# Quantifying the Opportunity Limits of Automatic Residential Electric Load Shaping

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## Abstract

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## 1. Introduction

## 2. Literature Review

## 3. Methodology

#### 3.1. Data and Methods

#### 3.2. Modeling TCL Behaviour Using NEEA RBSA Data

#### 3.3. Scaling Up the NEEA RBSA Dataset

## 4. Results

#### 4.1. Residential Appliance Load Profiles

#### 4.2. Residential Load Shaping Opportunities

#### 4.3. Spectral Visualization and Simulation of Appliance Loads

## 5. Conclusions and Outlook for Future Work

## Supplementary Materials

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Energy usage of TCL appliances on 3–4 July 2012, showing kWh per 15-min interval. House numbers appear after appliance names and vertical dashed lines separate days. Note diversity in energy usage along axes: (

**a**) two refrigerators, the one at right with a long run times in evenings and higher peak use; (

**b**) two freezers, the one at right with nearly symmetric run times and lower peak use; and (

**c**) two DHW heaters with typically low run times, the one at right with higher peaks.

**Figure 2.**Example diagram of wavelet decomposition and aggregation using the enhanced WARM. Whereas the standard Fourier transform is localized in frequency, wavelets are localized in both frequency and time.

**Figure 3.**Boxplots of TCL appliance annual energy use. Mean values are shown in red. Values below each plot indicate the number of appliances, sample observations, and average duty cycle from Q2 2012–Q1 2013 inclusive. Note the wide range of diversity, particularly among refrigerators and freezers.

**Figure 4.**Bounds of electric energy usage for heating DHW over interval 00:00 to 00:15 on 04-01-2012. Moving left to right towards more houses being sampled, note the tighter bounds, fewer outliers, and the median values approaching the mean energy usage of all electric water heaters.

**Figure 5.**Electric DHW heater energy usage in RBSA home 10388 per 15-min interval and per day from Q2 2012–Q1 2013 inclusive. Usage is representative of observations of electric DHW heaters in other homes.

**Figure 6.**DHW heater energy usage in RBSA home 10388 per hour of day from Q2 2012–Q1 2013 inclusive. Note that there were more outliers but lower interquartile variance in early morning hours.

**Figure 7.**A WARM-based curve fit of 5 a.m. hourly energy usage of DHW heater in RBSA home 10388 from Q2 2012–Q3 2012 inclusive. Prediction errors in the $ON$ state are depicted by the vertical offset between the observed value at the top of each bar and its corresponding wavelet reconstructed value denoted as a red dot; errors in the $OFF$ states include non-zero values viewed along the day-axis.

**Figure 8.**Energy usage profile in 15-min intervals of RBSA home 13019. The black line denotes the electric service for the whole-building. The vertical distance from the black line down to the green line is the instantaneous load that could be shed. The vertical distance from the black line up to the red line is the instantaneous load that could be added. The energy usage of 2 refrigerators and a freezer are depicted by purple, light blue, and dark blue dashed lines at the bottom of the graph. RBSA home 13019 is representative of homes with gas DHW heaters.

**Figure 9.**Aggregate load profile of 14 homes at 15-min intervals. The vertical distance from the black line down to the green line is the instantaneous load that could be shed. The vertical distance from the black line up to the red line is the instantaneous load that could be added. The large red spikes indicate significant load adding opportunities, e.g., after completion of morning DHW heating. Greater mid-day and evening load shaping opportunities were also evident.

**Figure 10.**Plots for the DHW heater in RBSA home 22284, from April 2012–April 2014 inclusive. At left, red denotes periods of greater hot water use. Red along the 24-h period indicates sustained diurnal use, which is also shown in the companion graph at right by the peak next to the left arrow. Less red at far left indicates less hot water was used in the 24-hour (and greater periods) from April through September 2012. Non-stationary usage was also observed in other homes and appliances.

**Figure 11.**Simulation of the wavelet decomposed 5 a.m. hourly energy usage by DHW heater in RBSA home 13088 from Q2 2012–Q1 2013 inclusive, using the phase randomization method.

