# Forecasting for Battery Storage: Choosing the Error Metric

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## Abstract

**:**

## 1. Introduction

- 1
- battery charging profile—For each half hour before 3:30 pm for each day of the upcoming week, prescribe how much charge the battery will take (up to a maximum of 2.5 MW over that half hour); and
- 2
- a battery discharging profile—For each half hour from 3:30 pm until 9 pm for each day of the upcoming week, prescribe how much the battery will discharge (up to a maximum of 2.5 MW over that half hour).

#### Competition Details

## 2. Data Provided

## 3. Materials and Methods

#### 3.1. Approach

#### 3.2. Forecasting Battery Charging Profiles

#### 3.3. Forecasting Battery Discharge Profiles

#### 3.3.1. Example Motivation

#### 3.3.2. Deriving the Optimal Discharge Profile

#### 3.3.3. Error Metric

#### 3.3.4. Forecasting

## 4. Results

#### 4.1. Charging Profiles

#### 4.2. Discharging Profiles

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**The posterior distributions of the linear regression fitting parameters for PV power generation against forecast solar luminosity for Task 4.

**Figure 3.**Various fits to the data including the prior simple model fitted to the full data, a best fit to the 49 data points of close periods and the minimum and maximum slope results from the MCMC posterior.

**Figure 4.**Two example electricity demand forecasts (units in MW) with data points for every half-hour of 3 days (144 in total). The forecast in the panel on the left has lower standard error metrics and is generally considered better for many applications. However, in our case of battery discharge scheduling, the forecast in the panel on the right is actually better. This is because it better follows the shape of the profile during the 3 afternoon peak times (shown between the vertical bars). The results can be seen in Table 1.

**Table 1.**Error metrics from Forecast 1 and Forecast 2. RMSE and ADPR units are in MW and MAPE is a percentage. ADPR is the Average Daily Peak Reduction.

Error Metric | Forecast 1 | Forecast 2 | Optimal |
---|---|---|---|

RMSE—lower is better | 0.24 | 0.47 | 0 |

MAPE—lower is better | 8.58 | 17.12 | 0 |

ADPR—higher is better | 1.21 | 1.56 | 1.56 |

**Table 2.**Percentage charge dervied from PV based on charging profiles from four different models. Our model is based on combining an average for the time of year with a Bayesian regression of the forecast solar luminosity.

W/c | Our Model | 49-pt Average | Regression | Benchmark |
---|---|---|---|---|

16 October 2018 | 89.89% | 89.81% | 88.12% | 86.95% |

10 March 2019 | 77.36% | 76.05% | 78.01% | 71.03% |

18 December 2019 | 43.24% | 43.28% | 42.60% | 40.10% |

3 July 2020 | 96.73% | 96.69% | 96.08% | 94.32% |

Average | 76.80% | 76.46% | 76.20% | 73.10% |

**Table 3.**The average daily peak reduction in MW achieved by the four forecast models. The greater the peak reduction the better. Presented are the results for each of the 4 task weeks averaged over the 7 days in those task weeks. In addition, the average result across those 4 task weeks is provided. Also presented are the “In-sample” calibration model peak reduction averaged over the 35 days closest to the task week and while some of those days are quite distant from the task week and are in-sample they do provide an average result across more days and so are more robust.

Task Week | W/c | Our Model | RMSE-MP | RMSE-S | Benchmark |
---|---|---|---|---|---|

In-sample | last 35 days | 1.511 | 1.507 | 1.504 | 1.492 |

1 | 16 October 2018 | 1.478 | 1.376 | 1.359 | 1.436 |

2 | 10 March 2019 | 1.440 | 1.438 | 1.455 | 1.406 |

3 | 18 December 2019 | 1.366 | 1.360 | 1.331 | 1.305 |

4 | 3 July 2020 | 1.303 | 1.299 | 1.273 | 1.259 |

Average | all 4 weeks | 1.397 | 1.368 | 1.354 | 1.351 |

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**MDPI and ACS Style**

Singleton, C.; Grindrod, P.
Forecasting for Battery Storage: Choosing the Error Metric. *Energies* **2021**, *14*, 6274.
https://doi.org/10.3390/en14196274

**AMA Style**

Singleton C, Grindrod P.
Forecasting for Battery Storage: Choosing the Error Metric. *Energies*. 2021; 14(19):6274.
https://doi.org/10.3390/en14196274

**Chicago/Turabian Style**

Singleton, Colin, and Peter Grindrod.
2021. "Forecasting for Battery Storage: Choosing the Error Metric" *Energies* 14, no. 19: 6274.
https://doi.org/10.3390/en14196274