# Realistic Nudging through ICT Pipelines to Help Improve Energy Self-Consumption for Management in Energy Communities

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## Abstract

**:**

## 1. Introduction

## 2. Background Material and Contributions

#### 2.1. Related Works

#### 2.2. Problem Statement

#### 2.3. Contributions

- First, we show numerically that, even with scarce information, and even when sending nudges with a few labelled periods, we manage to achieve significant consumption improvements.
- Second, we show numerically that, in some situations which we characterise, a load-forecasting based nudging pipeline outperforms the mere “weather based” one, which targets periods with high sunshine.
- Third, we identify two important aspects concerning the efficiency of our procedure:
- (a)
- There is a sweet spot in production, at which nudging is most efficient;
- (b)
- Increasing the number of labelled periods in the nudges increases performance, but this increase levels off, and huge improvements already occur for a few periods.

## 3. Model

#### 3.1. Household

**Household consumption.**We consider a household which possesses several electrical appliances. Each appliance consumes energy as it is used. The consumption of an appliance is a positive sequence ${\mathbf{l}}_{\mathrm{app}}={\left(\right)}_{{l}_{t}}t\in \mathbb{T}$, together with a finite family of non-overlapping intervals ${\left(\right)}_{{t}_{\mathrm{begin}}^{k}}$, with bounds in $\mathbb{T}$. The ${t}_{\mathrm{begin}}^{k}$ are the times of the beginning of the appliance usages, and the ${t}_{\mathrm{end}}^{k}$ are the ends of the usages. The load ${l}_{t}$ is non-zero if, and only if, there is a k (uniquely defined) such that ${t}_{\mathrm{begin}}^{k}<t<{t}_{\mathrm{end}}^{k}$. All residual consumption of all appliances is gathered in the “mains” appliance. The household consumption $\mathcal{L}={\left(\right)}_{{\mathbf{l}}^{\mathrm{app}}}\mathrm{app}\in \mathrm{appliances}$ is the family of appliance consumptions. The aggregate load at time t, ${L}_{t}$, is the sum over all appliances of the load at time t of each appliance, ${L}_{t}={\sum}_{t}{l}_{t}^{\mathrm{app}}$.

**Shiftable appliances.**An appliance may be as follows:

- Shiftable, meaning the household may be willing to shift its usage intervals, provided these periods are not too far away from the base use time, which depends on the appliance; the length of usage intervals, that is, the values ${t}_{\mathrm{end}}^{k}-{t}_{\mathrm{begin}}^{k}$, remain fixed.
- Not shiftable, meaning the times at which the appliance are used are fixed.

**Solar energy production.**Photovoltaic panels provide the building with the energy ${p}_{t}$ at time t. If it is not enough to cover ${L}_{t}$, the building feeds itself on the regular network to cover ${L}_{t}-{p}_{t}$. If ${p}_{t}>{L}_{t}$, excess production is “lost”. No storage capacity is used. At each time $t\in \mathbb{T}$, a smart meter measures the aggregate load ${L}_{t}$, as well as the solar production.

#### 3.2. Self-Consumption and Self-Sufficiency Rates

**Definition 1**

**.**For a household consumption $\mathcal{L}$, and two dates ${t}_{\mathrm{begin}}<{t}_{\mathrm{end}}$, we call the self-consumption rate between ${t}_{\mathrm{begin}}$ and ${t}_{\mathrm{end}}$ the ratio of self-consumption to the total production:

#### 3.3. Nudge

**Definition 2**

**.**We call the green period a tuple $\left(\right)$, where ${t}_{\mathrm{begin}},{t}_{\mathrm{end}}\in \mathbb{T}$ are the beginning points and ${t}_{\mathrm{end}}={t}_{\mathrm{begin}}+2H$ are the end points of the period, and $\sigma \ge 0$ is the strength of the period. A nudge is a set of green periods. We write $\mathcal{N}$ for the set of nudges.

**Model of human behaviour upon nudge reception.**We use an ideal model, to evaluate the maximum ideal potential of our ICT pipelines. Upon reception of a nudge, the household people try to shift their consumption as follows. For every shiftable appliance, the following occurs:

- They check whether there are use intervals outside of the green periods;
- If so, for every green period, ranked according to their strength, they check whether shifting the use of the appliance to the green period is admissible (the new use interval is not too far away from the old use interval);
- If so, the consumption is shifted; else, nothing is done.