**Figure 12.**Simulation of the wavelet decomposed 5 a.m. hourly energy usage by DHW heater in RBSA home 13088 from Q2 2012–Q1 2013 inclusive, using the Autoregressive method.

**Figure 13.**Simulation of the wavelet decomposed 5 a.m. hourly energy usage by DHW heater in RBSA home 13088 from Q2 2012–Q1 2013 inclusive, using the ARIMA method.

**Figure 14.**Comparison of phase randomization and ARIMA simulation techniques of the wavelet decomposed 5 a.m. hourly energy usage by DHW heater in RBSA home 13088 from Q2 2012–Q1 2013 inclusive.

**Figure 15.**Boxplots of mean and variance comparing the performance of reconstruction methods in simulating the 5 a.m. hourly energy usage by the electric DHW heater in RBSA home 13088, from Q2 2012–Q1 2013 inclusive. Statistics of empirical observations are denoted by red dots. For mean and variance, phase randomization provided superior performance.

**Figure 16.**Boxplots of skew and kurtosis comparing the performance of reconstruction methods in simulating the 5 a.m. hourly energy usage by the electric DHW heater in RBSA home 13088, from Q2 2012–Q1 2013 inclusive. Statistics of empirical observations are denoted by red dots. For skew and kurtosis, the phase randomization method had somewhat better performance.

**Figure 17.**Boxplots of maximum, minimum and sum compared the performance of reconstruction methods in simulating the 5 a.m. hourly energy usage by the electric DHW heater in RBSA home 13088, from Q2 2012–Q1 2013 inclusive. Statistics of empirical observations are denoted by red dots. Note: (a) the significant variances in the maximum statistic would adversely affect load shaping calculations, (b) the minimum statistic included unrealistic negative values, and (c) Mean values of zero in the AR and ARIMA sum statistics were unrealistic.

**Table 1.**Sample DHW heater non-overlapping setpoints. The `Not modeled’ entries reflect model constraints that limit operation between 120 and 130 F inclusive.

Temp. F | High $/kWh | Low $/kWh |
---|---|---|

131 and above | Not modeled | Not modeled |

130 | Always OFF | Turn Off |

129 | Always OFF | Stay ON |

128 | Always OFF | Stay ON |

127 | Always OFF | Stay ON |

126 | Always OFF | Stay ON |

125 | Turn OFF | Turn ON |

124 | Stay ON | Always OFF |

123 | Stay ON | Always OFF |

122 | Stay ON | Always OFF |

121 | Stay ON | Always OFF |

120 | Turn ON | Always OFF |

119 and below | Not modeled | Not modeled |

**Table 2.**Load-shaping opportunities across 15-min intervals for Home 13019 for the first six hours during 1 April 2012.

Opportunities | Maximum | Minimum | Mean |
---|---|---|---|

Increase load [kW] | 0.80 | 0.36 | 0.59 |

Decrease load [kW] | 0.64 | 0.30 | 0.44 |

© 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**

Cruickshank, R.; Henze, G.; Balaji, R.; Hodge, B.-M.; Florita, A.
Quantifying the Opportunity Limits of Automatic Residential Electric Load Shaping. *Energies* **2019**, *12*, 3204.
https://doi.org/10.3390/en12173204

**AMA Style**

Cruickshank R, Henze G, Balaji R, Hodge B-M, Florita A.
Quantifying the Opportunity Limits of Automatic Residential Electric Load Shaping. *Energies*. 2019; 12(17):3204.
https://doi.org/10.3390/en12173204

**Chicago/Turabian Style**

Cruickshank, Robert, Gregor Henze, Rajagopalan Balaji, Bri-Mathias Hodge, and Anthony Florita.
2019. "Quantifying the Opportunity Limits of Automatic Residential Electric Load Shaping" *Energies* 12, no. 17: 3204.
https://doi.org/10.3390/en12173204