# Power Flow Control Using Series Voltage Source Converters in Distribution Grids

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## Abstract

**:**

## 1. Introduction

- Bidirectional active power transfer;
- Bidirectional reactive power transfer;
- Voltage imbalance;
- Harmonic isolation;
- Protection scheme.

## 2. Formulation of the Problem

_{cc}= I

_{cc}

_{1}+ I

_{cc}

_{2}) for local protections. Through the interconnected ring (location of the installed converter) the short-circuit currents do not rise like they do in the indicated fault section point. Therefore, in terms of protection, this condition is less damaging to the series converter than at the section point. Regarding the short-circuit behavior, a series converter may be applied with an appropriate protection scheme, as in [31,34].

## 3. Modelling

_{1}and V

_{2}represent the loop interconnections.

_{A}and V

_{B}are the main feeder voltage sources, T

_{A}and T

_{B}are the main step-down transformers, Z

_{L}

_{1}and Z

_{L}

_{2}are the distribution line impedances, Z

_{1}and Z

_{2}are load impedances, L

_{F}

_{1}and L

_{F}

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

_{S}is the coupling transformer, and C

_{dc}is the series converter DC-link capacitance. V

_{1}, V

_{2}, and V

_{T}are the terminal voltages and the converter’s imposed voltages, respectively.

_{TA}and Z

_{TB}), the filter inductances (Z

_{F}

_{1}and Z

_{F}

_{2}), and the coupling transformer equivalent impedances (Z

_{S}

_{1}and Z

_{S}

_{2}).

_{k}

_{1}and i

_{k}

_{2}) as a function of the terminal voltages V

_{1}and V

_{2}and the load impedances (i.e., i

_{k}

_{1}= V

_{1}/Z

_{1}and i

_{k}

_{2}= V

_{2}/Z

_{2}). Additionally, the equivalent transformer models can be added to the line parameters for further simplification. Figure 5 shows the reduced model where Z

_{A}= Z

_{L}

_{1}+ Z

_{TA}, Z

_{B}= Z

_{L}

_{2}+ Z

_{TB}and Z

_{T}= Z

_{S}

_{1}+ Z

_{F}

_{1}+ Z

_{S}

_{1}+ Z

_{F}

_{2}.

_{T}and the behavior of the terminal voltage difference V

_{1}− V

_{2}under load variance disturbances to model the system as seen by the converter.

_{T}is derived in (2) as a function of the imposed voltage of the converter. The voltage drop, the loop impedance, or the power transfer between nodes V

_{1}and V

_{2}should be adjusted electronically by the converter controllers.

_{T}caused by the load variances (i

_{k}

_{1}and i

_{k}

_{2}), as shown in Figure 6.

_{1}− V

_{2}. So, Equation (6) can be derived from the converter branch of Figure 5,

_{1}− V

_{2})/I

_{T}symbolizing the current flowing through loop (I

_{T}) as a function of the terminal voltage difference (V

_{1}− V

_{2}) also considering the load variance as disturbances (Figure 6).

_{T}/V

_{T}and (V

_{1}− V

_{2})/I

_{T}can be derived in (8) and (9) from Equations (4) and (7) (disregarding the load disturbance parameters). Equations (8) and (9) describe the dynamics of the system using the proposed control strategy.

## 4. Control

_{T}current and the voltage difference V

_{1}− V

_{2}as feedback variables. The proposed converter controller is based on the MSRF [36] technique, as presented in Figure 1, and the AC system variables are converted into continuous variables (V

_{d}and V

_{q}for V

_{1}− V

_{2}) and (i

_{d}and i

_{q}for I

_{T}for the feedback, synchronized with V

_{1}(by the MSRF-PLL [36]), to be used in the cascaded PI controllers (for d and q axis).

_{A}and Z

_{B}) are more than two times the impedance of the L filter of the converter and the coupling transformer equivalent impedance Z

_{T}for the proposed small-rated converter. Thus, the control dynamics are strongly dependent on the line parameters. Additionally, the greater the X/R line ratio, the greater the coupling of variables i

_{d}and i

_{q}. In this case, an additional decoupling technique is needed.

_{d}and i

_{q}are the active and reactive currents, respectively. The current control (derived from Figure 1) composed of two P.I. controllers that track the current transfer (i

_{d}and i

_{q}) is compared to the reference values (i

_{dref}and i

_{qref}) generating the control signals (modulation indexes (mi

_{d}and mi

_{q}), which are multiplied by unity vectors sin (ωt) and cos (ωt) that are added to provide the voltage reference signal V

_{pwm}for the unipolar PWM. Furthermore, the outputs from the P.I. controllers (of the current controllers) have saturation limiters (mi

_{qmin}, mi

_{qmax}, mi

_{dmin}, and mi

_{dmax}) defined between +1 and −1. The current reference values also have limiters (i

_{drefmin}, i

_{drefmax}, i

_{qrefmin}, and i

_{qrefmax}) which are defined based on the converter’s power rating.