#### 3.4. Controllers

**Definition 3**

**.**A controller is a function taking as arguments weather forecasts and past household aggregate consumption data, and outputting a nudge, that is, a function

**Weather controller:**The first one is called “weather controller”. It takes as input the sunshine coefficient forecast for the coming week. It averages the predicted sunshine coefficient over 2 h periods. The strength parameter is set to these values. Namely, if ${\widehat{s}}_{t}$ is the forecast of the sunshine coefficient at time $t\in \mathbb{T}$, then the strength parameter at time ${t}_{\mathrm{begin}}$ equals

**Combined controller:**The second controller is called “combined controller”. It takes as inputs the sunshine coefficient forecast for the coming week, together with past aggregate consumption data, and past production data. It then uses load forecasting techniques to forecast excess production, that is, the difference between forecast production and forecast consumption (see Appendix C for details). It averages the predicted excess over 2 h periods, and sets the strength parameter to these averages. Finally, it outputs the three (say) best periods. Precisely, writing ${\widehat{l}}_{t}$ the forecast load at time t, and ${\widehat{p}}_{t}$ the forecast production at the same time, the predicted excess is

#### 3.5. Nudging Pipeline

## 4. Numerical Simulations

#### 4.1. Numerical Simulations Set-Up

**Synthetic data preparation.**We generated two synthetic datasets, representing two use cases: a commuting household (a commuting household refers to a group of individuals who live together in the same residence but travel to different locations for work or school, typically on a regular basis), and a non-commuting household (a non-commuting household refers to a group of individuals who live and work in the same place, without the need for regular travel to a workplace or school). The commuting household represents, for instance, the household of people going to work away from home but who have equipped their domestic electrical appliances with sensors, allowing them to launch, or stop, these appliances, remotely. The non-commuting household represents, for instance, the household of people working remotely.

**Real datasets preparation.**For the simulations using real datasets, we select a subset of appliances, which we define to be “shiftable”, and we fix their maximum shifting delay (see Table 2 for details). We divide each dataset into past data, on which we train our model, and future data, on which we conduct the simulation. Finally, we renormalise the data sampling steps to 30 min steps.

**Solar energy production.**As part of our simulator, we generate an artificial solar production as follows. We first simulate a sunshine coefficient as the product between the following:

- A value taking into account the time of day (representing the fact there is no sun at night);
- A value taking into account the month of year (representing the fact that the sun shines brighter during summer than winter);
- A value taking into account the amount of clouds (representing the fact that more clouds implies less light for photovoltaic panels).

**Controllers.**We use three controllers and an upper-bounding optimiser:

- The weather controller and combined controller, defined in Section 3.4, whose performance we want to assess.
- The “no control” controller, and the “OMEGAlpes” optimiser, described below, which we use as references.

**Simulation.**The simulations run over one month. For each setting, we run 20 simulations to account for the stochasticity of the production generation.

**Metrics displayed.**We display the self-consumption rates of the household, for the different controllers and OMEGAlpes. We also display the improvement of our controllers (self-consumption rate with the controller minus the self-consumption rate with no controller), as a percentage of the improvement of OMEGAlpes (self-consumption rate with OMEGAlpes minus self-consumption rate with no controller). For each statistic, we show its mean, as well as the 10–90% interval of values. The results for the self-production rates are similar to those with the self-consumption rate. We present them in Appendix B.

#### 4.2. Synthetic Data, Commuting Household

#### 4.3. Synthetic Data, Non-Commuting Household

#### 4.4. Iris Dataset and AMPds Dataset, Individual Building Simulation

#### 4.5. Iris Dataset, Collective Runs

#### 4.6. Influence of the Amount of Production

#### 4.7. Influence of the Number of Green Periods

## 5. Discussion and Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Appendix A. OMEGAlpes

#### Appendix A.1. OMEGAlpes Presentation

#### Appendix A.2. Self-Consumption System Modelling

Symbol | Description |
---|---|

t | The time period of optimisation, denoted by $t\in [{B}_{t},{E}_{t}]$, is defined as starting from ${B}_{t}$, the beginning of optimisation, and ending at ${E}_{t}$, the completion of optimisation. |

$\delta t$ | The change in time depends on the frequency/sample rate of the energy profile. |

${P}_{imp}$ | Power imported from the electric grid. |

${P}_{exp}$ | Power exported to the grid. |

${U}_{imp}$ | Network import status. It is a binary variable, a value of 1 indicates that the import from the grid is active, while a value of 0 indicates that the import from the grid is inactive. |

${U}_{exp}$ | Network export status. It is a binary variable, a value of 1 indicates that the export to the grid is active, while a value of 0 indicates that the export to the grid is inactive. |

${P}_{pv}$ | Power generated by the solar energy unit. |

${P}_{shift}$ | Power of the shiftable part of the total consumption. |

${U}_{shift}$ | Shiftable consumption status. It is a binary variable, a value of 1 indicates that the shiftable consumption is active, while a value of 0 indicates that there is no shiftable consumption. |

$St{p}_{shift}$ | The shiftable consumption start-up is represented by a binary variable. It equals 1 only when the shiftable consumption starts, i.e., when ${U}_{shift}$ changes from 0 to 1. |

${P}_{notshift}$ | Power of the non shiftable part of the total consumption. |

${E}_{shift}$ | Total shiftable consumption. |

${l}_{spp}$ | List of power profiles to shift. |

- Energy balance equation.

