# A Study on Fundamental Waveform Shapes in Microscopic Electrical Load Signatures

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## Abstract

**:**

## 1. Introduction

## 2. Background and Related Work

## 3. Preliminary Feasibility Study

- We determine the zero-crossings of the voltage channel in order to delineate the mains periods from each other. By separating the current signal at all temporal offsets where voltage zero-crossings with a positive slope are encountered, we ensure that the resulting current waveform fragments are exactly one mains period long and their phase shift (if any) is retained.
- We remove all periods with RMS currents just above the transducer noise level ( 1 $\mathrm{m}$$\mathrm{A}$) from the data, in order to exclude data solely composed of transducer noise rather than an actual appliance operating current.
- We determine the single most representative waveform from the data by using a k-means clustering algorithm with $k=1$. This step yields the template shown as a highlighted line in Figure 2b.

## 4. Data Processing Steps and System Design

#### 4.1. Preparing Data for the Template Extraction

#### 4.2. Template Identification by Clustering

- The clustering method used to combine similar waveforms into the same cluster,
- the required dis-similarity between clusters (i.e., their distance), and
- the metric to compute the similarity of two elements.

#### 4.3. Dissecting Aggregated Data into Parametric Templates

## 5. Evaluation

#### 5.1. Selecting the Input Data

#### 5.2. Determining the Minimum Required Number of Templates

#### 5.3. Single Appliance Approximation Accuracy

#### 5.4. Aggregated Appliance Approximation Accuracy

#### 5.5. Choice of the Heuristic

## 6. Conclusions and Outlook

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

AC | Alternating Current |

HAC | Hierarchical Agglomerative Clustering |

NILM | Non-Intrusive Load Monitoring |

PUP | Partial Usage Pattern |

RMS | Root Mean Square |

RMSE | Root Mean Square Error |

SAX | Symbolic Aggregate approXimation |

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**Figure 2.**Superposition of voltage and current waveforms during the appliance activity. The current waveform crosses the zero value slightly after the voltage’s zero-crossings, indicating a phase shift. (

**a**)Voltage waveforms; (

**b**) Current waveforms.

**Figure 3.**Approximation of the electrical current by amplitude-scaled copies of the waveform at the cluster center (the highlighted line in Figure 2b), plotted alongside the corresponding scaling factors and resulting reconstruction error.

**Figure 4.**Processing flow for the extraction and detection of templates in microscopic load signatures.

**Figure 5.**Observed RMSE values for eight distance/similarity metric combinations in relation to the number of templates extracted from the input data.

**Figure 6.**Dendrogram when running the hierarchical clustering method on the COOLL data set. The highlighted line depicts a minimum cluster distance value of 250, such that seven clusters are being returned. Values for distances below 50 were removed from the diagram for the sake of visual clarity. The horizontal highlighted line demarcates one possible threshold choice to yield seven templates.

**Figure 7.**Visualization of the seven most representative templates extracted for the COOLL data set; besides the highlighted template trajectories, the plots show the contributing waveforms in light color.

**Figure 8.**Example for the greedy heuristic to approximate the waveform of a planer appliance by means of parametric templates. (

**a**) A single input cycle vs. its parameterized template representation; only a small difference exists between the two; (

**b**) Distribution of RMSE values.

**Figure 9.**Resulting averaged RMSE versus the number of output clusters for the considered data sets.

**Figure 10.**Absolute reconstruction RMSE for each appliance type. (

**a**) COOLL data set (using a library size of 7 templates); (

**b**) WHITED data set (using 23 templates).

**Figure 11.**Reconstruction RMSE relative to each appliance’s nominal input current ${I}_{RMS}$ for each appliance type. (

**a**) COOLL data set (using 7 templates); (

**b**) WHITED data set (using 23 templates).

**Figure 12.**Results of the greedy optimization approach to approximate the superimposed current waveforms of a drill and a fan appliance by means of parametric templates. (

**a**) Aggregation of input data from two electrical appliances as well as a visualization of their reconstruction from templates; (

**b**) Distribution of RMSE values.

**Figure 13.**Resulting averaged RMSE versus the absolute number of templates used to represent the aggregation of COOLL data from two or three appliances each.

**Figure 14.**Results of the complete optimization approach to approximate the superimposed current waveforms of a drill and a fan appliance by means of parametric templates. (

**a**) Aggregation of input data from the same two electrical appliances as before, as well as a visualization of their reconstruction from templates; (

**b**) Distribution of RMSE values.

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## Share and Cite

**MDPI and ACS Style**

Younis, R.; Reinhardt, A.
A Study on Fundamental Waveform Shapes in Microscopic Electrical Load Signatures. *Energies* **2020**, *13*, 3039.
https://doi.org/10.3390/en13123039

**AMA Style**

Younis R, Reinhardt A.
A Study on Fundamental Waveform Shapes in Microscopic Electrical Load Signatures. *Energies*. 2020; 13(12):3039.
https://doi.org/10.3390/en13123039

**Chicago/Turabian Style**

Younis, Raneen, and Andreas Reinhardt.
2020. "A Study on Fundamental Waveform Shapes in Microscopic Electrical Load Signatures" *Energies* 13, no. 12: 3039.
https://doi.org/10.3390/en13123039