# Quantification of the Energy Storage Contribution to Security of Supply through the F-Factor Methodology

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## Abstract

**:**

## 1. Introduction

- Presentation of F-factors as a methodology for the quantification of the security contribution of ES.
- Demonstration of the mathematical formulation for the optimization problem that is solved for the evaluation of the F-factor metric.
- Sensitivity analysis of the security contribution of ES as a function of multiple quantities such as energy storage power capability, efficiency, energy capacity and characteristics of load patterns.

## 2. Literature Review

## 3. The F-Factor Methodology

#### 3.1. Definition of the Metric

#### 3.2. Optimization Problem

## 4. Case Study: Evaluation of the ES Security Contribution via F-factors

## 5. Discussion

## 6. Conclusions and Future Work

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Illustration of an electricity load profile where its peak demand is reduced through the use of energy storage (ES), which discharges during peak hours (i.e., acts as a generator of electricity) and charges during off-peak hours (i.e., acts as a load).

**Figure 2.**Diagrams of two substations: a bulk supply point substation (e.g., 132/33 kV) and a primary substation (e.g., 33/11 kV), each of which supplies a load.

**Figure 3.**Normalized time-series for load profiles 1 and 2. The profiles span a period of seven days, with the fourth day being the one that exhibits the peak demand.

**Figure 4.**Initial demand profile (in blue) and optimal demand profile (in red) following ES operation across the peak day for load profile 2.

**Figure 5.**Net power inflow (kW) in the ES unit presented in Figure 4.

**Figure 6.**The values on the horizontal axis indicate the number of identical ES units connected to the same bus. The height of the bars illustrates the corresponding F-factor value.

**Figure 7.**The graph illustrates the effect of degradation on the F-factors assuming that initially the unit has µ = 8 h and this value reduces through time, leading to a reduction of F-factor values. The horizontal axis indicates parameter µ, i.e., the number of hours required for a complete charging or discharging of the ES unit. The values on the vertical axis illustrate the corresponding F-factor value. The storage unit is 100% efficient with power capability $\tilde{P}$ equal to 20% of the peak and corresponding to load profile 2 as in Table 2.

**Table 1.**F-factors for an ES unit connected to the primary substation (load profile 1) and assuming that the state of charge (SOC) of the unit is within 0% and 100% of its energy capacity. Grey-coloured cells contain, at the top, the F-factor when the horizon is only the peak day, while the bottom value, shown in parentheses, corresponds to the case where the horizon is the entire 7-day period. White-coloured cells contain only one value for the F-factor, and this value is the same for the peak day and for the entire 7-day period.

$\mathit{\mu}$ | $\tilde{\mathit{P}}$ at 10% of Peak | $\tilde{\mathit{P}}$ at 20% of Peak | $\tilde{\mathit{P}}$ at 30% of Peak | $\tilde{\mathit{P}}$ at 50% of Peak | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Efficiency | Efficiency | Efficiency | Efficiency | |||||||||

100% | 80% | 60% | 100% | 80% | 60% | 100% | 80% | 60% | 100% | 80% | 60% | |

1 h | 62% | 62% | 62% | 46% | 46% | 46% | 37% | 37% | 37% | 27% | 27% | 27% |

2 h | 92% | 92% | 92% | 61% | 61% | 61% | 49% | 49% | 49% | 37% | 37% | 37% |

3 h | 100% | 100% | 100% | 73% | 73% | 73% | 59% | 59% | 59% | 45% | 45% | 45% |

4 h | 100% | 100% | 100% | 84% | 84% | 84% | 67% | 67% | 67% | 52% | 50% (52%) | 46% (52%) |

5 h | 100% | 100% | 100% | 93% | 93% | 93% | 74% | 74% | 73% (74%) | 54% (59%) | 50% (58%) | 46% (55%) |

6 h | 100% | 100% | 100% | 100% | 100% | 96% (100%) | 82% | 82% | 73% (82%) | 54% (62%) | 50% (59%) | 46% (56%) |

