# Storage Placement and Sizing in a Distribution Grid with High PV Generation

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. Cost Analysis

#### 3.1. Energy Storage Costs

#### 3.2. Grid Reinforcement Costs

## 4. Input Data and Scenario

#### 4.1. PV Generation

#### 4.2. Simulation Scenario

#### 4.3. Battery Sizing and Placement

## 5. Approach

#### 5.1. Grid Reinforcement

#### 5.2. Grid Reinforcement

#### 5.3. Battery Placement

#### 5.4. Comparison

## 6. Conclusions and Outlook

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

## References

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**Figure 1.**Voltage distribution for the selected worst-case scenario without battery or energy curtailment. The voltage limit is 1.05 p.u., which is clearly exceeded.

**Figure 2.**Flowchart of the heuristic grid reinforcement algorithm. The method shown above was repeated for all branches.

**Figure 3.**Voltage distribution for a day with high solar photovoltaic (PV) generation and one installed battery. In this case, the voltage limit is obeyed at all nodes. The algorithm selected a battery placement at buses 65 and 93 to avoid voltage limit violations. Whiskers were set to 1.5 × IQR, the circles represent data points exceeding that range.

**Figure 4.**Exemplary results from the automated grid reinforcement algorithm. On the left, a graph with the reinforced line segments is shown. The yellow node indicates the transformer and the red edges indicate reinforced line segments. A comparison of the resulting bus voltages is shown on the right. In this case, a voltage limit of 1.03 p.u. was used. (

**a**) Graph diagram of the reinforced grid; (

**b**) Voltage comparison of the reinforced grid.

**Figure 5.**Optimal battery placement for voltage stability within the test grid. (

**a**) 50% PV penetration, voltage limit 3%. (

**b**) 80% PV penetration, voltage limit 3%.

Type | Perc. | Costs/Value |
---|---|---|

capacity | 42% | 130 EUR/kwh |

periphery | 28% | 87 EUR/kwh |

power electronics | 30% | 93 EUR/kw |

installation | - | 20,000 EUR/batt |

batt. lifetime | - | 10 yr |

Line Type | Cost Type | Costs |
---|---|---|

0.4 kV, $4\times 50$ mm | installation | 60,000 EUR/km |

acquisition | 3500 EUR/km | |

0.4 kV, $4\times 120$ mm | installation | 60,000 EUR/km |

acquisition | 9900 EUR/km | |

0.4 kV, $4\times 150$ mm | installation | 60,000 EUR/km |

acquisition | 12,000 EUR/km | |

parallel line installation | installation | additional 15% of installation costs |

Trafo, 630 kVA | total | 21,000 EUR |

**Table 3.**Example result of the grid reinforcement algorithm: overview of the installed assets and costs.

From Bus | To Bus | n Parallel | Type | Cost [k€] |
---|---|---|---|---|

1 | 105 | 2 | NAYY $4\times 120$ SE | 109.5 |

1 | 73 | 2 | NAYY $4\times 120$ SE | 109.5 |

1 | 106 | 3 | NAYY $4\times 120$ SE | 131.1 |

2 | 28 | 1 | NAYY $4\times 120$ SE | 87.9 |

2 | 104 | 2 | NAYY $4\times 120$ SE | 109.5 |

3 | 61 | 1 | NAYY $4\times 120$ SE | 87.9 |

3 | 73 | 2 | NAYY $4\times 120$ SE | 109.5 |

6 | 43 | 1 | NAYY $4\times 50$ SE | 81.5 |

6 | 68 | 2 | NAYY $4\times 120$ SE | 109.5 |

28 | 29 | 1 | NAYY $4\times 50$ SE | 81.5 |

29 | 30 | 1 | NAYY $4\times 50$ SE | 81.5 |

50 | 57 | 1 | NAYY $4\times 120$ SE | 87.9 |

50 | 61 | 1 | NAYY $4\times 120$ SE | 87.9 |

56 | 57 | 1 | NAYY $4\times 120$ SE | 87.9 |

63 | 70 | 2 | NAYY $4\times 120$ SE | 109.5 |

63 | 69 | 2 | NAYY $4\times 120$ SE | 109.5 |

65 | 70 | 2 | NAYY $4\times 120$ SE | 109.5 |

65 | 106 | 1 | NAYY $4\times 120$ SE | 87.9 |

68 | 100 | 2 | NAYY $4\times 120$ SE | 109.5 |

69 | 100 | 2 | NAYY $4\times 120$ SE | 109.5 |

104 | 105 | 2 | NAYY $4\times 120$ SE | 109.5 |

PV Pen. | $\Delta {\mathit{V}}_{\mathbf{max}}$ | Batt. 1 | Batt. 2 | Batt. 3 | ||||||
---|---|---|---|---|---|---|---|---|---|---|

[${\mathit{P}}_{\mathbf{PV},\text{}\mathbf{max}}$] | [${\mathit{V}}_{\mathbf{nom}}$] | C [kWh] | P [kW] | Bus # | C [kWh] | P [kW] | Bus # | C [kWh] | P [kW] | Bus # |

50% | 5% | - | - | - | - | - | - | - | - | - |

3% | 61 | 15 | 30 | 99 | 20 | 42 | - | - | - | |

80% | 5% | 75 | 20 | 30 | 149 | 30 | 43 | - | - | - |

3% | 377 | 61 | 29 | 414 | 67 | 45 | 909 | 25 | 59 |

PV Pen. | $\Delta {\mathit{V}}_{\mathbf{max}}$ | Grid Reinf. | 5 Batt. | 10 Batt. | Unconstrained | |
---|---|---|---|---|---|---|

[${\mathit{P}}_{\mathbf{PV},\text{}\mathbf{max}}$] | [${\mathit{V}}_{\mathbf{nom}}$] | [k€] | [k€] | [k€] | [k€] | [n batt.] |

50% | 3% | 710 | 138 | 238 | 79 | 2 |

5% | - | - | - | - | - | |

80% | 3% | 1679 | 307 | 406 | 273 | 3 |

5% | 488 | 154 | 254 | 94 | 2 |

PV Pen. | $\Delta {\mathit{V}}_{\mathbf{max}}$ | Grid Reinf. | 5 Batt. | 10 Batt. | Unconstrained | |
---|---|---|---|---|---|---|

[${\mathit{P}}_{\mathbf{PV},\text{}\mathbf{max}}$] | [${\mathit{V}}_{\mathbf{nom}}$] | [k€] | [k€] | [k€] | [k€] | [n batt.] |

50% | 3% | 18 | 14 | 24 | 8 | 2 |

5% | 0 | 0 | 0 | 0 | 0 | |

80% | 3% | 42 | 31 | 41 | 27 | 3 |

5% | 12 | 15 | 25 | 9 | 2 |

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**MDPI and ACS Style**

Matthiss, B.; Momenifarahani, A.; Binder, J.
Storage Placement and Sizing in a Distribution Grid with High PV Generation. *Energies* **2021**, *14*, 303.
https://doi.org/10.3390/en14020303

**AMA Style**

Matthiss B, Momenifarahani A, Binder J.
Storage Placement and Sizing in a Distribution Grid with High PV Generation. *Energies*. 2021; 14(2):303.
https://doi.org/10.3390/en14020303

**Chicago/Turabian Style**

Matthiss, Benjamin, Arghavan Momenifarahani, and Jann Binder.
2021. "Storage Placement and Sizing in a Distribution Grid with High PV Generation" *Energies* 14, no. 2: 303.
https://doi.org/10.3390/en14020303