# Single-Phase PV Power Injection Limit due to Voltage Unbalances Applied to an Urban Reference Network Using Real-Time Simulation

## Abstract

**:**

## 1. Introduction

_{Unb}) and voltage violations on electrical distribution feeders [2,3,4]. When the power generated from distributed resources exceeds the load on a certain feeder or section of it, voltages may rise on that section. Moreover, distributed generation coupled with the existing load demand may cause congestions, feeder currents to approach, and even exceed rated currents. Furthermore, single-phase connections may contribute to a voltage increase in one phase, but to a decrease in another, making the system potentially unbalanced. Such an unbalance degrades the performance and shortens the life of certain equipment, such as motors, and may cause current unbalance, which leads to torque pulsations, increased vibrations, mechanical stresses, and increased losses, resulting in lower efficiency and winding overheating.

## 2. PV Systems and LV Network Context in Europe

#### 2.1. Legislation in Europe

_{PV}), divided by the total contracted power (P

_{C}) in the considered low-voltage network or consumer. This ratio can be found in some European Member States’ legislation or DSO technical recommendations.

#### 2.2. Voltage Unbalance from PV Penetration in LV Networks

#### 2.3. European Distribution Reference Networks

#### 2.3.1. Urban Low Voltage Network

## 3. Materials and Methods

_{0}) in µF/km, between an insulated conductor within a concentric sheath and the sheath was calculated using Equations (5) and (6) for Bus 2 (cable 95 mm

^{2}) and Bus 6 (cables 240 mm

^{2}). The thickness of insulation considered for the cables used was 1.6 mm and 2.2 mm, respectively [34]. “D” refers to the diameter (mm) over insulation, and “d” is the conductor diameter (mm). ${\mathsf{\epsilon}}_{r}$ is the relative permittivity of the insulation material, which considering cross-linked polyethylene (XLPE) is 2.3.

_{0}is the zero sequence capacitances per unit length. Equation (6) converts capacitance-per-kilometre to total ohms-per-phase reactance ${\mathrm{X}}_{{C}_{0}}$, where one is the length in kilometres: The zero sequence shunt capacitance reactance is hence given by:

_{Unb}was observed and the limits were recorded. The same was done with the minimum load scenarios. After the worst situations (buses with higher V

_{Unb}), were identified, the balanced model was run, and the maximum power injections were estimated.

## 4. Results and Discussion

_{Unb}or ≤3% (in some locations). Figure 4 shows the voltage unbalance for four different scenarios in an unbalanced situation (all PV connected to the same phase) with maximum load. As expected, without any PV generation, the system shows very low voltage unbalance that is very close to zero. Then, by inputting a generation of 1.7 kW per bus, the unbalance increases to approximately 1.00%.

_{Unb}in all of the buses when compared to the minimum load case, as can be observed in Figure 5 (bottom two curves). This can be explained by there being a voltage rise in all of the phases, and the absolute value of the difference between them being higher than when the higher load case occurs due to the counter phenomena by the loads, which makes the voltage drop. On the contrary, when all of the PVs are connected in the same phase, the case of when higher loads are connected presents higher values of V

_{Unb}. This is because the phase where all of the PVs are connected rises, whereas in the other phase, voltages decrease more than when compared to the minimum load case. Figure 6a presents the nominal voltage values variation, according to the distance of the bus from the power transformer. Both correspond to a 3.5-kW PV power injection balanced scenario, with maximum and minimum load power demand. The values shown are for phase 3, and it can be observed that the voltage decreases along the feeders when maximum loads are considered. The RNM base case (no PV and maximum load scenario) is also displayed for comparison. It can be seen that the voltage drop along the feeder is improved due to the PV power generation. Similarly, Figure 6b show the voltage variation in phase three with all of the PV injection made on this phase.

## 5. Conclusions

## Supplementary Materials

## Funding

## Conflicts of Interest

## References

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**Figure 4.**Voltage unbalance form an unbalanced distribution of a single-phase photovoltaic system (SPPS) with different power injection levels.

**Figure 5.**Voltage unbalance with unbalanced and balanced photovoltaic (PV) distributions with minimum and maximum loads.

**Figure 6.**Voltage variation with distance with balanced (

**a**) and unbalanced (

**b**) PV distributions, simulated with maximum and minimum load and maximum load with no PV (Phase 3).

**Figure 7.**Limit of power connection with voltage variation and voltage unbalance for a balanced PV distribution and minimum load scenario (phase 1).

**Table 1.**Limits of single-phase power connections on residential segment in Europe [23]. EU: European Union, SPSS: single-phase photovoltaic system.

EU Member State | SPPS Connection Limit (kWp) | Single-Phase Contracted Power (kVA) Levels |
---|---|---|

