phase VSI of an active DC-traction substation to the power supply has been proposed in this paper. The following elements of originality are outlined.
1) The theoretical substantiation is based on the frequency response from transfer functions related to currents, taking into account the existence of the series damping resistances.
2) The expressed amplitude response and resonance frequency highlight their dependence on only pairs L2Cf and RdCf, It is a very important finding for the conceived design algorithm.
3) The expression of the power losses in the damping resistances is highlighted and an equivalent resistance is introduced as a quantitative indicator of them.
4) By considering the switching frequency as main parameter and taking into consideration the frequency of the highest order harmonic to be compensated, the design algorithm is based on the imposition of the associated attenuations.
5) In the substantiation of the design algorithm, a detailed analysis is performed on the existence of physical-sense solutions, providing the domain in which the values of the parameters must be located.
6) As a large number of parameters values sets can be obtained, a new performance indicator (MPI) is proposed, to quantify the extent to which the harmonics to be compensated are influenced.
The analysis and the simulation results achieved for an active DC-traction substation with six-pulse diode rectifier and LCL coupling filter have indicated that the proposed method is valid and effective. The experimental tests conducted in a laboratory test bench of small scale reproducing the specific conditions of a DC-traction substation illustrate good performance of the system for active filtering and regeneration connected to the power supply by the passive damped LCL filter.
The design proposal can be applied in any three-phase LCL-filter-based shunt active power filter.
 A. Ghoshal and V. John, “Active damping of LCL filter at low switching to resonance frequency ratio,” IET Power Electron., vol. 8, no. 4, pp. 574–582, 2015.
 G. E. Mejia Ruiz, N. Munoz, and J. B. Cano, “Modeling, analysis and design procedure of LCL filter for grid connected converters,” in Proc. 2015 IEEE Workshop Power Electron. and Power Quality Appl. (PEPQA), pp. 1–6.
 M. Hanif, V. Khadkikar, W. Xiao, and J. L. Kirtley, “Two degrees of freedom active damping technique for filter-based grid connected PV systems,” IEEE Trans. Ind. Electron., vol. 61, no. 6, pp. 2795–2803, June 2014.
 X. Wang, F. Blaabjerg, and P. C. Loh, “Grid-current-feedback active damping for LCL resonance in grid-connected voltage source converters,” IEEE Trans. Power Electron., vol. 31, pp. 213–223, 2016.
 W. Xia, J. Kang, “Stability of LCL-filtered grid-connected inverters with capacitor current feedback active damping considering controller time delays,” J. Mod. Power Syst. Clean Energy, vol. 5, no. 4, pp. 584– 598, July 2017.