# Analysis of Traditional and Alternative Methods for Solving Voltage Problems in Low Voltage Grids: An Estonian Case Study

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## Abstract

**:**

## 1. Introduction

## 2. Techno-Economic Analysis of Classical and Alternative Methods to Solve Voltage Problems

- physical improvement of line properties, to increase transmission capacity and decrease impedance, or
- adding voltage control devices (i.e., automatic on-load tap changers, voltage stabilisers, reactive power compensation, etc.).

#### 2.1. Power Line Renovation

- Medium voltage insulated overhead contact line (MV OHL) with a life expectancy of 40 years;
- Low voltage bare wire overhead contact line (LV OHL) with life expectancy of 20 years; and
- Low voltage uninsulated messenger cable system (LV CS) with a life expectancy of 35 years.

#### 2.2. Voltage Stabilisers Compared to Power Line Renovation

#### 2.3. Uninterruptible Power Supply and Supply Interruption Costs

## 3. Classification and Description of Low Voltage Feeders for Simulations

#### 3.1. Group 1 Feeders

^{2}) (Figure 5). The substation and power lines were built in the 1980s. The total yearly consumption of the F4 feeder is approximately 78,500 kWh, and the feeder has six CPs.

#### 3.2. Group 2 Feeders

^{2}). The substation and power lines were built in the 1980s. The total yearly consumption of the F2 feeder is approximately 17,200 kWh, and the feeder has four CPs.

#### 3.3. Group 3 Feeders

^{2}) (Figure 7). The substation and power lines were built in 1977. The total yearly consumption of the F3 feeder is approximately 12,200 kWh, and the feeder has two CPs.

## 4. Voltage Quality Issues Discovered in the Sample Low Voltage Feeders

#### 4.1. Object 1 Voltage Quality

_{LXN}is the phase X (representing either one, two or three) short-circuit impedance; ΔU

_{LXN}is the voltage change for the corresponding phase between no-load and full load conditions; and ΔI

_{LXN}is the current change for the corresponding phase between no-load and full load conditions. Results of the estimation are summarised in Table 1.

- voltage unbalance describes the relation of negative sequence voltage to positive sequence voltage, mainly affecting three phase motors by increasing their losses; and
- flicker is caused by systematic voltage waveform variations due to random voltage changes, causing perceivable light output variation in luminaries [36].

_{ST}in a 10-min interval, and long-term flicker perceptibility P

_{LT}in a 120-min interval. However, only the long-term flicker perceptibility is standardised. According to [8], in normal conditions, flicker perceptibility may not exceed the value P

_{LT}= 1 in 95% of measured instances in a week. Long-term flicker perceptibility PLT at Object 1 was higher during daytime and lower at nights, while the short-term flicker perceptibility even reached as high as 6.7.

#### 4.2. Object 2 Voltage Quality

_{LT}values also exceeded the EN 50160 standard values, and the results are summarised in Table 4.

#### 4.3. Object 3 Voltage Quality

## 5. Description of Voltage Quality Improvement Devices for Simulations

- short-term supply interruptions (up to 60 s);
- flicker;
- voltage dips; and
- voltage unbalance in the case of three-phase feeders.

- dynamic voltage restorer (DVR), that are suitable for feeders with voltage dip and flicker problems;
- load balancing transformer (LBT) should be used in feeders with voltage unbalance issues, and;
- an UPS device is appropriate for feeders with various voltage problems including short-term supply interruptions.

## 6. Simulation Results

#### 6.1. Grid 1

#### 6.2. Grid 2

#### 6.3. Grid 3

## 7. Recommendations for Solving Voltage Problems

- feeder reconstruction plans;
- condition and lifetime expectation of existing substation and its components;
- type, length, and life expectance of power lines;
- long-term load forecasts and types of loads (three-phase, unbalanced, electronic, etc.); and
- existing and future PQ problems.

- for network segments with feeder lengths up to 3 km and where the long-term load forecast is decreasing, installing a DVR should be considered;
- for network segments with feeder lengths of over 3 km and where the long-term load forecast is decreasing, an off-grid solution should be considered;
- for network segments with feeder lengths up to 1.5 km and where the long-term load forecast is relatively constant, the replacement of existing lines with LV CS should be considered; and
- for network segments with feeder lengths of over 1.5 km and where the long-term load forecast is increasing, the replacement of existing lines with MV OHL should be considered.

