# Decoupling Weather Influence from User Habits for an Optimal Electric Load Forecast System

^{*}

## Abstract

**:**

## 1. Introduction

- the importance of an accurate forecast of photovoltaic output for low-voltage load estimation;
- how an estimate of the installed photovoltaic capacity can be inferred from the measured net power consumption and meteorological information;
- how—at least in this case—the use of separate models for the prediction of individual plants can yield better results than those obtainable by training a single regression model for the microgrid.

## 2. Data

#### 2.1. Borkum Grid

#### 2.2. Weather Forecast

## 3. Method

#### 3.1. Generated Power Forecast

#### 3.2. Load Forecast

#### 3.3. Power Exchange Forecast

## 4. Results and Discussion

#### 4.1. Load Forecast

#### 4.2. Power Exchange Forecast

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Scheme of the grid in Borkum. A photovoltaic (PV) power plant and two wind turbines are connected to the medium-voltage (MV) line. An energy storage system will be connected to the MV line in the future. The low-voltage (LV) line distributes power to the town, where several PV devices are connected. The available power measurements are relative to the total power exchange with the mainland (${p}_{e}$) and to the LV net load (${p}_{n}$). BESS: battery energy storage system.

**Figure 2.**Box plots of the net load and of the power exchange of the microgrid. The box represents the interquartile range, the line in the box is the median, and the whiskers are set at the 5 and 95 percentile of the data range.

**Figure 3.**Error in the LV load forecast as a function of the temperature 2 m above ground forecast. Coefficient of determination ${\mathrm{R}}^{2}$ = $-1.67$.

**Figure 4.**Root mean squared error (RMSE) and mean absolute error (MAE) for load forecast using the approach NL3 as a function of the distributed PV capacity assumed. The vertical line corresponds to the estimated real value obtained by summing up the single utility capacities.

**Figure 5.**Boxplot of the net load forecast error as a function of the hour of the day. The box represents the interquartile range, the line in the box is the median, and the whiskers are set at the 5 and 95 percentile of the data range. The uncertainty follows the same daily pattern of the PV generation. The improvement in the forecast accuracy obtained with the model NL3 is apparent.

**Figure 6.**Boxplot of the PE forecast error as a function of the hour of the day. The box represents the interquartile range, the line in the box is the median, and the whiskers are set at the 5 and 95 percentile of the data range. The improvement in the forecast accuracy is evident. The uncertainty is still related to the PV generation, but the pattern is less apparent compared to the net load forecasting case, due to the influence of the wind power forecast uncertainty.

**Table 1.**Number of samples for power measures available for the Borkum grid. Three years, with 15 min frequency, of power measures in two measurement points are available. The minimum, maximum, mean values, and the standard deviations are listed.

Power Exchange ${\mathit{p}}_{\mathit{e}}$ | Net Load ${\mathit{p}}_{\mathit{n}}$ | |
---|---|---|

number | 105,216 | 105,216 |

mean (kW) | 2029.5 | 3603.7 |

std (kW) | 1600.7 | 1137.1 |

min (kW) | $-2303.6$ | 1446.2 |

max (kW) | 6651.2 | 6928.9 |

**Table 2.**Models and feature set for each forecast model. The first column represents the distinguishing abbreviation of the model; in the second column, the forecast variable is indicated; in the third column, the predictive technique used; and finally in the fourth column, the predictors used are listed. PV: photovoltaic forecast model; WT: wind turbine forecast model; MVF: forecast system for the medium voltage production; NL: denotes net load models; PE: denotes power exchange models; ${\widehat{p}}_{pv}$: forecast of MV photovoltaic production; ${\widehat{p}}_{wt}$: forecast of MV wind turbine production; ${\widehat{p}}_{g}$: forecast of total MV power production; ${\widehat{p}}_{n}$: forecast of LV net load; ${\widehat{p}}_{e}$: forecast of power exchange; MARS: multivariate adaptive regression spline; DM: distribution mapping; SVR: support vector machine regression; GHI: Global Horizontal Irradiation; TCC: total cloud cover; WS100: wind speed at 100 m; T2: forecast of the temperature 2 m above ground; h: the hour of the day; dow: decimal for the day of the week; doy: days from the beginning of the year; work: indicates whether the day of the measure or forecast is a working day or not (including holidays); dst: indicates whether the time is relative to the period in which daylight saving is active; ${p}_{n2d}$ and ${p}_{n7d}$: net load 2 days and 7 days before the forecast; ${p}_{e2d}$ and ${p}_{e7d}$: power exchange 2 days and 7 days before the forecast; ${p}_{g2d}$ and ${p}_{g7d}$: power generated by the MV plants 2 days and 7 days before the forecast.