- Constraint equations.

- Objective equation.

## Appendix B. Self-Production Rates Results

**Synthetic data, efficiency of nudges**. We see on Table A2 that weather and combined controllers improve the self-production rate, in the case of synthetic data.**Synthetic data, production not correlated with excess**. When production is no longer correlated with excess production, the combined controller outperforms the weather controller: we see it in Table A3.**Iris dataset and AMPds dataset, individual building simulation**. Table A4 shows the performance results in the case of the Iris individual building and the AMPds building.**Iris dataset, collective runs**. We see in Table A5 the results averaged over all the buildings of the Iris dataset. The performance results are the same as for the self-consumption rate.**Influence of the amount of production**. Figure A2 shows that as the production level increases, the improvement in the self-production rate also increases; however, at a certain point (7000–8000 W), the increase in the self-production rate reaches a plateau and stops growing. All daylight consumption is already covered by solar production, so there is no longer room for improvement.**Influence of the Number of Green Periods**. Finally, we can see on Figure A3 that the efficiency of the nudges is already quite good for four periods.

**Table A2.**Mean self-production rate and mean improvement ratio with various controllers, synthetic data and general case.

Reference | Weather Controller | Combined Controller | OMEGAlpes | |
---|---|---|---|---|

Mean (%) | 25.17 | 28.91 | 29.01 | 33.35 |

Mean of improvement ratio (%) | 0 | 45.9 | 47.25 | 100 |

**Table A3.**Mean self-production rate and mean improvement ratio with various controllers, synthetic data, uncorrelated production and excess production.

Reference | Weather Controller | Combined Controller | OMEGAlpes | |
---|---|---|---|---|

Mean (%) | 22.36 | 22.79 | 23.53 | 24.85 |

Mean of improvement ratio (%) | 0 | 18.53 | 47.94 | 100 |

**Table A4.**Mean self-production rate, and mean improvement ratio, with various controllers, Iris 966 and AMPds.

Reference | Weather Controller | Combined Controller | OMEGAlpes | |
---|---|---|---|---|

Iris: Mean(%) | 22.53 | 23.83 | 24.25 | 28.63 |

AMPds: Mean (%) | 34.44 | 34.84 | 34.86 | 35.84 |

Iris: Mean of improvement ratio (%) | 0 | 21.37 | 27.99 | 100 |

AMPds: Mean of improvement ratio (%) | 0 | 27.74 | 29.72 | 100 |

**Table A5.**Mean of self-production rate and mean of the improvement ratio with various controllers, collective simulation on the Iris dataset.

Reference | Weather Controller | Combined Controller | OMEGAlpes | |
---|---|---|---|---|

Mean (%) | 28.07 | 28.75 | 28.93 | 32.16 |

Mean of improvement ratio (%) | 0 | 17.22 | 21.6 | 100 |

**Figure A2.**Augmentation of the self-production rate due to the combined controller (orange)/weather controller (blue) with respect to a reference with no controller as a function of the production.

**Figure A3.**Augmentation of the self-production rate due to the combined controller (orange)/weather controller (blue) with respect to a reference with no controller, as a function of the number of green periods by nudge.

## Appendix C. Load Forecasting

MAPE (%) | Prediction Capability | R2Score |
---|---|---|

<10 | Highly accurate prediction (HAP) | >0.9 |

10–20 | Good prediction (GPR) | 0.7–0.9 |

20–50 | Reasonable prediction (RP) | 0.4–0.7 |

>50 | Inaccurate prediction (IPR) | <0.4 |

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**Figure 2.**Augmentation of the self-consumption rate due to the combined controller (orange)/weather controller (blue) with respect to a reference with no controller, as a function of the production.

**Figure 3.**Augmentation of the self-consumption rate due to the combined controller (orange)/weather controller (blue) with respect to a reference with no controller as a function of the number of green periods by nudge.

