# Multi-Labeled Recognition of Distribution System Conditions by a Waveform Feature Learning Model

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Modeling the Power Signals and Acquisition Processes

#### 2.1. Field-Measured Waveform Data Processing

#### 2.2. Modeling Disturbance Waveforms

#### 2.3. Symmetrical Component Processing

^{c}is determined as:

#### 2.4. Signal Filtering for Feature Extraction

#### 2.5. Waveform Representation with Variable Windows

_{w}is the updated sampling window. The variable window ${{r}_{w}}^{\infty}$ is determined as ${r}_{w}=r\xb7{g}^{\alpha}$, where $g$ and $\alpha $ denote the base window width and incremental parameter, respectively. As indicated by the window reset condition, the incremental sequence $\alpha $ is derived as follows:

#### 2.6. Feature Modeling and Extraction

## 3. Learning for Waveform Pattern Recognition

#### 3.1. Using OS-ELM with Condition Signals

_{o}is constrained selectively; and the extracted features of the signal ${\mathrm{x}}_{n}{=\mathrm{W}}_{n}\xb7{\mathsf{\Phi}}_{n}^{m}$ with the feature weight W

_{n}and t

_{n}are the labeled classes of disturbances. The initial data size implies the hidden node has a certain condition requiring that the rank of the initial network be defined as ${N}_{0}\ge L,$ to retain the learning performance in batch ELM [36]. The hidden layer output matrix ${\mathrm{H}}_{0}$ with the determined $L$ layers in terms of features is modeled as:

#### 3.2. Condition Classification Model Process

## 4. Model Validation

## 5. Discussion and Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**On-field waveform acquisition devices (sensors). (

**a**) A DL measuring unit location; (

**b**) Feeder remote terminal unit allocations on DLs.

**Figure 7.**Feature value distributions of classified disturbance types and trigger conditions. (

**a**) Model-generated waveforms; (

**b**) Field obtained voltage waveforms and its classification; (

**c**) Field obtained current waveforms and its classification.

Types | Models |
---|---|

Magnitude (1-norm) | ${\mathsf{\Phi}}_{n}^{1}={\Vert {\mathbf{s}}_{c,q}\Vert}_{1},\text{\hspace{1em}}\forall c,q$ |

Signal deviation | ${\mathsf{\Phi}}_{n}^{2}={\displaystyle {\sum}_{w=1}^{W}{\displaystyle {\sum}_{q=1}^{{r}_{w}}{\left({s}_{w,q}-{\overline{s}}_{w}\right)}_{}^{2}}}$ |

Disturbance duration | ${\mathsf{\Phi}}_{n}^{3}={\displaystyle {\sum}_{t=1}^{T}\left|{s}_{t}\right|}/T$ |

Zero crossing counts | ${\mathsf{\Phi}}_{n}^{4}={\displaystyle {\sum}_{t=1}^{T}\left|\mathrm{sign}\left({s}_{t-1}\right)-\mathrm{sign}\left({s}_{t}\right)\right|}/C$ |

Window average | ${\mathsf{\Phi}}_{n}^{5}={\displaystyle {\sum}_{w=1}^{W}\left|{\overline{s}}_{w}\right|}$ |

Window peak values | ${\mathsf{\Phi}}_{n}^{6}={\displaystyle {\sum}_{w=1}^{W}\mathrm{max}({\mathbf{s}}_{w})}$ |

Window differential | ${\mathsf{\Phi}}_{n}^{7}={\displaystyle {\sum}_{w=1}^{W}\left|\mathrm{diff}[\mathrm{max}({\mathbf{s}}_{w})]\right|}$ |

Cycle RMS deviation^{a} | ${\mathsf{\Phi}}_{n}^{8}={({s}_{\mathrm{rms},c}-{\overline{\mathbf{s}}}_{\mathrm{rms}})}^{2}$ |

Peak to RMS | ${\mathsf{\Phi}}_{n}^{9}=\mathrm{peaktorms}({\mathbf{s}}_{c,q})$ |

Amplitude of waveforms | $\begin{array}{l}{\mathsf{\Phi}}_{n}^{10}=\stackrel{\xb7}{\mathrm{statelevel}}[{({\mathbf{s}}_{t})}^{T}]\\ \text{\hspace{1em}\hspace{1em}}-\underset{\xb7}{\mathrm{statelevel}}[{({\mathbf{s}}_{t})}^{T}],\text{}{s}_{t}0\end{array}$ |

^{a}Root mean square follows the standard one cycle calculation.

Class | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | ||
---|---|---|---|---|---|---|---|---|---|---|

Types | Steady | Fluc. | Swell | Int. | Flicker | Osc. | Notch | Har. | Total | |

Voltage changes | V | 57 | 620 | 221 | 30 | 164 | 456 | 316 | 115 | 1979 |

I | 48 | 732 | 27 | 4 | 65 | 953 | 117 | 33 | 1979 | |

Fault currents | V | 15 | 79 | 40 | 13 | 35 | 190 | 41 | 124 | 537 |

I | 5 | 15 | 24 | 68 | 133 | 79 | 169 | 44 | 537 | |

Abnormal triggers | V | 972 | 2450 | 140 | 26 | 50 | 548 | 96 | 111 | 4393 |

I | 123 | 1658 | 36 | 11 | 125 | 2339 | 66 | 35 | 4393 |

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**MDPI and ACS Style**

Moon, S.-K.; Kim, J.-O.; Kim, C.
Multi-Labeled Recognition of Distribution System Conditions by a Waveform Feature Learning Model. *Energies* **2019**, *12*, 1115.
https://doi.org/10.3390/en12061115

**AMA Style**

Moon S-K, Kim J-O, Kim C.
Multi-Labeled Recognition of Distribution System Conditions by a Waveform Feature Learning Model. *Energies*. 2019; 12(6):1115.
https://doi.org/10.3390/en12061115

**Chicago/Turabian Style**

Moon, Sang-Keun, Jin-O Kim, and Charles Kim.
2019. "Multi-Labeled Recognition of Distribution System Conditions by a Waveform Feature Learning Model" *Energies* 12, no. 6: 1115.
https://doi.org/10.3390/en12061115