# Framework Integrating Lossy Compression and Perturbation for the Case of Smart Meter Privacy

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## Abstract

**:**

## 1. Introduction

## 2. State of the Art

#### 2.1. Data Compression in General

#### 2.2. Protection of Privacy Power Usage

#### 2.3. Compression Approaches for Privacy Power Usage

#### 2.4. Perturbation with Gaussian Distribution Encoding

## 3. Approach 1: Compression and Classification Based Smart Meter Privacy

#### 3.1. Lossy Compression Methodologies

#### 3.1.1. Triangular Function Algorithm (TFA)

**(I)**Import the whole dataset and choose preferred percentiles (e.g.,: ${Q}_{1}$, ${Q}_{99}$).

**(II)**Determine percentiles and store these data points ${y}_{iQ},{x}_{iQ},$. The remainder of the dataset will be smoothed by the moving average filter.

**(III)**Read a step width of ${a}_{0}$ data points.

**(IV)**Perform a least square fit $\Lambda $ to generate the intercept ${b}_{0}$ and slope ${b}_{1}$, see Equation (1).

**(V)**Read the next data point ${y}_{i}$ and check if its value is within ±m$\sigma $ (unbiased standard deviation $\sigma $ with factor m) of the predicted values in Equation (2). If yes, jump to (III), otherwise start a new segment and go to (IV).

**(VI)**In order to complete the algorithm, insert percentiles (${y}_{iQ}$, ${x}_{iQ}$) after the compression of the complete dataset. A schematic overview of the approach is shown in Figure 2. A detailed explanation of a simplified methodology of this TFA can be found in [34].

#### 3.1.2. Rectangular Function Algorithm (RFA)

#### 3.1.3. Singular Value Decomposition (SVD)

#### 3.1.4. Wavelet Transform (WT)

#### 3.2. Classification of the Compressed Dataset

## 4. Approach 2: Perturbation with Gaussian Distribution Based Smart Meter Privacy

#### 4.1. General Approach

#### 4.2. Comparison to Approach 1

## 5. Evaluation

#### 5.1. Description of Evaluation and Key Metrics

#### 5.2. Dataset

## 6. Results and Discussion

#### 6.1. Approach 1: Compression and Classification Approach

#### 6.2. Approach 2: Gaussian Distribution Approach

## 7. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

AF | All Features |

DF | Distorted Features |

DGO | Distribution Grid Operator |

FC | Fully Connected |

GDA | Gaussian Distribution Approach |

LSTM | Long Short-Term Memory |

NILM | Non-Intrusive Load Monitoring |

OTF | Optimal-Transmission-Factor |

RFA | Rectangular Function Algorithm |

SVD | Singular Value Decomposition |

TFA | Triangular Function Algorithm |

WT | Wavelet Transform |

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**Figure 3.**Temporal LSTM (long short-term memory)-FC (fully connected) classification network (

**a**) and unit configuration (

**b**).

**Figure 5.**Probability of the TFA (triangular function algorithm) (

**a**), RFA (rectangular function algorithm) (

**b**), SVD (singular value decomposition) (

**c**) and WT (wavelet transformation) method (

**d**).

**Figure 6.**Feature detection results of approach 1 (mean values over one day), top: without LMF (linear mean filter), bottom: using the LMF.

Properties Smart Meter | |
---|---|

Smart meter, read out from remote location | 109 |

Time series resolution | 15-min |

Transferred accounting data | Active energy |

Transferred energy network data | $U,I,f,P,Q$ |

Transmission technique | GSM, GPRS |

Transmitted data (daily) | 157,248 data points |

TFA | RFA | SVD | WT | |
---|---|---|---|---|

$C{R}_{\overline{\mathbf{DS}}}$ | 20.1 | 20.4 | 20.5 | 20.4 |

time ($C{R}_{\overline{\mathbf{DS}}}$) | 35.6 s | 1.7 s | 38.1 s | 4.3 s |

$Ac{c}_{\mathbf{DS}}$ | 0.68 | 0.70 | 0.69 | 0.70 |

$OT{F}_{\mathbf{DS}}$ | 13.67 | 14.28 | 14.15 | 14.28 |

DF/AF | DF/AF after LMF | |
---|---|---|

Original | 100.00% | - |

Approach 1: Attack during transmission | ||

TFA, RFA, SVD, WT | <0.01% | <0.05% |

Approach 1: Attack after decompression | ||

TFA | 80.29% | 79.88% |

RFA | 78.74% | 79.29% |

SVD | 79.27% | 79.65% |

WT | 80.97% | 79.45% |

Approach 2: Attack during transmission | ||

DSF = 5 | 4.10% | 14.84% |

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**MDPI and ACS Style**

Plenz, M.; Dong, C.; Grumm, F.; Meyer, M.F.; Schumann, M.; McCulloch, M.; Jia, H.; Schulz, D.
Framework Integrating Lossy Compression and Perturbation for the Case of Smart Meter Privacy. *Electronics* **2020**, *9*, 465.
https://doi.org/10.3390/electronics9030465

**AMA Style**

Plenz M, Dong C, Grumm F, Meyer MF, Schumann M, McCulloch M, Jia H, Schulz D.
Framework Integrating Lossy Compression and Perturbation for the Case of Smart Meter Privacy. *Electronics*. 2020; 9(3):465.
https://doi.org/10.3390/electronics9030465

**Chicago/Turabian Style**

Plenz, Maik, Chaoyu Dong, Florian Grumm, Marc Florian Meyer, Marc Schumann, Malcom McCulloch, Hongjie Jia, and Detlef Schulz.
2020. "Framework Integrating Lossy Compression and Perturbation for the Case of Smart Meter Privacy" *Electronics* 9, no. 3: 465.
https://doi.org/10.3390/electronics9030465