7 h | 100% | 100% | 100% | 100% | 100% | 96% (100%) | 89% | 82% (89%) | 73% (89%) | 54% (63%) | 50% (60%) | 46% (57%) |

8 h | 100% | 100% | 100% | 100% | 100% | 96% (100%) | 90% (96%) | 82% (96%) | 73% (92%) | 54% (64%) | 50% (61%) | 46% (57%) |

**Table 2.**F-factors for an ES unit that is connected to the bulk supply point substation characterized by load profile 2 and assuming that the SOC of the unit is within 0% and 100% of its energy capacity.

$\mathit{\mu}$ | $\tilde{\mathit{P}}$ at 10% of Peak | $\tilde{\mathit{P}}\text{}\mathbf{at}\text{}20\%\text{}\mathbf{of}\text{}\mathbf{Peak}\text{}$ | $\tilde{\mathit{P}}\text{}\mathbf{at}\text{}30\%\text{}\mathbf{of}\text{}\mathbf{Peak}$ | $\tilde{\mathit{P}}\mathbf{at}\text{}50\%\text{}\mathbf{of}\text{}\mathbf{Peak}$ | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Efficiency | Efficiency | Efficiency | Efficiency | |||||||||

100% | 80% | 60% | 100% | 80% | 60% | 100% | 80% | 60% | 100% | 80% | 60% | |

1 h | 49% | 49% | 49% | 40% | 40% | 40% | 34% | 34% | 34% | 25% | 25% | 25% |

2 h | 80% | 80% | 80% | 58% | 58% | 58% | 45% | 45% | 45% | 33% | 33% | 33% |

3 h | 100% | 100% | 100% | 68% | 68% | 68% | 53% | 53% | 53% | 41% | 41% | 41% |

4 h | 100% | 100% | 100% | 76% | 76% | 76% | 61% | 61% | 61% | 48% | 45% (48%) | 41% (46%) |

5 h | 100% | 100% | 100% | 84% | 84% | 84% | 68% | 68% | 66% (68%) | 49%(53%) | 45% (51%) | 41% (49%) |

6 h | 100% | 100% | 100% | 91% | 91% | 87% (91%) | 75% | 75% | 66% (75%) | 49% (56%) | 45% (53%) | 41% (49%) |

7 h | 100% | 100% | 100% | 98% | 98% | 87% (98%) | 82% | 75% (82%) | 66% (78%) | 49% (57%) | 45% (53%) | 41% (49%) |

8 h | 100% | 100% | 100% | 100% | 98% (100%) | 87% (100%) | 82% (88%) | 75% (85%) | 66% (79%) | 49% (57%) | 45% (53%) | 41% (49%) |

**Table 3.**F-factors for an ES unit connected to the primary substation (load profile 1) and assuming that the SOC of the unit is within 20% and 80% of its energy capacity.

$\mathit{\mu}$ | $\tilde{\mathit{P}}\mathbf{at}\text{}10\%\text{}\mathbf{of}\text{}\mathbf{Peak}$ | $\tilde{\mathit{P}}\mathbf{at}\text{}20\%\text{}\mathbf{of}\text{}\mathbf{Peak}\text{}$ | $\tilde{\mathit{P}}\mathbf{at}\text{}30\%\text{}\mathbf{of}\text{}\mathbf{Peak}$ | $\tilde{\mathit{P}}\mathbf{at}\text{}50\%\text{}\mathbf{of}\text{}\mathbf{Peak}$ | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Efficiency | Efficiency | Efficiency | Efficiency | |||||||||