_{1}− V

_{2}), also obtained using MSRF by generating the current references (i

_{dref}and i

_{qref}) comparing V

_{d}and V

_{q}with the desired reference values V

_{dref}and V

_{qref}.

_{dref}and V

_{qref}. The current control P.I. gains are set to be faster than the voltage control in Figure 7.

## 5. Prototype

## 6. Experimental and Simulation Results

- Tests performed in a three-phase 13.8 kV substation laboratory together with simulation results;
- Field tests performed in an actual 13.8 kV distribution grid.

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

_{A}, L

_{A}, R

_{B}, and L

_{B}), the step-up transformers (T

_{A}and T

_{B}), and the test loads (R, R

_{1}, R

_{2}, C

_{1}, and L

_{2}) with the series VSC interconnecting both ends of the feeders using a coupling transformer T

_{S}. As shown in Figure 1, each phase of the series VSC comprises a three-phase diode rectifier, a DC-link capacitor (C

_{dc}), a low-voltage IGBT-based H-bridge, and an inductive switching filter (L

_{F}

_{1}and L

_{F}

_{2}).

_{S}, i

_{1}, and i

_{2}from Figure 11) and from terminal voltages V

_{1}and V

_{2}. Additionally, the terminal voltage V

_{1}and the transferred current I

_{T}, will be used to show the P&Q transfer between the feeders. The measurements were made using power quality meters (Fluke 435) and the sampling period was every 0.5 s. Additionally, the load transitions were performed every 3 min. Table 1 shows the parameters of the converter, the lines, and the loads used in the lab experimental results.

_{A}, T

_{B}, and T

_{S}are the step-up transformers and the coupling transformer.

#### 6.1. Active Power Behavior

- Initial condition;
- R
_{1}insertion; - R
_{1}removal; - R
_{2}insertion; - R
_{2}removal.

_{1}and V

_{2}) for both the radial (without the series VSC) and meshed configurations (with the series VSC manipulating the power flow). One should note that the series converter improves the voltage profile of the overloaded feeder while it decreases the voltage of the less loaded feeder, which converts the interconnected terminal voltages into an intermediate value via power transfer. It also shows that the main feeder V

_{s}also undergoes smaller voltage variations.

_{1}insertion) the feeder A terminal voltage V

_{1}drops from 7.4 kV to 6.4 kV and the feeder B terminal voltage V

_{2}also drops but slightly less than the first.

_{1}was removed, returning the whole system to the initial voltage conditions. In stage 4, the inserted R

_{2}shows a V

_{2}voltage drop less than in stage 2 because feeder B is stronger than feeder A.

_{2}that returns the terminal voltages to the initial voltage conditions.

_{1}insertion) shows the transferred power from feeder B to feeder A, which consequently improves the terminal voltages by an intermediate value via power transfer. Stage 4 (R

_{2}insertion), shows the power transfer from feeder A to feeder B, also improving the terminal voltages more than in the radial configuration. This shows the power transfer levels achieved from the series converter tracking the best terminal voltage profiles in the interconnected feeders.

_{T}approximately 180° from both terminal voltages, equal the same values after the power transfer, i.e., the flow from feeder B to Feeder A. It shows that the converter always tracks the best terminal voltage profile, consequently alleviating the overloaded feeder.

_{1}was removed.

#### 6.2. Reactive Power Behavior

- Initial condition;
- L
_{2}insertion; - C
_{1}insertion; - C
_{1}removal; - L
_{2}removal.

_{S}also experiences small voltage variations because of the impedance Z

_{S}effect (Figure 11).

_{2}insertion), the terminal voltage V

_{2}drops, and the terminal voltage V

_{1}also drops but slightly less. In stage 3, C

_{1}was inserted, which slightly improved the terminal voltage profile. In stage 4, C

_{1}was removed, returning to the voltage condition in stage 2, with only L

_{2}inserted. Finally, stage 5 showed the initial voltage profile. Figure 18b presents the active and reactive power transfer from the series converter, which shows predominant reactive power manipulation for the same control strategy. The small active power is provided via losses in the line parameters and via the reactive loads, which are also simultaneously manipulated.

_{1}is inserted into feeder A, and inductance L

_{2}is inserted into feeder B, to compensate for the inductive reactive power of both feeders using the series converter.

_{2}and C

_{1}. It also shows current I

_{T}-90° from the equalized terminal voltages.

_{1}was inserted (stage 3), the provided reactive power was reduced in both feeders. Consequently, this results in a reduced reactive power requirement from the main source V

_{S}(Figure 11) with the converter operation, ZS and V2chuit Boardbances in damentals resulting in technical loss reductions when both radial feeders are interconnected using the series converter power flow manipulation.

_{1}in feeder A, compensates for the reactive inductance present in feeder B, provided by L

_{2}with the same control strategy that takes decisions looking at the behavior of the terminal voltages.

