# Integration of Demand Response and Short-Term Forecasting for the Management of Prosumers’ Demand and Generation

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

- Firstly, short-term forecasting methods are used to predict hourly load and photovoltaic generation with a horizon of 24 h.
- Secondly, the predicted daily PV generation of the training dataset is grouped into homogeneous clusters according to their shape. Next, a representative PV curve is obtained for each cluster, and a discriminant analysis is developed to assign each predicted PV curve of the test dataset to a cluster.
- Finally, Demand Response strategies are applied to those days with a predicted PV curve in the suitable cluster (the one that provides more accurate predictions).

## 2. Materials and Methods

#### 2.1. Methodology Overview

#### 2.2. Characteristics of the Customers: Demand, Photovoltaic Generation, and End-Uses

#### 2.3. Short-Term Forecasting Methods

#### 2.3.1. Random Forest

#### 2.3.2. Stochastic Gradient Boosting (SGB)

#### 2.4. Time-Series Clustering

_{i}) I = 1, …,m and (y

_{j}) j = 1, …, m, it starts calculating a nxm matrix D = (Dij) with the distance between every possible pair of point x

_{i}and y

_{j}in the two time series, Dij = d(x

_{i},y

_{j}), I = 1,…, n, j = 1, …, m, where d(x

_{i},y

_{j}) can represents the Euclidean or the absolute distance. According to [30], a warping path w is a contiguous set of matrix elements which defines a mapping between (x

_{i}) and (y

_{j}) that satisfies the following conditions:

- Boundary conditions: w
_{1}= (1; 1) and w_{k}= (m; n), where k is the length of the warping path. - Continuity: if w
_{i}= (a, b) then w_{i}_{−1}= (a’, b’), where a − a’ ≤ 1 and b − b’ ≤ 1. - Monotonicity: if w
_{i}= (a, b) then w_{i}_{−1}= (a’, b’), where a − a’ ≥ 0 and b − b’ ≥ 0.

#### 2.5. Demand Response Strategies

_{ON}is the time in this period where a “representative” (average) load remains switched ON and demands power.

_{sw}, H

_{w}) or internal gains due to inhabitants (H

_{r}) or appliances (H

_{a}) (Figure 4a); the model takes into account heat storage from the specific heat of external walls (C

_{w}), indoor masses (C

_{a}, C

_{1}and C

_{2}, especially important for WH) or roof/ground (C

_{rg}); and it considers the control mechanisms which drive appliances (for instance thermostats m(t) and DR policies u(t)). Moreover, their state variables are temperatures: indoor (X

_{i}), walls (X

_{w}), roof/ground (X

_{rg}) for HVAC loads (Figure 4a), and X

_{1}, X

_{2}for the stratification of water in the reservoir (“hot” WH1 and “cold” WH2 sub-tanks, Figure 4b), that is to say, characteristics that allow the evaluation of energy flows and storage capabilities (i.e., the indirect capacity of storage in the envelope of buildings), the direct storage in WH or the loss of customer service due to the application of DR (i.e., internal or hot water temperature).

_{sup}is the upper temperature of load’s thermostat, which is set as a simple hysteresis cycle with dead-band db (usually ranging from 0.01–0.03 pu), and X

_{lim}is the maximum reasonable temperature inside the dwelling (for example 22–23 °C in the case of HVAC, in winter) or the maximum temperature of water inside the tank (68 °C), which avoids risk of burns if a mixing valve is not used for the control of hot water pipeline. X

_{i}

^{serv}is a minimum service level for the appliance (a minimum comfort temperature inside the dwelling, for example 16 °C, or a minimum temperature of hot water inside the WH, for example 36 °C).

_{lim}). Otherwise, if demand must fall to balance a decrease in PV generation (with respect to 24 h forecast), the thermostat or the supply is controlled to reduce demand. Notice that a “baseline”, (i.e., load demand evaluated without control m(t, t + k)) is also needed as reference for controlled load. This baseline also comes from PBLM models (Figure 1).

## 3. Results and Discussion

#### 3.1. Prediction Results for the Electricity Consumption

#### 3.2. Prediction Results for the Photovoltaic Generation

#### 3.3. Classification Results of Photovoltaic Curves

#### 3.4. Results for Demand Response Strategies

#### 3.4.1. Very Short-Term PV Adjusted Forecasting

_{upl}is the upper limit considered as acceptable for any correction through the adjusted factor af(d, t). Therefore, Equation (7) is improved by Equation (9):

#### 3.4.2. Balancing Net Demand through DR

#### 3.4.3. Analysis of DR Flexibility

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

`,`the Ministerio de Educación (Spanish Government) under doctorate grant FPU17/02753, and the special support of EU FEDER funds.