Model | Variable | Technique | Features |
---|---|---|---|

PV | ${\widehat{p}}_{pv}$ | MARS | GHI, TCC |

WT | ${\widehat{p}}_{wt}$ | DM | WS100 |

MVF | ${\widehat{p}}_{g}$ | Equation (2) | ${\widehat{p}}_{pv}$, ${\widehat{p}}_{wt}$ |

NL0 | ${\widehat{p}}_{n}$ | SVR | ${p}_{n2d}$, ${p}_{n7d}$, h, dow, doy, work, dst |

NL1 | ${\widehat{p}}_{n}$ | SVR | $T2$, ${p}_{n2d}$, ${p}_{n7d}$, h, dow, doy, work, dst |

NL2 | ${\widehat{p}}_{n}$ | SVR | $GHI$, ${p}_{n2d}$, ${p}_{n7d}$, h, dow, doy, work, dst |

NL3 | ${\widehat{p}}_{n}$ | SVR, Equations (3), (6) | ${\widehat{p}}_{pv}$, ${p}_{n2d}$, ${p}_{n7d}$, h, dow, doy, work, dst |

PE0 | ${\widehat{p}}_{e}$ | SVR | ${p}_{e2d}$, ${p}_{e7d}$, h, dow, doy, work, dst |

PE1 | ${\widehat{p}}_{e}$ | SVR | $GHI$, $WS100$, ${p}_{e2d}$, ${p}_{e7d}$, h, dow, doy, work, dst |

PE2 | ${\widehat{p}}_{e}$ | SVR | ${p}_{e2d}$, ${p}_{e7d}$, ${p}_{g2d}$, ${p}_{g7d}$, ${p}_{n2d}$, ${p}_{n7d}$, h, dow, doy, work, dst |

PE3 | ${\widehat{p}}_{e}$ | Equation (7) | ${\widehat{p}}_{n}$, ${\widehat{p}}_{g}$ |

**Table 3.**Error analysis on the load forecast, from +24 to +48 h, for different forecast approaches. Row NL0 shows the results without taking into account weather influence and using as predictor only statistics about load two and seven days before. Row NL1 refers to the forecast obtained adding as predictor forecast of temperature at 2 m from the ground; NL2 as before but using as predictor, forecast for GHI instead of T2. The last row shows the results for model NL3, in which a separate model forecasts the photovoltaic distributed generation. The values of nMAE and nRMSE are normalized mean absolute error and root mean squared error with respect to the mean value of the measured quantity.

Model | ${\mathrm{R}}^{2}$ (-) | MAE (kW) | RMSE (kW) | nMAE (%) | nRMSE (%) | Q1 (kW) | Q3 (kW) |
---|---|---|---|---|---|---|---|

NL0 | 0.950 | 182.1 | 247.0 | 5.23 | 7.10 | $-87.7$ | 165.5 |

NL1 | 0.950 | 182.8 | 247.8 | 5.25 | 7.12 | $-87.5$ | 167.2 |

NL2 | 0.955 | 173.2 | 233.7 | 4.97 | 6.71 | $-89.9$ | 156.6 |

NL3 | 0.957 | 170.3 | 228.7 | 4.89 | 6.57 | $-85.3$ | 158.1 |

**Table 4.**Error analysis on net load forecast for different prediction strategies. PE1 is the net load forecast obtained using a SVR using as predictors the time series of net load itself and the meteorological forecast for GHI and wind speed at 100 m from the ground; PE2 is the SVR predictor using all the predictors used for PE1 with the addition of the features used for NL3; PE3 is the net algebraic sum obtained summing the NL3 forecast with the MVF forecast; MVF shows errors of the medium voltage production forecast. The values of nMAE and nRMSE are normalized with respect to the mean value of the measured quantity.

Model | ${\mathrm{R}}^{2}$ (-) | MAE (kW) | RMSE (kW) | nMAE (%) | nRMSE (%) | Q1 (kW) | Q3 (kW) |
---|---|---|---|---|---|---|---|

MVF | 0.820 | 336.5 | 482.4 | 22.16 | 31.76 | $-274.7$ | 188.7 |

PE0 | 0.375 | 971.4 | 1239.3 | 49.50 | 63.15 | $-661.0$ | 968.6 |

PE1 | 0.784 | 555.7 | 729.2 | 28.32 | 37.16 | $-390.3$ | 465.7 |

PE2 | 0.864 | 429.9 | 577.7 | 21.91 | 29.44 | $-296.7$ | 356.8 |

PE3 | 0.880 | 400.7 | 542.8 | 20.42 | 27.66 | $-213.7$ | 368.9 |

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**MDPI and ACS Style**

Massidda, L.; Marrocu, M.
Decoupling Weather Influence from User Habits for an Optimal Electric Load Forecast System. *Energies* **2017**, *10*, 2171.
https://doi.org/10.3390/en10122171

**AMA Style**

Massidda L, Marrocu M.
Decoupling Weather Influence from User Habits for an Optimal Electric Load Forecast System. *Energies*. 2017; 10(12):2171.
https://doi.org/10.3390/en10122171

**Chicago/Turabian Style**

Massidda, Luca, and Marino Marrocu.
2017. "Decoupling Weather Influence from User Habits for an Optimal Electric Load Forecast System" *Energies* 10, no. 12: 2171.
https://doi.org/10.3390/en10122171