# Comparison of Control Techniques for Harmonic Isolation in Series VSC-Based Power Flow Controller in Distribution Grids

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Series Compensator Description

## 3. Fundamental Frequency and Harmonic Control

_{A}and V

_{B}represent the power grid HV voltage sources, T

_{A}and T

_{B}are the substation transformers, Z

_{L}

_{1}and Z

_{L}

_{2}are the distribution feeder impedances, Z

_{1}and Z

_{2}are the lumped load impedances, L

_{F}

_{1}and L

_{F}

_{2}are the inductances of the converter switching filter, T

_{S}is the coupling transformer and C

_{dc}is the converter dc-link capacitor. V

_{1}and V

_{2}are the feeder voltages at the connection point and V

_{T}is the converter output voltage.

_{T}flowing between the two feeders while keeping the minimum terminal voltage difference V

_{1}–V

_{2}. However, this should be carried out only for the fundamental frequency so that the distortion present in one feeder does not pollute the adjacent feeder. To perform this task, the main control loop is separated in two parts: one manipulates the fundamental component of the transferred current and the second performs the blocking of harmonic voltages.

#### 3.1. Synchronous Reference Frame

_{d}and i

_{q}(or v

_{d}and v

_{q}), which can be decomposed into continuous and alternating components according to (1) and (2):

_{d}and i

_{q}, as in (3) and (4), without phase-shift errors.

#### Modified Synchronous Reference Frame

_{d}and i

_{q}in the MSRF have half the amplitude of the original signals in the abc frame, so a gain of two must be used in the MSRF loop, as shown in Figure 4.

#### 3.2. MSRF-Based Controller

_{T}). Additionally, for a higher X/R line ratio, there will be a higher coupling between i

_{d}and i

_{q}variables when an additional decoupling technique might be required.

_{d}corresponds to the active component of the fundamental current and i

_{q}to the reactive component. This loop compares the actual transferred current (i

_{d}and i

_{q}) to their reference values (i

_{dref}and i

_{qref}), generating the modulation indexes mi

_{d}and mi

_{q}. These modulation indexes are multiplied by unit vectors sin(ꞷt) and cos(ꞷt) and then summed to generate the PWM reference signal (V

_{pwm}).

_{T}using a high-pass filter in the MSRF and feeds this harmonic content back to the converter voltage reference signal V

_{pwm}by means of a proportional gain K. This provides a very high impedance for the harmonics, preventing harmonics from flowing from one distribution feeder to the other.

#### 3.3. Proportional Resonant Based Controller

_{p}is the proportional gain, k

_{r}is the resonant term gain and ω is the resonance frequency. Due to the high gain at the resonance frequency ω, this controller can track a sinusoidal reference at this frequency without steady-state error. This characteristic is similar to that presented by a PI controller with a dc reference.

_{c}.

_{0}is the filter tuning frequency of (60 Hz) and ω

_{c}is the frequency that defines the controller bandwidth. Several resonant controllers can be used in parallel, as in (7), to provide compensation of multiple harmonics at the same time. The main harmonics present in the distribution networks are the low order odd ones, so resonant terms were used for the third, fifth, seventh, ninth and eleventh harmonics.

## 4. Simulations

^{®}/Simulink software (version 2019b, licensed for UNIFEI at Itajuba, Brazil).

- (a)
- The simulation is started with the series converter imposing zero voltage and with only linear loads turned on.
- (b)
- At 0.05 s, one of the non-linear loads is inserted into the system.
- (c)
- At 0.15 s, the series converter begins to operate in the harmonic block mode.

#### 4.1. Without Harmonic Isolation

_{a}) with a THD of 99.89%.

#### 4.2. Harmonic Isolation with vs. Type of Load

_{a}and the converter voltage (V

_{SS}

_{1}). One can clearly see the reduction in the distortion of the transferred current at 0.05 s when the converter starts blocking the harmonics.

_{a}after harmonic isolation, with a THD of 4.01%, a value considerably lower than previously presented in Figure 8 without compensation.

_{a}and V

_{2a}, respectively. V

_{a}has a THD of 3.46%, a value greater than shown in Figure 7, which shows the terminal voltages before harmonic isolation. However, V

_{2a}has a THD of 0.49 because the non-load is connected to Feeder 1, so Feeder 2 is practically unaffected by the harmonic distortion of the other feeder, demonstrated by the ability of the series converter to perform harmonic isolation both with MSRF and PR controllers.

#### 4.3. Harmonic Isolation with CS Type of Load

_{a}and the converter voltage (V

_{SS}

_{1}). The sinusoidal waveform of the transferred current can be seen at 0.05 s when the converter starts blocking the harmonics.