## Conflicts of Interest

## References

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**Figure 2.**Load, Temperature and PV Generation profiles: (

**a**) example of winter and summer Load Curves in the power substation; (

**b**) example of winter and summer temperature behavior; (

**c**) example of winter and summer power generation in the PV plant on peak production days.

**Figure 3.**Daily end-uses and customer service: (

**a**) HP profile; (

**b**) daily use of residential Water Heater. (

**c**) Daily profiles for main end-uses (winter). Acronyms: EH: Heating (Electric heaters and Heat pumps), WH: Water Heating; CO: cooking; LIG: lighting; FR: fridges; WM: washing machines; DW: dishwasher; OV: Oven; PC: computers; DRY: dryers; OT: Others; and CUST: overall customer demand.

**Figure 4.**Example of PBLM for: (

**a**) HVAC (Heating, Ventilation and Air Conditioning); (

**b**) WH (Water Heater).

**Figure 5.**Goodness-of-fit measures by hour of the day in the test dataset: (

**a**) using RMSE; (

**b**) using MAPE.

**Figure 9.**Comparisons of actual PV and 24 h forecast PV generation for some days in Cluster 1: (

**a**) day 3; (

**b**) day 4; (

**c**) day 9; (

**b**) day 28.

**Figure 10.**Differences between 24-h-ahead and 1-h-ahead forecasts (day 23): (

**a**) PV generation; (

**b**) Net consumption.

**Figure 15.**Differences between 24-h-ahead and 1-h-ahead forecasts (day 14): (

**a**) PV generation; (

**b**) Net consumption.

**Figure 16.**Load demand variations among 24-h forecast, 1-h forecasts and final load consumption after DR (day 14): (

**a**) WH; (

**b**) HVAC.

**Figure 19.**Net consumption profiles: 24-h forecasts, after DR and without DR: (

**a**) day 16; (

**b**) day 28.

**Figure 20.**Cumulative absolute error (CAE) between the final net consumption (without DR and after DR actions) and the target (the 24 h-ahead forecast of the net consumption).

Type of End-Use | USA (2015) All Fuels | USA (2015) Electricity | EU (2016) All Fuels | Spain (2014) All Fuels | Spain (2014) Electricity |
---|---|---|---|---|---|

Space Heating | 43 | 14.76 | 64.7 | 42.9 | 7.36 |

Water Heater | 19 | 13.65 | 14.5 | 17.9 | 7.47 |

Air Conditioning | 6.24 | 16.89 | 0.3 | 0.98 | 2.33 |

Refrigerators | 4.75 | 7.02 | - | 7.94 | - |

Other * | 29.8 | 47.67 | 20.5 | 39.22 | 82.84 |

Predictors | Description |
---|---|

H2, H3, …H24 | Hourly dummy variables corresponding to the hour of the day |

WH2, WH3, …WH7 | Hourly dummy variables corresponding to the day of the week |

MH2, MH3, …, MH12 | Hourly dummy variables corresponding to the month of the year |

FH1 | Hourly dummy variable corresponding to national, regional or local holidays |

