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

A Clustering Framework for Residential Electric Demand Profiles M. Jain 1 , 2 , T. AlSkaif 3 , and S. Dev 1 , 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 . SEST2020 Istanbul Clustering Framework 1/7

Dataset Clustering Framework Validation PARENT Project Renewable Load Consumption (Watts) Median of Raw Data Normalized Median (Scaled Up by 1000) 2500 2000 1500 1000 500 0 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 Renewable Load Consumption (Watts) Median of Raw Data Normalized Median (Scaled Up by 1000) 2000 1500 1000 500 0 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 Box-plots of daily consumption pattern for 2 different households, also depicting the median and the scaled up version of normalized median. SEST2020 Istanbul Clustering Framework 2/7

Dataset Clustering Framework Validation Pre-processing the Dataset Nomenclature: n Number of households Hourly resolution of original data r d 1 Optimal number of reduced dimensions Optimal number of clusters k 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 M n ˆ d Ð median daily consumption of each household stored row-wise 5 M 1 1 1 n ˆ d Ð ℓ 2 -Normalization( M , row-wise) 1 6 return M 1 1 SEST2020 Istanbul Clustering Framework 3/7

Dataset Clustering Framework Validation Clustering Framework Determine number Determine optimal of dimensions in number of clusters output Unsupervised Unsupervised Dimensionality Clustering Reduction Generalized Clustering Framework In this work, ‚ 2 dimensionality reduction algorithms - elbow heuristics at intermediate stage ‚ 2 clustering algorithms - gap statistics at intermediate stage 6 d 1 FA “ 7; d 1 PCA “ 7; and k FA ` SC “ 7; k FA ` KMC “ 7; k PCA ` SC “ 7; k PCA ` KMC “ 7 SEST2020 Istanbul Clustering Framework 4/7

Dataset Clustering Framework Validation Objective Validation Strategy Algorithm 2: Objective Validation Strategy 1 p Ð number of partitions for each household 2 dist p¨ , ¨q Ð function to calculate Euclidean distance Ź Output from clustering algorithm 3 labels Ð labels assigned to each household 4 C p k ˆ d 1 q Ð cluster centers of each cluster 5 Initialize: match , misMatch , counter “ 0; Results obtained by performing objective 6 repeat foreach household do 7 validation of the 4 clustering frameworks. D Ð data for each household (days ˆ 24/r); 8 D’ Ð randomly shuffled data by rows; 9 Make p equal partitions from rows of D’ ; 10 Ź Perform Pre-Processing steps Clustering Framework %Matches %Mis-Matches M p p ˆp 24 { r qq Ð new medians of p partitions; 11 p M 1 FA ` SC 22.67 77.33 p Ð ℓ 2 -Normalization( M p , row-wise); 12 p = 2 FA ` KMC 29.07 70.93 Ź Do Dimensionality Reduction N p p ˆ d 1 q Ð dimReduce( M 1 p , d 1 ); PCA ` SC 18.78 81.22 13 p foreach partition P t 1 ¨ ¨ ¨ p u as part do PCA ` KMC 76.28 23.72 14 Ź Find Closest Cluster FA ` SC 21.34 78.66 CC Ð argmin i p dist p N p r part s , C [i, :] qq ; 15 p = 3 FA ` KMC 24.98 75.02 if CC ““ labels r household s then 16 PCA ` SC 17.60 82.40 match++ ; 17 else PCA ` KMC 67.15 32.85 18 19 misMatch++ ; counter++ ; 20 21 until counter ă 100; 22 avgMatches “ match { 100; 23 avgMisMatches “ misMatch { 100; Result: avgMatches & avgMisMatches SEST2020 Istanbul Clustering Framework 5/7

Dataset Clustering Framework Validation Subjective Validation Load Consumption (Watts) - Normalized Load Consumption (Watts) - Normalized 0.6 0.6 Daily profile of House ID 5 Daily profile of House ID 9 Daily profile of House ID 8 Daily profile of House ID 10 0.5 0.5 Daily profile of House ID 20 0.4 0.4 0.3 0.3 0.2 0.2 0.1 0.1 0.0 0.0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 : 1 : 2 : 3 : 4 : 5 : 6 : 7 : 8 : 9 : 0 : 1 : 2 : 3 : 4 : 5 : 6 : 7 : 8 : 9 : 0 : 1 : 2 : 3 : 0 : 1 : 2 : 3 : 4 : 5 : 6 : 7 : 8 : 9 : 0 : 1 : 2 : 3 : 4 : 5 : 6 : 7 : 8 : 9 : 0 : 1 : 2 : 3 : 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 2 2 2 2 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 2 2 2 2 Time Of The Day Time Of The Day Two sample clusters as identified by the recommended framework Load Consumption (Watts) - Normalized Load Consumption (Watts) - Normalized 0.6 0.6 Daily profile of House ID 0 Daily profile of House ID 0 Daily profile of House ID 13 Daily profile of House ID 1 Daily profile of House ID 1 Daily profile of House ID 14 0.5 0.5 Daily profile of House ID 5 Daily profile of House ID 7 Daily profile of House ID 17 Daily profile of House ID 7 0.4 0.4 Daily profile of House ID 8 0.3 0.3 0.2 0.2 0.1 0.1 0.0 0.0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 : 1 : 2 : 3 : 4 : 5 : 6 : 7 : 8 : 9 : 0 : 1 : 2 : 3 : 4 : 5 : 6 : 7 : 8 : 9 : 0 : 1 : 2 : 3 : 0 : 1 : 2 : 3 : 4 : 5 : 6 : 7 : 8 : 9 : 0 : 1 : 2 : 3 : 4 : 5 : 6 : 7 : 8 : 9 : 0 : 1 : 2 : 3 : 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 2 2 2 2 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 2 2 2 2 Time Of The Day Time Of The Day Sample ill-defined clusters from other frameworks (left: PCA ` SC; right: FA ` KMC) SEST2020 Istanbul Clustering Framework 6/7

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 SEST2020 Istanbul Clustering Framework 7/7