This paper presents a new method for forecasting the load of individual electricity consumers using smart grid data and clustering. The data from all consumers are used for clustering to create more suitable training sets to forecasting methods. Before clustering, time series are efficiently preprocessed by normalisation and the computation of representations of time series using a multiple linear regression model. Final centroid-based forecasts are scaled by saved normalisation parameters to create forecast for every consumer. Our method is compared with the approach that creates forecasts for every consumer separately. Evaluation and experiments were conducted on two large smart meter datasets from residences of Ireland and factories of Slovakia. The achieved results proved that our clustering-based method improves forecasting accuracy and decreases high rates of errors (maximum). It is also more scalable since it is not necessary to train the model for every consumer.

1. New Clustering-based Forecasting Method for
Disaggregated End-consumer Electricity Load
Using Smart Grid Data
Peter Laurinec, and Mária Lucká
14.11.2017
Slovak University of Technology in Bratislava

2. Motivation
More accurate forecast of electricity consumption is needed due to:
• Optimization of electricity consumption.
• Distribution (utility) companies. Deregulation of the market.
Purchase and sale of electricity.
• Ecological factors.
However, it is very difficult task for individual end-consumers due to:
• Stochastic behaviour (processes).
• Many factors influencing the consumption:
• Seasonality
• Weather
• Holidays
• Market
1

3. Example of consumers electricity load
20
40
60
0 250 500 750 1000
Time (3 weeks)
Load(kW)
2

4. Example of consumers electricity load
3.0
3.5
4.0
4.5
0 250 500 750 1000
Time (3 weeks)
Load(kW)
3

5. Example of consumers electricity load
0.0
2.5
5.0
7.5
10.0
12.5
0 250 500 750 1000
Time (3 weeks)
Load(kW)
4

6. Example of consumers electricity load - residential
0
1
2
3
0 250 500 750 1000
Time (3 weeks)
Load(kW)
5

7. Classical vs. our approach
The classical way is to train a model for every consumer
separately (drawbacks).
Our approach uses data from all consumers in a smart grid to
overcome stochastic changes and noisy character of data (time
series).
Solution: clustering of all consumers.
6

8. Our method
We will suppose that N is a number of consumers, the length of the training set is 21
days (3 weeks) whereby in every day we will consider 24 × 2 = 48 measurements, and
we will execute one hour ahead forecasts.
1. Starting with iteration iter = 0.
2. Creating of time series for each consumer of the lengths of three weeks.
3. Normalisation of each time series by z-score (keeping a mean and a standard
deviation in memory for every time series).
4. Computation of representations of each time series.
5. K-means clustering of representations and an optimal number of clusters is
computed.
6. The extraction of K centroids and using them as training set to any forecasting
method.
7. The denormalisation of K forecasts using the stored mean and standard
deviation to produce N forecasts.
8. iter = iter + 1. If iter is divisible by 24 (iter mod 24 = 0 mod 24) then steps 4) and
5) are performed otherwise they are skipped and the stored centroids are used.
7

9. Representation of time series
After normalisation -> computation of representations of time
series.
We conducted from our previous works 1 that clustering
model-based representations significantly improves accuracy
of the forecast of the global (aggregate) consumption.
For a representation, regression coefficients from the multiple
linear regression is used. The linear model is composed of
daily and weekly seasonal parameters.
xt = βd1utd1 + · · · + βdsutds + βw1utw1 + · · · + βw6utw6 + εt
1
Laurinec et al., WCECS (2016) and ICDMW (2016)
8

10. Representation of time series
−1
0
1
2
3
0 250 500 750 1000
Length
NormalizedLoad
Original Time Series
Daily Period
Weekly
Period
−1
0
1
0 20 40
Length
RegressionCoefficients
Final Representation of Time Series
9