## 5. Prototype

## 6. Experimental Results

_{A}and L

_{A}) connected at the low voltage side, two step-up transformers (220 V:13.8 kV), a voltage source type non-linear load and the series power converters interconnecting the feeders through a coupling transformer T

_{1}. Measurements were performed with three Fluke 435 power quality meters connected at the points indicated in Figure 24.

_{F}

_{1}and L

_{F}

_{2}), the resistance and inductance of the lines (R

_{A}and L

_{A}) and the loads used in the lab experimental results. The data for the transformers used in the test setup are presented in Table 2, where T

_{A}and T

_{B}are the source step-up transformers and T

_{1}is the coupling transformer. Table 3 shows the controller gains of the current and voltage control loops, at fundamental frequency, and the parameters of the harmonic isolation strategies.

- With radial topology (switch k1 in Figure 24 is open).
- In mesh with the converter transferring power from Feeder 2 to Feeder 1, without harmonic isolation.
- In mesh with the converter transferring power from Feeder 2 to Feeder 1 and performing harmonic isolation.

_{dref}and i

_{qref}) were defined as i

_{dref}= 0.15 A and i

_{qref}= 0 A, without changes during all of experimental tests.

#### 6.1. Results of SRF-Based Harmonic Isolation Algorithm

_{1}is shown in Figure 25a while that of voltage V

_{2}is shown in Figure 25b. Upon comparing both THDs, it can be verified that voltage V

_{1}is more distorted than V

_{2}.

_{1}and the current transferred by the equipment. Note that the transferred current is not purely sinusoidal, which can be proved by the harmonic spectrum shown in Figure 26b with a THD of 10.7%.

_{1}and Figure 29b that of voltage V

_{2}. Comparing the two figures, the THD of V

_{1}is higher, with 3.0%, while that of V

_{2}is lower, with 2.2%. These THD values demonstrate that most of the distortion from Feeder 1 is kept in Feeder 1 and does not propagate as much to Feeder 2 as in the case where there is no harmonic isolation.

_{dref}= 0 and i

_{qref}= 0) with the non-linear load still connected to Feeder 1. Figure 30a shows the terminal voltage and loop current waveforms without harmonic isolation. Due to the voltage distortion difference, there is a harmonic current flow between the two feeders even with the current reference set to zero. Figure 30b shows the same waveforms with harmonic mitigation enabled. One can see that the harmonic current transferred is reduced from Figure 30a to Figure 30b; however, there are still some minor components that are not blocked by the SRF-based algorithm.

#### 6.2. Results of PR-Based Harmonic Isolation Algorithm

_{1}(Figure 31a) has a more distorted waveform than Feeder 2 voltage V

_{2}(Figure 31b), since the load is connected to Feeder 1. The harmonic spectrum of V

_{1}is shown in Figure 32a while that of voltage V

_{2}is shown in Figure 32b. Upon comparing the two THDs, it can be verified that voltage V

_{1}is more distorted than V

_{2}.

_{1}and the current transferred by the equipment. Note that the transferred current is not purely sinusoidal, which can be proved by the harmonic spectrum shown in Figure 33b with a THD of 12.8%. In Figure 34 the voltage harmonic spectrum of the two feeders is presented, showing that the greater harmonic distortion present in the voltage of Feeder 1 (previously with THD = 6.6%) is propagated to Feeder 2 (previously with THD = 1.6%), resulting in a THD of 2.9% at both terminal voltages.

_{1}and Figure 35b that of voltage V

_{2}. Comparing the two figures, the THD of V

_{1}is higher, with 5.3%, while that of V

_{2}is lower, with 1.9%. These values are very close to Case 1, in which the feeders were not interconnected. Observing the current transferred between the feeders, as shown in Figure 36, it can be seen that it is composed almost entirely of the fundamental component (THD = 4%, in Figure 36b), which was previously 12.8% in Figure 33b.

_{dref}= 0 and i

_{qref}= 0), with the non-linear load still connected to Feeder 1. Figure 37a shows the terminal voltage and loop current waveforms without harmonic isolation. Due to the voltage distortion difference, there is a harmonic current flow between the two feeders even with the current reference set to zero. Figure 37b shows the same waveforms with harmonic mitigation enabled. It can be seen that the harmonic current transferred is reduced from Figure 37a to Figure 37b, and that the remaining harmonic content is even lower than what was obtained with the SRF-based algorithm shown in Figure 30b.