Notation | Definition | Meaning |
---|---|---|

$\mathbb{T}$ | sequence $0\le {t}_{0}<{t}_{1}<\dots $ | time scale at which power is sampled |

${l}_{t}$ | ${l}_{t}\in {\mathbb{R}}_{+}$ | load of an appliance at time t |

${L}_{t}$ | ${L}_{t}\in {\mathbb{R}}_{+}$ | aggregate load at time t |

${p}_{t}$ | ${p}_{t}\in {\mathbb{R}}_{+}$ | solar production at time t |

${\mathsf{\Lambda}}_{{t}_{\mathrm{begin}},{t}_{\mathrm{end}}}$ | $0\le {\mathsf{\Lambda}}_{{t}_{\mathrm{begin}},{t}_{\mathrm{end}}}\le 1$ | self-consumption rate |

${\mathsf{\Pi}}_{{t}_{\mathrm{begin}},{t}_{\mathrm{end}}}$ | $0\le {\mathsf{\Pi}}_{{t}_{\mathrm{begin}},{t}_{\mathrm{end}}}\le 1$ | self-sufficiency rate |

$\mathcal{N}$ | - | nudge set |

${\mathcal{W}}_{{t}_{\mathrm{begin}},{t}_{\mathrm{end}}}$ | — | weather forecast set |

${\mathcal{H}}_{t}$ | - | past data at time t |

Shiftable Appliance | Maximum Shift Delay |
---|---|

Washing machine and clothes dryer | 540 min |

Dishwasher | 540 min |

Water heater for domestic hot water | 600 min * |

**Table 3.**Commuting household: mean self-consumption rate, and mean improvement ratio, with various controllers.

Reference | Weather Controller | Combined Controller | OMEGAlpes | |
---|---|---|---|---|

Mean (%) | 67.4 | 77.35 | 77.63 | 89.12 |

Mean of improvement ratio (%) | 0 | 45.9 | 47.25 | 100 |

**Table 4.**Non-commuting household: mean self-consumption rate, and mean improvement ratio, with various controllers.

Reference | Weather Controller | Combined Controller | OMEGAlpes | |
---|---|---|---|---|

Mean (%) | 89.01 | 90.9 | 93.82 | 99.08 |

Mean of improvement ratio (%) | 0 | 18.53 | 47.94 | 100 |

**Table 5.**Mean self-consumption rate, and mean improvement ratio, with various controllers, Iris and AMPds.

Dataset | Reference | Weather Controller | Combined Controller | OMEGAlpes |
---|---|---|---|---|

Mean (%) | ||||

Iris | 63.13 | 66.77 | 67.9 | 80.89 |

AMPds | 70.06 | 70.86 | 70.92 | 72.9 |

Mean of improvement ratio (%) | ||||

Iris | 0 | 21.37 | 27.99 | 100 |

AMPds | 0 | 27.73 | 29.72 | 100 |

**Table 6.**Mean of self-consumption rate and mean of the improvement ratio with various controllers, collective simulation on the Iris dataset.

Reference | Weather Controller | Combined Controller | OMEGAlpes | |
---|---|---|---|---|

Mean (%) | 62.21 | 63.78 | 64.23 | 72.25 |

Mean of improvement ratio (%) | 0 | 17.22 | 21.59 | 100 |

**Table 7.**Mean of self-consumption rate and mean of the improvement ratio with various controllers, collective simulation on the Iris subsets.

Dataset | Shiftable Appliances Number | Reference | Weather Controller | Combined Controller | OMEGAlpes |
---|---|---|---|---|---|

Mean (%) | |||||

Iris_1 | 1 | 54.4 | 54.97 | 55.18 | 58.45 |

Iris_2 | 2 | 66.77 | 68.64 | 69.1 | 78.51 |

Iris_3 | 3 or more | 60.91 | 64.16 | 65.31 | 81.32 |

Mean of improvement ratio (%) | |||||

Iris_1 | 1 | 0 | 16.32 | 20.86 | 100 |

Iris_2 | 2 | 0 | 18.43 | 22.86 | 100 |

Iris_3 | 3 or more | 0 | 15.40 | 19.37 | 100 |

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Ling, H.; Massé, P.-Y.; Rihet, T.; Wurtz, F.
Realistic Nudging through ICT Pipelines to Help Improve Energy Self-Consumption for Management in Energy Communities. *Energies* **2023**, *16*, 5105.
https://doi.org/10.3390/en16135105

**AMA Style**

Ling H, Massé P-Y, Rihet T, Wurtz F.
Realistic Nudging through ICT Pipelines to Help Improve Energy Self-Consumption for Management in Energy Communities. *Energies*. 2023; 16(13):5105.
https://doi.org/10.3390/en16135105

**Chicago/Turabian Style**

Ling, Haicheng, Pierre-Yves Massé, Thibault Rihet, and Frédéric Wurtz.
2023. "Realistic Nudging through ICT Pipelines to Help Improve Energy Self-Consumption for Management in Energy Communities" *Energies* 16, no. 13: 5105.
https://doi.org/10.3390/en16135105