A Clustering Framework for Residential Electric Demand Profiles M. - - PowerPoint PPT Presentation

A Clustering Framework for Residential Electric Demand Profiles

• M. Jain1,2, T. AlSkaif3, and S. Dev1,2

1 UCD School of Computer Science, Dublin, Ireland 2 ADAPT SFI Research Centre, Dublin, Ireland 3 Wageningen University and Research, Wageningen, The Netherlands

Send correspondence to M.Jain, e-mail: mayank.jain@adaptcentre.ie

Dataset Clustering Framework Validation

Introduction

‚ Availability of huge amount of electricity consumption data made possible due to large scale adoption of smart-meter systems. ‚ This data is available with high temporal resolutions, often half-hourly or hourly. ‚ Crucial task of analyzing energy consumption patterns in the residential areas is now possible with this data. ‚ Clustering households based on their electricity consumption trends is an important step in this analysis. ‚ A 2-step clustering framework is defined and an objective validation strategy to validate and compare different frameworks is proposed.

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Dataset Clustering Framework Validation

PARENT Project

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00

Time Of The Day

500 1000 1500 2000 2500

Renewable Load Consumption (Watts)

Median of Raw Data Normalized Median (Scaled Up by 1000) 00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00

Time Of The Day

500 1000 1500 2000

Renewable Load Consumption (Watts)

Median of Raw Data Normalized Median (Scaled Up by 1000)

Box-plots of daily consumption pattern for 2 different households, also depicting the median and the scaled up version of normalized median.

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Dataset Clustering Framework Validation

Pre-processing the Dataset

Nomenclature: n Number of households r Hourly resolution of original data d1 Optimal number of reduced dimensions k Optimal number of clusters

Algorithm 1: Pre-Processing the Dataset

1 n Ð number of households 2 r Ð hourly resolution of original data 3 d Ð 24{r (dimensionality) 4 Mnˆd Ð median daily consumption of each household stored

row-wise

5 M1 1 1 nˆd Ð ℓ2-Normalization(M, row-wise) 6 return M1 1 1

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Dataset Clustering Framework Validation

Clustering Framework

Unsupervised Dimensionality Reduction Unsupervised Clustering Determine number

• f dimensions in
• utput

Determine optimal number of clusters

Generalized Clustering Framework

In this work, ‚ 2 dimensionality reduction algorithms - elbow heuristics at intermediate stage ‚ 2 clustering algorithms - gap statistics at intermediate stage 6 d1

FA “ 7; d1 PCA “ 7; and

kFA`SC “ 7; kFA`KMC “ 7; kPCA`SC “ 7; kPCA`KMC “ 7

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Dataset Clustering Framework Validation

Objective Validation Strategy

Algorithm 2: Objective Validation Strategy

1 p Ð number of partitions for each household 2 distp¨, ¨q Ð function to calculate Euclidean distance

Ź Output from clustering algorithm

3 labels Ð labels assigned to each household 4 Cpkˆd1q Ð cluster centers of each cluster 5 Initialize:

match, misMatch, counter “ 0;

6 repeat 7

foreach household do

8

D Ð data for each household (daysˆ24/r);

9

D’ Ð randomly shuffled data by rows;

10

Make p equal partitions from rows of D’; Ź Perform Pre-Processing steps

11

Mppˆp24{rqq

p

Ð new medians of p partitions;

12

M1

p Ð ℓ2-Normalization(Mp, row-wise);

Ź Do Dimensionality Reduction

13

Nppˆd1q

p

Ð dimReduce(M1

p, d1); 14

foreach partition P t1 ¨ ¨ ¨ pu as part do Ź Find Closest Cluster

15

CC Ð argminipdistpNprparts, C [i, :]qq;

16

if CC ““ labels rhouseholds then

17

match++;

18

else

19

misMatch++;

20

counter++;

21 until counter ă 100; 22 avgMatches “ match{100; 23 avgMisMatches “ misMatch{100;

Result: avgMatches & avgMisMatches

Results obtained by performing objective validation of the 4 clustering frameworks.

Clustering Framework %Matches %Mis-Matches p = 2 FA ` SC 22.67 77.33 FA ` KMC 29.07 70.93 PCA ` SC 18.78 81.22 PCA ` KMC 76.28 23.72 p = 3 FA ` SC 21.34 78.66 FA ` KMC 24.98 75.02 PCA ` SC 17.60 82.40 PCA ` KMC 67.15 32.85 SEST2020 Istanbul Clustering Framework 5/7

Dataset Clustering Framework Validation

Subjective Validation

: 1 : 2 : 3 : 4 : 5 : 6 : 7 : 8 : 9 : 1 : 1 1 : 1 2 : 1 3 : 1 4 : 1 5 : 1 6 : 1 7 : 1 8 : 1 9 : 2 : 2 1 : 2 2 : 2 3 :

Time Of The Day

0.0 0.1 0.2 0.3 0.4 0.5 0.6

Load Consumption (Watts) - Normalized Daily profile of House ID 5 Daily profile of House ID 8

: 1 : 2 : 3 : 4 : 5 : 6 : 7 : 8 : 9 : 1 : 1 1 : 1 2 : 1 3 : 1 4 : 1 5 : 1 6 : 1 7 : 1 8 : 1 9 : 2 : 2 1 : 2 2 : 2 3 :

Time Of The Day

0.0 0.1 0.2 0.3 0.4 0.5 0.6

Load Consumption (Watts) - Normalized Daily profile of House ID 9 Daily profile of House ID 10 Daily profile of House ID 20

Two sample clusters as identified by the recommended framework

: 1 : 2 : 3 : 4 : 5 : 6 : 7 : 8 : 9 : 1 : 1 1 : 1 2 : 1 3 : 1 4 : 1 5 : 1 6 : 1 7 : 1 8 : 1 9 : 2 : 2 1 : 2 2 : 2 3 :

Time Of The Day

0.0 0.1 0.2 0.3 0.4 0.5 0.6

Load Consumption (Watts) - Normalized Daily profile of House ID 0 Daily profile of House ID 1 Daily profile of House ID 5 Daily profile of House ID 7 Daily profile of House ID 8

: 1 : 2 : 3 : 4 : 5 : 6 : 7 : 8 : 9 : 1 : 1 1 : 1 2 : 1 3 : 1 4 : 1 5 : 1 6 : 1 7 : 1 8 : 1 9 : 2 : 2 1 : 2 2 : 2 3 :

Time Of The Day

0.0 0.1 0.2 0.3 0.4 0.5 0.6

Load Consumption (Watts) - Normalized Daily profile of House ID 0 Daily profile of House ID 1 Daily profile of House ID 7 Daily profile of House ID 13 Daily profile of House ID 14 Daily profile of House ID 17

Sample ill-defined clusters from other frameworks (left: PCA`SC; right: FA`KMC)

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Conclusion

Contributions: ‚ Defined a 2-step generalized clustering framework ‚ Proposed a novel objective validation strategy to compare results of different frameworks ‚ Cross-verified the recommendations by subjective validation Future work: ‚ Gather data for longer duration to incorporate seasonal variations in consumption behaviour ‚ Consider more algorithms used in more recent studies ‚ Compare results of the proposed objective validation strategy with more standard clustering validation indices

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