household electricity demand forecast based on context information and user daily schedule analysis...

1551-3203 (c) 2013 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. Seehttp://www.ieee.org/publications_standards/publications/rights/index.html for more information.

This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI10.1109/TII.2014.2363584, IEEE Transactions on Industrial Informatics

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Abstract—The very short-term load forecasting problem (VSTLF) is of particular interest for use in smart grid and automated demand response applications. An effective solution for VSTLF can facilitate real-time electricity deployment and improve its quality. In this paper, a novel approach to model the very short-term load of individual households based on context information and daily schedule pattern analysis is proposed. Several daily behavior pattern types were obtained by analyzing the time series of daily electricity consumption, and context features from various sources were collected and used to establish a rule set for use in anticipating the likely behavior pattern type of a specific day. Meanwhile, an electricity consumption volume prediction model was developed for each behavior pattern type to predict the load at a specific time point in a day. This study was concerned with solving the VSTLF for individual households in Taiwan. The proposed approach obtained an average mean absolute percentage error (MAPE) of 3.23% and 2.44% for forecasting individual household load and aggregation load 30 minutes ahead, respectively, which is more favorable than other methods do.

Index Terms—Behavior pattern, context features, individual household, load forecast

I. INTRODUCTION

FFICIENT energy usage has recently emerged as a critical concern because of an increasing shortage of energy

sources and an upsurge of environmental consciousness. The electric power grid is a highly complex system, and its management and the balancing of electricity consumption and production presents a great challenge. Any imbalance between electricity demand and supply causes grid instabilities and failures, and the financial impact on both suppliers and consumers is profound. Electricity demand (load) forecasting has been recognized as a key concern regarding the achievement of the economical, reliable, and secure operation and planning of a power system. A slight increase in load forecasting errors always leads to a considerable increase in the operating costs of an electric utility [1]. Because of the impact of load forecasting, it is imperative to model the load accurately.

Load forecasting can be divided into four types, characterized according to the time horizon with which their predictions are concerned, as follows: very short-term load

Manuscript received June 20, 2014. Accepted for publication October 13, 2014. This work was supported in part by the National Science Council of Taiwan under Contract NSC 101-2410-H-305-079-.

Copyright © 2009 IEEE. Personal use of this material is permitted. However, permission to use this material for any other purposes must be obtained from the IEEE by sending a request to [email protected].

Y. H. Hsiao is with the Department of Business Administration, National Taipei University, New Taipei City 23741, Taiwan (e-mail: [email protected]).

forecasting (VSTLF), which targets a prediction range of a few minutes to an hour [2–7]; short-term load forecasting (STLF), which targets a range of one hour to one week [8–23] and is the assumed forecast horizon for most applications; medium-term load forecasting (MTLF), which targets a range of one week to one year [24, 25]; and long-term load forecasting (LTLF), which targets a range of more than a year [9, 26, 27]. A wide variety of techniques for use in solving load forecasting problems have been proposed in the last decades. Statistical method-based approaches include the linear regression, stochastic, and time series methods [2, 9, 13, 14, 17, 24, 26]. Most of the conventional statistical models assume a stationary load series and cannot appropriately represent the complex nonlinear relationships between the load and a series of factors, such as daily and weekly time rhythms, which causes substantial errors regarding load forecasting. To incorporate this nonlinearity factor, many modifications have been proposed [6, 18, 20]. Approaches using artificial intelligence have received substantial attention because of their excellent ability to model an unspecified nonlinear structure between load and the factors affecting it [7, 8, 12, 15, 16]. Machine learning and soft computing techniques have also been used for load forecasting and have demonstrated relatively favorable performances [3–5, 11, 15, 19, 22, 25, 27]. On the other hand, certain studies have used the concept of similarity or pattern-base, which measures the degree of similarity in, for example, day type, weather, or load shape, between the historical data and the predicted day; the similar historical patterns are then identified to form a forecasting learning base [8, 10, 12, 21, 27, 28]. Furthermore, some researchers believe that applying prefiltering techniques to denoise load data or to decompose the load data into different frequency levels is a critical method by which to improve the effectiveness of load forecasting. The wavelet decomposition [7, 12] and singular value decomposition [24] methods have been discussed in the literature.

Although numerous methods have been developed for use in STLF, the existing literature regarding VSTLF is considerably limited. However, it has been indicated that the VSTLF problem is of particular interest for use in smart grid and automated demand response applications [29–32]. With the continual construction of advanced metering infrastructure system and smart meter, it becomes possible to immediately collect electricity consumption data from individual households and initiate two-way communication between electricity suppliers and individual households. Consequently, this accelerates the implementation of a personalized auto demand response in individual households, which allows for personalized electricity contracts and rates, such as a dynamic rate and two-way transaction bidding, and leads to effective electricity deployment. Considering this purpose, the first of all is to understand the individual household's electricity

Yu-Hsiang Hsiao

Household Electricity Demand Forecast Based on Context Information and User Daily Schedule Analysis from Meter Data