Austria | 3.68 | 2.3, 3.68, 4.83, 5.75, 7.36, 9.2, 11.5 |

Belgium | 5 | 3.68, 4.6, 5.75, 7.36, 9.2, 11.5, 14.49 |

Bulgaria | 5 | 6, 7–15 |

Croatia | 5 | 4.6, 5.75, 7.36, 9.2, 11.5 |

Cyprus | 4 | 9.2 |

Czech Rep. | 3.68 | 5.75 |

Denmark | 3.68 | 5.75 |

Estonia | 3.68 | 1.38, 2.3, 3.68, 4.6, 5.75 |

Finland | 3.68 | 5.75 |

France | 6 | 3, 6, 9, 12, 15, 18 |

Germany | 4.6 | 4.6 |

Greece | 5 | 8, 12 |

Hungary | 5 | 1.38, 2.3, 3.68, 4.6, 5.75, 7, 36, 9.2, 11.5, 14.49, 18.4 |

Ireland | 5.75 | 12, 16 |

Italy | 6 | 1.5, 3, 4.5, 6 |

Latvia | 3.68 | 3.68, 4.6, 5.75 |

Lithuania | <10 | 3, 4, 5, 6, 7, 8, 9, 10 |

Luxembourg | <30 (3Φ) | 9.2, 11.5, 14.49, 18.4 (3Φ) |

Malta | 3.68 | 9.2 |

Netherlands | 5 | 1.38, 2.3, 5.75, 8.05, 9.2 |

Poland | 4.6 | 1.38, 2.3, 3.68, 4.6, 5.75, 7.36, 9.2, 11.5 |

Portugal | 5.75 | 1.15, 2.3, 3.45, 4.6, 5.75, 6.9, 10.35, 13.8 |

Romania | 10 (3Φ) | <3, 3–6, >6 |

Slovakia | 4.6 | 5.75 |

Slovenia | 4.6 | 3, 6, 8 |

Spain | 5 | 1.73, 2.3, 3.45, 4.6, 5.75, 6.9, 8.05, 9.2, 10.35, 11.5, 14.49 |

Sweden | 2 and 4 | 3.68, 4.6, 5.75, 8.05, 11.5, 14.49 |

Great Britain | 3.68; 17 | 5.75, 13.8, 15, 18.4, 23 |

Bus ID | Length (km) | Num. Consumers | P (MW) | Q (MVAr) | r (p.u.) | x (p.u.) | Capacity (MVA) |
---|---|---|---|---|---|---|---|

1 | 0.035 | 0 | 0.0000 | 0.0000 | 8.60 × 10^{−4} | 1.65 × 10^{−4} | 0.177 |

2 | 0.023 | 3 | 0.0024 | 0.0007 | 5.56 × 10^{−4} | 1.07 × 10^{−4} | 0.177 |

3 | 0.028 | 10 | 0.0800 | 0.0240 | 6.76 × 10^{−4} | 1.30 × 10^{−4} | 0.177 |

4 | 0.033 | 10 | 0.0400 | 0.0120 | 8.14 × 10^{−4} | 1.56 × 10^{−4} | 0.177 |

5 | 0.019 | 15 | 0.0120 | 0.0036 | 4.72 × 10^{−4} | 9.08 × 10^{−5} | 0.177 |

6 | 0.031 | 10 | 0.0080 | 0.0024 | 2.68 × 10^{−4} | 1.53 × 10^{−4} | 0.291 |

7 | 0.021 | 15 | 0.0600 | 0.0180 | 5.13 × 10^{−4} | 9.87 × 10^{−5} | 0.177 |

8 | 0.021 | 3 | 0.0240 | 0.0072 | 5.13 × 10^{−4} | 9.87 × 10^{−5} | 0.177 |

9 | 0.018 | 10 | 0.0240 | 0.0072 | 4.30 × 10^{−4} | 8.26 × 10^{−5} | 0.177 |

10 | 0.025 | 1 | 0.0240 | 0.0072 | 6.00 × 10^{−4} | 1.15 × 10^{−4} | 0.177 |

11 | 0.001 | 15 | 0.0360 | 0.0108 | 4.00 × 10^{−5} | 2.00 × 10^{−5} | 0.177 |

12 | 0 | 15 | 0.1200 | 0.0360 | 1.83 × 10^{−4} | 6.35 × 10^{−4} | 0.630 |

Voltage (kV) | Rated Power (kVA) | Rsc (p.u.) | Xsc (p.u.) |
---|---|---|---|

20/0.4 | 630 | 0.012 | 0.04 |

Network Indicator | Urban |
---|---|

LV network length per LV Consumer | 0.0024 |

LV underground ratio | 100% |

No. of LV consumers per MV/LV substation | 107 |

MV/LV substation capacity per LV consumer | 5.9 kVA |

Voltage (kV) | Type ID | Section (mm^{2}) | Type | Rated Current | R (ohms/km) | X (ohms/km) |
---|---|---|---|---|---|---|

0.4 | LV_UU_1 | 3 × 95 | Underground | 255 (A) | 0.39 | 0.075 |

0.4 | LV_UU_2 | 3 × 240 | Underground | 420 (A) | 0.14 | 0.080 |

Reactance | Type ID | X_{C} (Ω) | Length (km) | X_{C} (MΩ·km) |
---|---|---|---|---|

X_{C1} (Branch1) | LV_UU_1 | 0.181822 | 0.035 | 6.364 × 10^{−9} |

X_{C2} (Branch6) | LV_UU_2 | 0.180461 | 0.031 | 5.594 × 10^{−9} |

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**MDPI and ACS Style**

Lucas, A. Single-Phase PV Power Injection Limit due to Voltage Unbalances Applied to an Urban Reference Network Using Real-Time Simulation. *Appl. Sci.* **2018**, *8*, 1333.
https://doi.org/10.3390/app8081333

**AMA Style**

Lucas A. Single-Phase PV Power Injection Limit due to Voltage Unbalances Applied to an Urban Reference Network Using Real-Time Simulation. *Applied Sciences*. 2018; 8(8):1333.
https://doi.org/10.3390/app8081333

**Chicago/Turabian Style**

Lucas, Alexandre. 2018. "Single-Phase PV Power Injection Limit due to Voltage Unbalances Applied to an Urban Reference Network Using Real-Time Simulation" *Applied Sciences* 8, no. 8: 1333.
https://doi.org/10.3390/app8081333