#### 6.3. Field Test

_{dref}and i

_{qref}). Figure 24 presents the P and Q measurements during the field test.

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

SSSC | Static Synchronous Series Compensator |

VSC | Voltage Source Converter |

FACTS | Flexible AC Transmission Systems |

DG | Distributed Generation |

MSRF | Modified Synchronous Reference Frame |

RACDS | Resilient AC Distribution Systems |

DSP | Digital Signal Processor |

DVR | Dynamic Voltage Restorer |

PST | Phase Shift Transformer |

IGBT | Insulated Gate Bipolar Transistor |

UPFC | Unified Power Flow Controller |

CD-PAR | Compact Dynamic Phase Angle Regulator |

DSSSC | Distribution Static Synchronous Series Compensator |

CNT | Controllable Network Transformer |

BTB | Back-to-Back |

SCADA | Supervisory Control and Data Acquisition |

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**Figure 12.**Behavior of the phase-to-ground terminal voltages and the power flow; (

**a**) V

_{1}and V

_{2}; (

**b**) transferred P and Q.

**Figure 13.**Simulation results with the series VSC operation; (

**a**) V

_{1}and V

_{2}; (

**b**) transferred P and Q.

**Figure 14.**Phasors before and after power flow manipulation; (

**a**) R

_{1}insertion stage–without the converter operation; (

**b**) R

_{1}insertion stage–with the converter operation.

**Figure 15.**Active power delivered by each feeder; (

**a**) P provided from feeder A; (

**b**) P provided from feeder B.

**Figure 16.**Simulation results for active and reactive power delivered by each feeder; (

**a**) P and Q provided from feeder A; (

**b**) P and Q provided from feeder B.

**Figure 18.**Phase-to-ground terminal voltages behavior and power flow; (

**a**) V

_{1}and V

_{2}; (

**b**) transferred P and Q.

**Figure 19.**Simulation results of phase-to-ground terminal voltages behavior and the power flow with the converter operation; (

**a**) V

_{1}and V

_{2}; (

**b**) transferred P and Q.

**Figure 20.**With and without converter operation voltage analysis; (

**a**) C

_{1}insertion stage–without the converter operation; (

**b**) C

_{1}insertion stage–with converter operation.

**Figure 21.**Reactive power delivered by each feeder; (

**a**) Q provided by feeder A; (

**b**) Q provided by feeder B.

**Figure 22.**Simulation results for P and Q delivered by each feeder; (

**a**) P and Q provided by feeder A; (

**b**) P and Q provided by feeder B.

Feeders | Three-Phase Loads | Converters |
---|---|---|

R_{A} = 0.6 Ω | R_{1} = 12 Ω | L_{F}_{1} = 250 µH |

L_{A} = 530 µH | R_{2} = 12 Ω | L_{F}_{2} = 250 µH |

R_{B} = 0.5 Ω | C_{1} = 7 kVAr | C_{dc} = 6666 µF |

L_{B} = 530 µH | L_{2} = 12 kVAr | |

R = 12 kW |

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_{S} | 37.5 kVA 600:1800 V | 5.3% | 0.06 | 0.26 | 0.54 | 2.34 |

Current Control | Voltage Control | ||
---|---|---|---|

Kp_{d} = 10 | Kp_{q} = 0.8 | Kp_{vd} = −0.000003 | Kp_{vq} = −0.000001 |

Ki_{d} = 100 | ki_{q} = 120 | Ki_{vd} = 180 | ki_{vq} = 800 |

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## Share and Cite

**MDPI and ACS Style**

Pinheiro, G.G.; da Silva, C.H.; Guimarães, B.P.B.; Gonzatti, R.B.; Pereira, R.R.; Sant’Ana, W.C.; Lambert-Torres, G.; Santana-Filho, J.
Power Flow Control Using Series Voltage Source Converters in Distribution Grids. *Energies* **2022**, *15*, 3337.
https://doi.org/10.3390/en15093337

**AMA Style**

Pinheiro GG, da Silva CH, Guimarães BPB, Gonzatti RB, Pereira RR, Sant’Ana WC, Lambert-Torres G, Santana-Filho J.
Power Flow Control Using Series Voltage Source Converters in Distribution Grids. *Energies*. 2022; 15(9):3337.
https://doi.org/10.3390/en15093337

**Chicago/Turabian Style**

Pinheiro, Guilherme Gonçalves, Carlos Henrique da Silva, Bruno P. B. Guimarães, Robson Bauwelz Gonzatti, Rondineli Rodrigues Pereira, Wilson Cesar Sant’Ana, Germano Lambert-Torres, and Joselino Santana-Filho.
2022. "Power Flow Control Using Series Voltage Source Converters in Distribution Grids" *Energies* 15, no. 9: 3337.
https://doi.org/10.3390/en15093337