Temperature | Predicted hourly external temperature. |

LOAD_lag_i | Hourly load lagged “i” hours, with i = 24, 48, …,168. |

Measure | Regular Days | Special Days | All Days |
---|---|---|---|

Error_mean_train (kW) | 6.88 | −11.87 | 0.83 |

Error_mean_test (kW) | 35.39 | −4.94 | 22.84 |

Error_sd_train (kW) | 114.29 | 107.18 | 112.39 |

Error_sd_test (kW) | 173.84 | 154.95 | 169.19 |

Error_skewness_train | −0.16 | −0.19 | −0.15 |

Error_skewness_test | 0.37 | 0.45 | 0.42 |

Error_kurtosis_train | 10.93 | 8.48 | 10.21 |

Error_kurtosis_test | 4.05 | 5.74 | 4.44 |

RMSE_train (kW) | 114.49 | 107.83 | 112.39 |

RMSE_test (kW) | 177.34 | 154.92 | 170.68 |

R-squared_train | 0.98 | 0.94 | 0.98 |

R-squared_test | 0.95 | 0.81 | 0.95 |

MAPE_train | 2.05 | 2.45 | 2.18 |

MAPE_test | 3.36 | 3.63 | 3.44 |

Name | Description |
---|---|

swflx | Surface downwelling shortwave flux (W·m^{−2}) |

temp | Temperature at 2 m (Kelvin) |

pres | Surface sea level pressure (hPa) |

mod | Wind speed at 10 m (m/s) |

dir | Wind direction at 10 m (degrees) |

rh | Relative humidity at 2 m (per unit) |

cft | Global cloud cover (per unit) |

cfl | Cloud cover at low levels (per unit) |

cfm | Cloud cover at medium levels (per unit) |

cfh | Cloud cover at high levels (per unit) |

prec | Accumulated rainfall in the hour (kg·m^{−2}) |

vis | Visibility (m) |

clear | Clear-sky global horizontal irradiance (W·m^{−2}) |

aghi | Average global horizontal irradiance (W·m^{−2}) |

aip | Average irradiance on panel (W·m^{−2}) |

h1 | Cosine of the day fraction for the hour |

h2 | Sine of the day fraction for the hour |

**Table 5.**Goodness-of-fit measures in the training and test datasets for the PV power forecasting model.

Measure | Value |
---|---|

Error_mean_train (kW) | 4.96 |

Error_mean_test (kW) | −19.52 |

Error_sd_train (kW) | 308.60 |

Error_sd_test (kW) | 362.12 |

Error_skewness_train | −0.021 |

Error_skewness_test | −0.173 |

Error_kurtosis_train | 0.906 |

Error_kurtosis_test | 0.994 |

RMSE_train (kW) | 302.52 |

RMSE_test (kW) | 350.34 |

R-squared_train | 0.78 |

R-squared_test | 0.70 |

MAPE_train | 237.31 |

MAPE_test | 310.06 |

**Table 6.**Dates of the test period (2011) classified into Cluster 1 (and therefore selected for DR actions).

Day (Number) | Date (dd/mm) | Day (Number) | Date (dd/mm) | Day (Number) | Date (dd/mm) |
---|---|---|---|---|---|

1 | 4 February | 11 | 10 March | 21 | 20 February |

2 | 5 February | 12 | 11 March | 22 | 20 March |

3 | 5 March | 13 | 12 February | 23 | 21 March |

4 | 6 February | 14 | 14 January | 24 | 22 March |

5 | 6 March | 15 | 14 February | 25 | 3 January |

6 | 7 February | 16 | 16 January | 26 | 23 March |

7 | 7 March | 17 | 18 February | 27 | 24 January |

8 | 8 February | 18 | 18 March | 28 | 25 February |

9 | 9 February | 19 | 19 March | 29 | 28 March |

10 | 10 February | 20 | 20 January | 30 | 29 March |

31 | 31 March |

Day | MAPE (%) of PVF (24 h-Ahead Forecast) | MAPE (%) of PVBL (1 h-Ahead Forecast) |
---|---|---|

1 | 12.5 | 7.7 |

2 | 13.9 | 9.1 |

4 | 18.6 | 8.7 |

5 | 4.8 | 5.6 |

14 | 28.2 | 11.1 |

16 | 128.1 | 30.6 |

17 | 39.2 | 11.9 |

20 | 22.9 | 5.8 |

23 | 52.6 | 21.7 |

26 | 9.7 | 9.9 |

28 | 8.2 | 6.7 |

Energy 24-h (MWh) | Energy w/o DR (MWh) | Energy w/DR (MWh) | CAE 24 h-w/o DR (MWh) | CAE 24 h-w/DR (MWh) | Error w/o DR (%) | Error w/DR (%) | Max. ∆P w/o DR (kW) | Max. ∆P w/DR (kW) |
---|---|---|---|---|---|---|---|---|

42.16 | 45.96 | 40.37 | 6.02 | 2.96 | 14.27 | 7.02 | 1256.93 | 579.32 |

Energy 24-h (MWh) | Energy w/o DR (MWh) | Energy w/DR (MWh) | CAE 24 h-w/o DR (MWh) | CAE 24 h-w/DR (MWh) | Error w/o DR (%) | Error w/DR (%) | Max. ∆P w/o DR (kW) | Max. ∆P w/DR (kW) |
---|---|---|---|---|---|---|---|---|