- for network segments with feeder lengths not exceeding 2 km and where the long-term load forecast remains unchanged, a voltage regulating system (VRS) should be considered in the case the total cost over the full lifetime does not exceed the difference between the total costs of the MV OHL and the LV CS;
- for network segments with feeder lengths over 3 km and where the long-term load forecast is decreasing, an off-grid solution should be considered; and
- for network segments with feeder lengths over 2 km and where the long-term forecast remains relatively constant, the replacement of the existing lines with MV OHL should be considered.

## 8. Conclusions and Future Work

_{n}.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Figure A1.**Method for determining the solution at the end of line lifetime or to solve voltage problems.

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**Figure 1.**Difference between the total costs of the MV OHL and the LV OHL (positive cost if LV OHL is more feasible, and negative cost if MV OHL is more feasible).

**Figure 2.**Difference between the total costs of the MV OHL and the LV CS (positive cost if LV CS is more feasible, negative cost if MV OHL is more feasible).

**Figure 3.**Difference between the total costs of the LV CS and the LV OHL (positive cost if LV OHL is more feasible, negative cost if LV CS is more feasible).

**Figure 5.**DIgSILENT PowerFactory single-line diagram model representation of Grid 1 from Group 1, representing a typical low voltage feeder with very small one phase short-circuit impedances and long distances to consumers.

**Figure 6.**DIgSILENT PowerFactory single-line diagram model representation of Grid 2 from Group 2, representing a typical low voltage feeder with relatively high one phase short-circuit impedances and shortest distances to consumers.

**Figure 7.**DIgSILENT PowerFactory single-line diagram model representation of Grid 3 from Group 3, representing the most common (40% of all low voltage feeders) type of low voltage feeder in distribution grids.

**Figure 8.**Voltage measurements according to standard EN 50160 at Object 1 (three phases, average of 10-min intervals).

**Figure 9.**Flicker values for Object 1 in phase L1, according to standard EN 50160–PST in 10-min interval and PLT in 2-h average intervals (allowed limit <1.0 95% of the time).

**Figure 10.**Phase L1 voltage–current curve based on measurements with polynomial function describing the voltage drop dependency from the capacity of the load in Object 1.

**Figure 11.**Voltage measurements according to standard EN 50160 at Object 2 (three phases, average of 10-min intervals).

**Figure 12.**Flicker values for Object 2 in phase L1, according to standard EN 50160–PST in 10-min intervals and PLT in 2-h average intervals (allowed limit <1.0 95% of the time).

**Figure 13.**Phase L1 voltage–current curve with polynomial function describing the voltage drop dependency from the capacity of the load based on measurements in Object 2.

**Figure 14.**Voltage measurements according to standard EN 50160 at Object 1 (1 phase, average of 10-min intervals).

**Figure 15.**Flicker values for Object 3 in phase L1, according to standard EN 50160–PST in 10-min intervals and PLT in 2-h average intervals (allowed limit <1.0 95% of the time).

**Figure 16.**Phase L1 voltage–current curve with polynomial function describing the voltage drop dependency from the capacity of the load based on measurements in Object 3.

**Figure 18.**Methodology for deriving one-second data for simulations in other CPs (PQ–power quality).

Phase L1, (Ω) | Phase L2, (Ω) | Phase L2, (Ω) |
---|---|---|

3.2 | 2.8 | 4.1 |

Parameter | EN 50160 Recommendations | Min | Max |
---|---|---|---|

Unbalance | 2% | 0.7% | 3.3% |

P_{LT} | 1 | 0.8 | 3.5 |

Phase L1, (Ω) | Phase L2, (Ω) | Phase L2, (Ω) |
---|---|---|

4.4 | 3.0 | 3.8 |

Parameter | EN 50160 Recommendations | Min | Max |
---|---|---|---|

Unbalance | 2% | 0.5% | 3.9% |

P_{LT} | 1 | 0.3 | 2.5 |

Device Placement | Minimum Relative Voltage at Different Phases of Connection Points, p.u. | ||||||||
---|---|---|---|---|---|---|---|---|---|

