# Suppression of Supply Current Harmonics of 18-Pulse Diode Rectifier by Series Active Power Filter with LC Coupling

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## Abstract

**:**

## 1. Introduction

## 2. Converter System Characteristic

_{S}, resistance R

_{S}, and inductance L

_{S}, which also represents the leakage inductance of a rectifier’s magnetic circuits. The system is composed of two separate modules: an 18-pulse rectifier, and a series active filter. Three system configurations are possible: (1) only 18-pulse rectifier, (2) rectifier with additional series reactor, and (3) rectifier with the series active filter. The main element of the system is the 18-pulse rectifier based on current dividing transformer (CDT) for preliminary current division, and the set of coupled three-phase reactors (CTR) [5]. The above magnetic elements compose three 3-phase voltage systems, shifted by 20° in relation to each other. Six-pulse rectifiers with a shared output capacitor are connected to CTR outputs. The 18-pulse rectifier enables reduction of undesired higher harmonics from the supply network currents, mainly of the order of 5, 7, 11, and 13.

_{F}) and capacitance (C

_{F}) of the switching ripple filter were selected assuming the maximum ripple of the inductor current and the capacitor voltage. Figure 2a shows a simplified circuit diagram of the VSI and its output filter to define the signals, the waveforms of which are presented on Figure 2b. It shows the branch voltages u

_{1}, u

_{2}and the output voltage u

_{o}of the VSI, as well as the capacitor voltage u

_{C}and its averaged value over the sampling period u

_{C,avg}. In addition to the voltages, the figure also shows, in an idealized way, the VSI output current i

_{o}and its averaged value over the sampling period i

_{o,avg}. In the case of unipolar modulation with the double update mode the largest ripples of inductor current occur when the duty cycle m = u

_{o}/u

_{dc}is equal to 0.5. The simplified waveforms in Figure 2b apply to this case.

_{s}/2 (Figure 2b), in which the current i

_{o}increases from the minimum value to the maximum, the peak-to-peak value of the current ripple ∆i

_{o}can be calculated from the formula [14]:

_{dc}is the maximum dc link voltage equal to 500 V.

_{F}= 20 mH was selected. The maximum current ripple is at 11% of the peak nominal input current of the 18-pulse rectifier current, referred to the primary side of the transformer Tr.

_{s}/2, in which the capacitor voltage u

_{C}varies from the minimum to the maximum value (Figure 2b), the maximum capacitor voltage ripple ∆u

_{C}can be estimated by the equation [14]:

_{dc}in the worst case. Finally, the value of C

_{F}= 560 nF was selected, for which maximum ∆u

_{C}equals 3.5 V (0.7% of the U

_{dc}).

_{Sa}, u

_{Sb}, u

_{Sc}), transformer phase currents (i

_{Fa}, i

_{Fb}, i

_{Fc}) on the inverter side, and the rectifier output voltage u

_{dc}.

## 3. The Structure of Multiple Reference Frame Current Controller

_{a}, x

_{b}, and x

_{c}were converted using the space vector defined as:

_{1}is the frequency of the fundamental component, and θ

_{1}is its instantaneous phase.

_{m}, the number of which is equal to the number of compensated current harmonics. The error signal is converted to m synchronous coordinate systems by multiple Park transformations defined by the formula:

_{m}rotating with frequency mω

_{S}, ω

_{S}is the estimated frequency of fundamental component, and θ

_{S}= ω

_{S}t is the estimated instantaneous phase. After transformation, the control error harmonic of the order m becomes a constant component in dq

_{m}frame and is amplified by the integral term of current controller which corresponds to this harmonic. Simultaneously, the remaining harmonic components in the output signal ${\underset{\_}{U}}_{\mathrm{F}dqm}$ are suppressed:

_{0}is the time of control algorithm activation, and ${\underset{\_}{K}}_{i}\left(\mathrm{j}m{\omega}_{1}\right)$ is the complex-value gain of the frequency-dependent integral term of the controller.

## 4. Selection of Controller Settings

_{p}= 44.

_{Fαβ}(s) is the Laplace transform of the control system error, U

_{I}(s) is the Laplace transform of the output signal of the integral part (corresponding to the sum of output signals from individual integral terms), and G

_{cp}(s) is the transfer function of the closed-loop system when only the proportional controller is used:

_{i}= 0.5/f

_{1}= 10 ms.