50.13 | 47.23 | 49.43 | 4.13 | 1.79 | 8.25 | 3.58 | 805.45 | 451.54 |

Day | Energy 24-h (MWh) | Energy w/o DR (MWh) | Energy w/DR (MWh) | CAE 24 h-w/o DR (MWh) | CAE 24 h-w/DR (MWh) | Error w/o DR (%) | Error w/DR (%) | Max. ∆P w/o DR (kW) | Max. ∆P w/DR (kW) |
---|---|---|---|---|---|---|---|---|---|

1 | 44.84 | 43.41 | 43.09 | 3.09 | 3.04 | 6.90 | 6.78 | 629.51 | 558.59 |

2 | 32.52 | 30.93 | 31.22 | 2.39 | 2.00 | 7.37 | 6.14 | 732.47 | 449.26 |

4 | 27.06 | 25.19 | 26.42 | 3.24 | 1.71 | 11.99 | 6.32 | 581.92 | 411.86 |

5 | 22.34 | 22.07 | 21.86 | 1.32 | 1.44 | 5.94 | 6.48 | 419.74 | 380.21 |

14 | 50.13 | 47.23 | 49.43 | 4.13 | 1.79 | 8.25 | 3.58 | 805.45 | 451.54 |

16 | 29.70 | 38.64 | 30.09 | 9.39 | 1.99 | 31.63 | 6.70 | 1622.69 | 472.04 |

17 | 47.15 | 41.59 | 45.25 | 6.40 | 2.85 | 13.58 | 6.05 | 1108.13 | 538.99 |

20 | 48.31 | 47.04 | 48.74 | 2.89 | 1.68 | 5.99 | 3.49 | 622.92 | 342.69 |

21 | 27.59 | 23.97 | 25.27 | 3.86 | 2.59 | 13.99 | 9.40 | 776.20 | 534.47 |

23 | 42.16 | 45.96 | 40.37 | 6.02 | 2.96 | 14.27 | 7.02 | 1256.93 | 579.32 |

26 | 41.01 | 42.38 | 42.08 | 2.01 | 1.90 | 4.92 | 4.63 | 487.96 | 572.66 |

28 | 41.97 | 41.25 | 39.32 | 2.75 | 4.19 | 6.55 | 9.99 | 792.76 | 1124.70 |

Day | Balance Mileage (MWh) | Demand Mileage (MWh) | Mileage Ratio (%) | Symmetry Equation (12) | Performance Equation (13) |
---|---|---|---|---|---|

1 | 2.64 | 5.54 | 47.5 | 0.95 | 0.27 |

2 | 2.62 | 4.52 | 57.5 | 1.59 | 0.34 |

4 | 2.86 | 4.06 | 70.17 | 4.24 | 0.05 |

5 | 1.52 | 3.92 | 38.89 | 0.83 | 1.89 |

14 | 3.12 | 5.72 | 54.50 | 7.06 | 0.047 |

16 | 3.06 | 4.12 | 74.20 | 0.008 | 0.036 |

17 | 4.32 | 5.34 | 80.9 | 17.92 | 0.064 |

20 | 1.66 | 5.54 | 28.9 | 5.24 | 0.268 |

23 | 4.14 | 5.28 | 78.13 | 0.038 | 0.073 |

26 | 1.88 | 5.16 | 36 | 0.953 | 0.467 |

28 | 2.08 | 5.22 | 39.8 | 0.224 | 2.34 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Ruiz-Abellón, M.C.; Fernández-Jiménez, L.A.; Guillamón, A.; Falces, A.; García-Garre, A.; Gabaldón, A.
Integration of Demand Response and Short-Term Forecasting for the Management of Prosumers’ Demand and Generation. *Energies* **2020**, *13*, 11.
https://doi.org/10.3390/en13010011

**AMA Style**

Ruiz-Abellón MC, Fernández-Jiménez LA, Guillamón A, Falces A, García-Garre A, Gabaldón A.
Integration of Demand Response and Short-Term Forecasting for the Management of Prosumers’ Demand and Generation. *Energies*. 2020; 13(1):11.
https://doi.org/10.3390/en13010011

**Chicago/Turabian Style**

Ruiz-Abellón, María Carmen, Luis Alfredo Fernández-Jiménez, Antonio Guillamón, Alberto Falces, Ana García-Garre, and Antonio Gabaldón.
2020. "Integration of Demand Response and Short-Term Forecasting for the Management of Prosumers’ Demand and Generation" *Energies* 13, no. 1: 11.
https://doi.org/10.3390/en13010011