## 7. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

ANF | Adaptive Notch Filter |

ANN | Artificial Neural Network |

CT | Current Transformer |

CS | Current Source |

DSP | Digital Signal Processor |

DVR | Dynamic Voltage Restorer |

IGBT | Insulated Gate Bipolar Transistor |

LPF | Low-pass Filter |

MSRF | Modified Synchronous Reference Frame |

MV | Medium Voltage |

PAPF | Parallel Active Power Filter |

PI | Proportional Integral |

PR | Proportional Resonant |

RACDS | Resilient AC Distribution Systems |

SAPF | Shunt Active Power Filter |

SRF | Synchronous Reference Frame |

VSC | Voltage Source Converter |

VS | Voltage Source |

VT | Voltage Transformer |

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**Figure 2.**Simplified model of two distribution feeders interconnected by the series power flow controller.

**Figure 4.**Modular algorithm for power flow control and harmonic isolation based on modified synchronous reference frame.

**Figure 5.**Modular Algorithm for power flow control based on modified synchronous reference frame and harmonic isolation based on proportional resonant control.

**Figure 7.**Terminal voltage of both feeders (V

_{a}and V

_{2a}) with vs. type of load connected to Feeder 1 and without harmonic isolation.

**Figure 9.**Terminal voltage of both feeders (V

_{a}and V

_{2a}) with CS type of load and without harmonic isolation.

**Figure 11.**Simulated waveforms of loop current (I

_{a}) and the converter voltage (V

_{SS}

_{1}) with vs. type of load.

**Figure 13.**Harmonic spectrum of Feeder 1 terminal voltage (V

_{a}) with vs. type of load and harmonic isolation.

**Figure 14.**Harmonic spectrum of Feeder 2 terminal voltage ranch 1 (V

_{2a}) with vs. type of load and harmonic isolation.

**Figure 15.**Simulated waveforms of loop current (I

_{a}) and the converter voltage (V

_{SS}

_{1}) with CS type of load.

**Figure 16.**Loop current (I

_{a}) harmonic spectrum with CS type of load and harmonic isolation using SRF.

**Figure 17.**Loop current (I

_{a}) harmonic spectrum with CS type of load and harmonic isolation using PR controller.

**Figure 18.**Harmonic spectrum of Feeder 1 terminal voltage (V

_{a}) with CS type of load and harmonic isolation using SRF.

**Figure 19.**Harmonic spectrum of Feeder 1 terminal voltage (V

_{a}) with CS type of load and harmonic isolation using PR controller.

**Figure 20.**Harmonic spectrum of Feeder 2 terminal voltage (V

_{2a}) with CS type of load and harmonic isolation using SRF.

**Figure 21.**Harmonic spectrum of Feeder 2 terminal voltage (V

_{2a}) with CS type of load and harmonic isolation using PR controller.

**Figure 25.**Voltage harmonic spectrums with radial grid topology and the load connected to Feeder 1. (

**a**) Terminal voltage of Feeder 1 (V

_{1}) and (

**b**) Terminal voltage of Feeder 2 (V

_{2}).

**Figure 26.**Terminal voltage of Feeder 1 and loop current with grid in mesh topology before harmonic isolation (

**a**) waveforms and (

**b**) current harmonic spectrum.

**Figure 27.**Harmonic spectra of the terminal voltages in mesh topology before harmonic isolation with SRF-based algorithm. (

**a**) Feeder 1 voltage and (

**b**) Feeder 2 voltage.

**Figure 28.**Waveforms of the terminal voltage of Feeder 1 and loop current with grid in mesh topology after harmonic isolation with SRF.

**Figure 29.**Harmonic spectra of the terminal voltages in mesh topology after harmonic isolation with SRF-based algorithm. (

**a**) Feeder 1 voltage and (

**b**) Feeder 2 voltage.

**Figure 30.**Terminal voltage of Feeder 1 and loop current with grid in mesh topology and (i

_{dref}= 0 and i

_{qref}= 0) (

**a**) without harmonic isolation (

**b**) with harmonic isolation using SRF-based algorithm.

**Figure 31.**Voltage waveforms with radial grid topology and the load connected to Feeder 1. (

**a**) Terminal voltage of Feeder 1 (V

_{1}) and (

**b**) Terminal voltage of Feeder 2 (V

_{2}).

**Figure 32.**Voltage harmonic spectrums with radial grid topology and the load connected to Feeder 1. (

**a**) Terminal voltage of Feeder 1 (V

_{1}) and (

**b**) Terminal voltage of Feeder 2 (V

_{2}).