_{Fαβm}, without additional trigonometric function calculations.

## 5. Laboratory Results

_{R}(Figure 5c,d), and (3) for rectifier with series active filter (S-APF) (Figure 5e,f). The waveforms of the phase currents with their amplitude spectra and THD (total harmonic distortion) values were recorded and calculated using the Precision Power Analyzer LMG670 made by Zes Zimmer. The amplitude spectra of the supply currents are given in logarithmic scale.

_{S}with the S-APF system improves the quality of supply currents within the entire output power range. For the configuration with S-APF operating at nominal load, the THD of supply currents remains at the approximate level of 2%. Significant improvement in quality of supply currents can be observed during converter system operation at low load. Compared to the configuration with additional series reactor, the system with S-APF also ensures slightly higher output voltage.

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Schematic diagram of the proposed ac/dc supply system based on 18-pulse rectifier and series active power filter with LC output stage.

**Figure 2.**Simplified circuit diagram of the VSI and switching ripple filter (

**a**) and waveforms of the characteristic signals in the case of maximum ripples of capacitor voltage and inductor current (

**b**).

**Figure 5.**Oscillograms and spectra of converter supply currents at nominal load: (

**a**,

**b**) system without reactor L

_{R}and S-APF; (

**c**,

**d**) system with reactor L

_{R}and without S-APF; (

**e**,

**f**) system without reactor L

_{R}and with S-APF.

**Figure 6.**THD of supply currents (

**top**) and rectifier output voltage (

**bottom**) as functions of input power for three converter system configurations.

**Figure 7.**Supply current waveforms and THD values recorded after initiating the current control algorithm.

Symbol | Description | Value |
---|---|---|

E_{S} | Phase voltage of the supply (50 Hz) | 230 V |

L_{Sp} | Supply inductance referred to the primary side of the transformer | 7.2 mH |

R_{Sp} | Supply resistance referred to the primary side of the transformer | 57.6 Ω |

P_{REC} | Nominal output power of the 18-pulse rectifier | 15 kW |

C_{L} | Rectifier output capacitance | 10 mF |

S_{T} | Nominal power of the series injection transformer (Tr) | 800 VA |

U_{Tp} | Nominal primary voltage of the transformer Tr | 300 V |

I_{Tp} | Nominal primary current of the transformer Tr | 2.9 A |

N_{T} | Turns-ratio of the series injection transformer Tr | 12 |

L_{T} | Leakage inductance of the windings of the transformer referred to the primary side | 3.46 mH |

R_{T} | Resistance of the windings of the transformer referred to the primary side | 3.7 Ω |

L_{TS} | Equivalent inductance, sum of L_{T} and L_{Sp} | 10.66 mH |

R_{TS} | Equivalent resistance, sum of R_{T} and R_{Sp} | 61.3 Ω |

L_{F} | Inductance of the switching ripple filter inductor | 20 mH |

R_{F} | Resistance of the switching ripple filter inductor | 0.5 Ω |

C_{F} | Capacitance of the switching ripple filter | 0.56 µF |

T_{d} | Delay introduced by control system and VSI | 75 µs |

f_{s} | Sampling and PWM switching frequency | 20 kHz |

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**MDPI and ACS Style**

Sleszynski, W.; Cichowski, A.; Mysiak, P. Suppression of Supply Current Harmonics of 18-Pulse Diode Rectifier by Series Active Power Filter with LC Coupling. *Energies* **2020**, *13*, 6060.
https://doi.org/10.3390/en13226060

**AMA Style**

Sleszynski W, Cichowski A, Mysiak P. Suppression of Supply Current Harmonics of 18-Pulse Diode Rectifier by Series Active Power Filter with LC Coupling. *Energies*. 2020; 13(22):6060.
https://doi.org/10.3390/en13226060

**Chicago/Turabian Style**

Sleszynski, Wojciech, Artur Cichowski, and Piotr Mysiak. 2020. "Suppression of Supply Current Harmonics of 18-Pulse Diode Rectifier by Series Active Power Filter with LC Coupling" *Energies* 13, no. 22: 6060.
https://doi.org/10.3390/en13226060