CP2 | CP4 | Object1 | |||||||

L1 | L2 | L3 | L1 | L2 | L3 | L1 | L2 | L3 | |

Base Case | 0.890 | 0.855 | 0.731 | 0.856 | 0.863 | 0.725 | 0.854 | 0.861 | 0.722 |

DVR at CP1 | 0.917 | 0.963 | 0.950 | 0.927 | 0.971 | 0.960 | 0.920 | 0.964 | 0.952 |

UPS at CP3 | 0.935 | 0.894 | 0.820 | 0.984 | 0.990 | 0.980 | 0.975 | 0.983 | 0.971 |

LBT at Object 1 | 0.864 | 0.908 | 0.896 | 0.977 | 0.914 | 0.899 | 0.871 | 0.909 | 0.895 |

Device Placement | Minimum Relative Voltage at Different Phases of Connection Points, p.u. | |||||
---|---|---|---|---|---|---|

CP2 | Object 2 | |||||

L1 | L2 | L3 | L1 | L2 | L3 | |

Initial | 0.910 | 0.909 | 0.895 | 0.854 | 0.853 | 0.827 |

DVR at IP2 | 0.973 | 0.974 | 0.974 | 0.957 | 0.962 | 0.956 |

UPS at Object 2 | 0.981 | 0.980 | 0.975 | 0.999 | 0.999 | 0.999 |

LBT at Object 2 | 0.972 | 0.974 | 0.964 | 0.970 | 0.970 | 0.960 |

Device Placement | Minimum Relative Voltage at Different Connection Points, p.u. | |
---|---|---|

CP1 | Object 3 | |

Initial | 0.909 | 0.895 |

DVR at CP1 | 0.974 | 0.974 |

UPS at CP1 | 0.980 | 0.975 |

UPS at IP1 | 0.974 | 0.964 |

Long-Term Load Forecast | Existing Line Type | Recommended Solution Based on Distance, m | |||
---|---|---|---|---|---|

0…1500 | 1501…2000 | 2001…3000 | >3000 | ||

Decreasing | LV OHL | VRS | VRS | VRS | Off-grid |

LV CS | VRS | VRS | VRS | Off-grid | |

Standing/unchanged | LV OHL | LV CS | MV OHL | MV OHL | MV OHL |

LV CS | Other | Other | MV OHL | MV OHL | |

Growing | LV OHL | LV CS | MV OHL | MV OHL | MV OHL |

LV CS | Other | Other | MV OHL | MV OHL |

Description | Criteria | Solution | Location |
---|---|---|---|

Voltage unbalance in phases (asymmetry) | Asymmetry balancing device/transformer | Near object | |

Voltage dip/swell | Within ±20–40%Un, | Electronic or electromagnetic voltage restorer/stabiliser/ booster or dynamic voltage restorer | Near object or weighted centre of load |

Supply interruption, strong voltage fluctuations, transient overvoltage, frequency problems, etc. | >±40%Un | On-line UPS, dynamic voltage restorers with storage | Near object or weighted centre of load |

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**MDPI and ACS Style**

Rosin, A.; Drovtar, I.; Mõlder, H.; Haabel, K.; Astapov, V.; Vinnal, T.; Korõtko, T.
Analysis of Traditional and Alternative Methods for Solving Voltage Problems in Low Voltage Grids: An Estonian Case Study. *Energies* **2022**, *15*, 1104.
https://doi.org/10.3390/en15031104

**AMA Style**

Rosin A, Drovtar I, Mõlder H, Haabel K, Astapov V, Vinnal T, Korõtko T.
Analysis of Traditional and Alternative Methods for Solving Voltage Problems in Low Voltage Grids: An Estonian Case Study. *Energies*. 2022; 15(3):1104.
https://doi.org/10.3390/en15031104

**Chicago/Turabian Style**

Rosin, Argo, Imre Drovtar, Heigo Mõlder, Kaija Haabel, Victor Astapov, Toomas Vinnal, and Tarmo Korõtko.
2022. "Analysis of Traditional and Alternative Methods for Solving Voltage Problems in Low Voltage Grids: An Estonian Case Study" *Energies* 15, no. 3: 1104.
https://doi.org/10.3390/en15031104