11. Clustering
17 18 19 20
13 14 15 16
9 10 11 12
5 6 7 8
1 2 3 4
0 20 40 0 20 40 0 20 40 0 20 40
−1
0
1
2
3
−2
−1
0
1
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−2
0
2
−2
0
2
−2
−1
0
1
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3
−1
0
1
2
−3
−2
−1
0
1
2
−2
0
2
−2
−1
0
1
2
0
2
4
−2
0
2
4
−1
0
1
2
−2
0
2
4
−2
0
2
−2
−1
0
1
2
3
−1
0
1
2
−1
0
1
2
3
0
2
4
−2
−1
0
1
2
−2
−1
0
1
2
Length
RegressionCoefficients
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12. Final centroids
17 18 19 20
13 14 15 16
9 10 11 12
5 6 7 8
1 2 3 4
0 250 500 750 1000 0 250 500 750 1000 0 250 500 750 1000 0 250 500 750 1000
−0.5
0.0
0.5
1.0
1.5
−1.5
−1.0
−0.5
0.0
0.5
1.0
−0.50
−0.25
0.00
0.25
−1
0
1
−1.0
−0.5
0.0
0.5
−1.0
−0.5
0.0
0.5
1.0
−1.0
−0.5
0.0
0.5
−1.0
−0.5
0.0
0.5
1.0
−1.0
−0.5
0.0
0.5
1.0
−0.5
0.0
0.5
1.0
0
1
0
1
2
−0.5
0.0
0.5
−1.0
−0.5
0.0
0.5
1.0
−0.5
0.0
0.5
1.0
1.5
0
1
0
1
2
0
1
2
3
4
5
−1.0
−0.5
0.0
0.5
1.0
−1
0
1
Time
NormalizedLoad
11

13. Forecasting methods
Four methods were implemented
• Seasonal naive method (SNAIVE)
• Multiple Linear Regression (MLR)
• Random Forest (RF)
• Triple exponential smoothing (ES)
MAE (Mean Absolute Error):
1
n
n∑
t=1
|xt − xt|,
where xt is a real consumption, xt is the forecasted load and n
is a length of data.
12

14. Scaling forecasts
Denormalising K centroid-based forecasts by stored mean and
standard deviation from every consumer (N).
13

15. Data for experiments
We used two different datasets consisting of a large number of
variable patterns that were gathered from smart meters. This
measurement data includes Irish and Slovak electricity load
data.
For the Irish residential testing dataset (3639 consumers) the
data measurements from 1.2.2010 to 21.2.2010.
For the Slovak factories testing dataset (3607 consumers) the
data measurements from 10.2.2014 to 2.3.2014.
14

16. Evaluation
MAE Ireland dataset
Mean Median Max
SNAIVE_DisAgg 0.3807 ± 0.203 0.1928 ± 0.147 3.014 ± 1.3
SNAIVE_Clust 0.3373 ± 0.178 0.235 ± 0.143 2.6605 ± 1.192
MLR_Clust 0.3403 ± 0.18 0.2394 ± 0.146 2.6453 ± 1.187
RF_Clust 0.3394 ± 0.18 0.2425 ± 0.147 2.675 ± 1.192
ES_Clust 0.3359 ± 0.177 0.2387 ± 0.144 2.6629 ± 1.189
MAE Slovak dataset
Mean Median Max
SNAIVE_DisAgg 2.6903 ± 2.854 1.769 ± 2.27 16.1599 ± 14.621
SNAIVE_Clust 2.7873 ± 2.858 2.1479 ± 2.452 14.0958 ± 12.711
MLR_Clust 2.9326 ± 2.984 2.3109 ± 2.612 14.0306 ± 12.673
RF_Clust 2.7639 ± 2.836 2.0765 ± 2.388 14.4476 ± 13.081
ES_Clust 2.6752 ± 2.771 2.0283 ± 2.357 14.1695 ± 12.816
15

17. Ireland dataset results
0
1
2
3
4
5
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Hour
MAE
Method
ES_Clust
MLR_Clust
RF_Clust
SNAIVE_Clust
SNAIVE_DisAgg
16

18. Slovak dataset results
0
20
40
60
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Hour
MAE
Method
ES_Clust
MLR_Clust
RF_Clust
SNAIVE_Clust
SNAIVE_DisAgg
17

19. Conclusion
• Newly proposed clustering-based forecasting method for end-consumer load
using all data from a smart grid.
• We proved that our clustering-based method decreases the forecasting error in
the meaning of an average and the maximum (high rates of error).
• However, the error rates did not decrease with respect to the median because
of the nature of smart meter data.
• Our method needs to train only K models (in our case about 28) instead of N
models (thousands) that is leading to a huge decrease of the computational
load.
Future work:
• More experiments to find the number of optimal clusters.
• Other centroid-based clustering methods like K-medians, K-medoids and Fuzzy
C-means can be also used.
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