100% | 80% | 60% | 100% | 80% | 60% | 100% | 80% | 60% | 100% | 80% | 60% | |

1 h | 47% | 47% | 47% | 34% | 34% | 34% | 29% | 29% | 29% | 22% | 22% | 22% |

2 h | 69% | 69% | 69% | 51% | 51% | 51% | 39% | 39% | 39% | 29% | 29% | 29% |

3 h | 87% | 87% | 87% | 59% | 59% | 59% | 46% | 46% | 46% | 35% | 35% | 35% |

4 h | 100% | 100% | 100% | 66% | 66% | 66% | 53% | 53% | 53% | 40% | 40% | 40% |

5 h | 100% | 100% | 100% | 73% | 73% | 73% | 59% | 59% | 59% | 45% | 45% | 45% |

6 h | 100% | 100% | 100% | 80% | 80% | 80% | 64% | 64% | 64% | 49% | 49% | 46% (49%) |

7 h | 100% | 100% | 100% | 86% | 86% | 86% | 68% | 68% | 68% | 53% | 50% (53%) | 46% (53%) |

8 h | 100% | 100% | 100% | 92% | 91% | 91% | 73% | 73% | 73% | 54% (57%) | 50% (57%) | 46% (55%) |

**Table 4.**F-factors for an ES unit that is connected to the BSP substation characterized by load profile 2 and assuming that the SOC of the unit is within 20% and 80% of its energy capacity.

$\mathit{\mu}$ | $\tilde{\mathit{P}}\mathbf{at}\text{}10\%\text{}\mathbf{of}\text{}\mathbf{Peak}$ | $\tilde{\mathit{P}}\mathbf{at}\text{}20\%\text{}\mathbf{of}\text{}\mathbf{Peak}\text{}$ | $\tilde{\mathit{P}}\mathbf{at}\text{}30\%\text{}\mathbf{of}\text{}\mathbf{Peak}$ | $\tilde{\mathit{P}}\mathbf{at}\text{}50\%\text{}\mathbf{of}\text{}\mathbf{Peak}$ | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Efficiency | Efficiency | Efficiency | Efficiency | |||||||||

100% | 80% | 60% | 100% | 80% | 60% | 100% | 80% | 60% | 100% | 80% | 60% | |

1 h | 34% | 34% | 34% | 28% | 28% | 28% | 25% | 25% | 25% | 21% | 21% | 21% |

2 h | 56% | 56% | 56% | 45% | 45% | 45% | 38% | 37% | 37% | 27% | 27% | 27% |

3 h | 75% | 75% | 75% | 56% | 56% | 56% | 43% | 43% | 43% | 32% | 32% | 32% |

4 h | 90% | 90% | 90% | 62% | 62% | 62% | 48% | 48% | 48% | 36% | 36% | 36% |

5 h | 100% | 100% | 100% | 68% | 68% | 68% | 53% | 53% | 53% | 41% | 41% | 41% |

6 h | 100% | 100% | 100% | 73% | 73% | 73% | 58% | 58% | 58% | 45% | 45% | 41% (45%) |

7 h | 100% | 100% | 100% | 77% | 77% | 77% | 62% | 62% | 62% | 49% | 45% (49%) | 41% (47%) |

8 h | 100% | 100% | 100% | 82% | 82% | 82% | 67% | 67% | 67% | 49% (53%) | 45% (51%) | 41% (49%) |

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**MDPI and ACS Style**

Giannelos, S.; Djapic, P.; Pudjianto, D.; Strbac, G.
Quantification of the Energy Storage Contribution to Security of Supply through the F-Factor Methodology. *Energies* **2020**, *13*, 826.
https://doi.org/10.3390/en13040826

**AMA Style**

Giannelos S, Djapic P, Pudjianto D, Strbac G.
Quantification of the Energy Storage Contribution to Security of Supply through the F-Factor Methodology. *Energies*. 2020; 13(4):826.
https://doi.org/10.3390/en13040826

**Chicago/Turabian Style**

Giannelos, Spyros, Predrag Djapic, Danny Pudjianto, and Goran Strbac.
2020. "Quantification of the Energy Storage Contribution to Security of Supply through the F-Factor Methodology" *Energies* 13, no. 4: 826.
https://doi.org/10.3390/en13040826