**Figure 33.**(

**a**) Waveforms of the terminal voltage of Feeder 1 (V

_{1}) and loop current with grid in mesh topology after harmonic isolation with PR. (

**b**) Loop current spectrum.

**Figure 34.**Harmonic spectra of the terminal voltages in mesh topology before harmonic isolation with PR-based algorithm. (

**a**) Feeder 1 voltage and (

**b**) Feeder 2 voltage.

**Figure 35.**Harmonic spectra of the terminal voltages in mesh topology after harmonic isolation with PR-based algorithm. (

**a**) Feeder 1 voltage and (

**b**) Feeder 2 voltage.

**Figure 36.**Terminal voltage of Feeder 1 and loop current in mesh topology after harmonic isolation, (

**a**) waveforms and (

**b**) current harmonic spectrum.

**Figure 37.**Terminal voltage of Feeder 1 and loop current with grid in mesh topology and (i

_{dref}= 0 and i

_{qref}= 0) (

**a**) without harmonic isolation (

**b**) with harmonic isolation using PR-based algorithm.

Feeders | Non-Linear Load | Converters |
---|---|---|

R_{A} = 0.6 ΩL _{A} = 530 µH | Single-phase diode rectifier R = 10.67 Ω | L_{F}_{1} = 250 µHL _{F}_{2} = 250 µH |

C = 3333 µF |

Transformer Data | Z% | r_{1} | x_{1} | r_{2} | x_{2} | ||
---|---|---|---|---|---|---|---|

T_{A}, T_{B} | 66.0 kVA | 0.22:13.8 kV | 6% | 0.013 | 0.043 | 51.15 | 168.6 |

T_{1} | 37.5 kVA | 600:1800 V | 5.3% | 0.06 | 0.26 | 0.54 | 2.34 |

Fundamental Frequency Control Loops | ||||

Current controller gains | ||||

Kp_{d} = 10 | Ki_{d} = 100 | Kp_{q} = 0.8 | Ki_{q} = 120 | |

Harmonic Frequency Control Loops | ||||

SRF-based Control | PR-based Control | |||

K = −0.034 | Kp = 50 | |||

Kr_{h}_{3} = 9000 | Kr_{h}_{5} = 16,000 | Kr_{h}_{7} = 12,000 | ||

Kr_{h}_{9} = 7000 | Kr_{h}_{11} = 7000 |

Simulation Results | ||
---|---|---|

VS Type Non-Linear Load | Feeder 1THDv (%) | Feeder 2THDv (%) |

Without harmonic isolation | 2.28 | 2.28 |

With harmonic isolation—PR and SRF-based control | 3.46 | 0.49 |

CS type non-linear load | ||

Without harmonic isolation | 1.23 | 1.23 |

With harmonic isolation—SRF-based control | 0.49 | 3.46 |

With harmonic isolation—PR-based control | 0.53 | 2.05 |

Experimental Results: with vs. Type Non-Linear Load | ||

SRF-Based Control | Feeder 1THDv (%) | Feeder 2THDv (%) |

Radial | 4.7 | 1.6 |

Meshed without harmonic isolation | 2.2 | 2.2 |

Meshed with harmonic isolation | 3.0 | 2.2 |

PR-based Control | ||

Radial | 6.6 | 1.6 |

Meshed without harmonic isolation | 2.9 | 2.8 |

Meshed with harmonic isolation | 5.3 | 1.9 |

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## Share and Cite

**MDPI and ACS Style**

Pinheiro, G.G.; Gonzatti, R.B.; da Silva, C.H.; Pereira, R.R.; Guimarães, B.P.B.; Foster, J.G.L.; Lambert-Torres, G.; da Silva, K.S.; Santana-Filho, J.
Comparison of Control Techniques for Harmonic Isolation in Series VSC-Based Power Flow Controller in Distribution Grids. *Energies* **2023**, *16*, 2729.
https://doi.org/10.3390/en16062729

**AMA Style**

Pinheiro GG, Gonzatti RB, da Silva CH, Pereira RR, Guimarães BPB, Foster JGL, Lambert-Torres G, da Silva KS, Santana-Filho J.
Comparison of Control Techniques for Harmonic Isolation in Series VSC-Based Power Flow Controller in Distribution Grids. *Energies*. 2023; 16(6):2729.
https://doi.org/10.3390/en16062729

**Chicago/Turabian Style**

Pinheiro, Guilherme Gonçalves, Robson Bauwelz Gonzatti, Carlos Henrique da Silva, Rondineli Rodrigues Pereira, Bruno P. Braga Guimarães, João Gabriel Luppi Foster, Germano Lambert-Torres, Kleverson Sinezio da Silva, and Joselino Santana-Filho.
2023. "Comparison of Control Techniques for Harmonic Isolation in Series VSC-Based Power Flow Controller in Distribution Grids" *Energies* 16, no. 6: 2729.
https://doi.org/10.3390/en16062729