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consumption behavior and then to precisely predict the electricity demand. However, existing studies were inadequate for this purpose at both the application and methodology. Regarding application, despite the fact that most studies have investigated the aggregated load forecasting of large spatial regions, the applications regarding individual households are few. According to the risk pooling phenomenon in supply chain demand forecasting, aggregated demand exhibits a smoother pattern, and thus exhibits a more accurate predictability than individual demand. Therefore, it is understood that the electricity demand prediction regarding individual households is more complex and less accurate than predictions regarding aggregate special regions, because of the lack of an error offset [23]. Regarding methodology, the importance of user daily schedule patterns has been neglected in the development of existing load forecasting methods. It can be observed that, in an individual household, the daily electricity consumption behavior is primarily governed by daily schedule. Furthermore, the daily schedule is primarily affected by context features, such as weather, special events (e.g., FIFA World Cup), economics, and day type. Therefore, context features are effective predictors of electricity consumption behavior. In this study, two types of context feature were defined: day-dependent and minute-dependent. The day-dependent context features affect an individual household’s overall daily electricity consumption behavior, whereas the minute-dependent context features affect the electricity consumption volume at various time points in a day or cause different days to have different consumption even if they display similar daily electricity consumption behavior.

This paper proposes a novel approach to model the load of an individual household based on context information and its daily schedule patterns. A case of load forecasting problem for individual households in Taiwan was examined. The meter data collected from individual households were recorded from October 31st, 2010 to March 1st, 2012 and in time resolution of 15 minutes. VSTLF with forecasting horizon of 30 minutes and STLF with forecasting horizon of 2 hours and 1 day were demonstrated in this study.

The paper is organized as follows: Section 2 introduces the proposed approach. Section 3 details the implementation of this approach on the real load data of an individual household. Section 4 presents and discusses the overall experimental results and provides a comparison with other methods. Finally, Section 5 concludes the paper.

II. LOAD MODELING AND PREDICTION BASED ON CONTEXT

INFORMATION AND USER DAILY SCHEDULE PATTERNS

This paper proposes a load modeling method to predict the load of individual households by using an analysis of the context information and user daily schedule patterns. The behavioral pattern of the daily electricity consumption was extracted by smoothing the sporadic consumption sharp and impulse, and then granulating the data into finite granules with discrete intervals. The accuracy of any load forecasting technique is heavily dependent on the consistency of the load data. A clustering technique was used to determine various daily schedule pattern types (or electricity consumption behavior pattern types) for an individual household by

measuring the similarities among the exhibited daily electricity consumption behavior curves. The days that were grouped into the same cluster were assumed to exhibit shared features that caused their daily schedule and daily electricity consumption behavior to be similar. A diverse range of day-dependent context features caused an individual household to display varying daily schedule pattern types, which produced varying daily electricity consumption behaviors. Therefore, the next step was to investigate the features that caused the daily electricity consumption behaviors to exhibit the same or different patterns. The day-dependent context features regarding the individual household were collected. Pattern cluster labels were treated as class labels to represent the various types of electricity consumption behaviors, and classification and feature selection techniques were employed to construct a classification model using only the significant context features. Using this classification model, the likely pattern of electricity demand for a particular day in the future can be predicted as soon as the corresponding day-dependent context features are accurately estimated in advance. Next, the electricity consumption volume at a specific time point in a day belonging to certain type of behavior was then investigated. Although various days were grouped into one cluster (behavior type) because they exhibited similar consumption patterns, a distinct electricity volume was observed among them when the individual time point was analyzed. This was assumed to occur because there were minute-dependent context features that affected the volume. Therefore, various minute-dependent context features were collected and prediction technologies were used to model the relationship between the time-point (date-hour-minute) electricity volume and minute-dependent context features for each behavior class. Additionally, historical load data that were considered helpful in predicting the future electricity demand were used in the prediction models. Once the type of electricity consumption behavior pattern of a day is known, the corresponding prediction model is used to predict the electricity consumption volume at a particular time point by entering the estimated minute-dependent context features and historical data as inputs in the model. In summary, two models were developed to be used in the proposed procedure: the intercluster classification model and the intracluster prediction model. To forecast the electricity demand at a specific time point in a particular day, the first step is to use the estimated day-dependent context features to classify the day into one of the consumption pattern types, and the second step is to use the corresponding prediction model with the estimated minute-dependent context features and historical load data as inputs to predict the electricity demand volume. The estimation of the context features is beyond the scope of this study, and it was assumed that this information can be well obtained. For example, the local weather is one of the most important context features in our proposed model, and the high quality weather forecasting data are always open for public and can be obtained from specialized department of government, e.g. the weather forecasts can be obtained from the Central Weather Bureau of Taiwan (http://www.cwb.gov.tw). The proposed procedure is depicted in Fig. 2.1 and detailed as follows.



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Stage 1: Meter Data Collection and Preprocess Step 1-1: The time series of daily electricity consumption

was collected from an individual household meter for an adequate time period. The time series were composed of consecutive data points, each of which recorded the cumulative electricity consumption over a consecutive and nonoverlapping time slot.

Step 1-2: The daily time series was sorted and preprocessed. This step was necessary because it was unavoidable that noisy and missing data appeared during meter data transmission.

Stage 2: Extraction of Daily Electricity Consumption Behavior Patterns and Pattern Type Induction

Step 2-1: The moving average method was applied to the daily time series to smooth the sporadic consumption sharp and impulse.

Step 2-2: Granular intervals were defined according to the average and standard deviation of daily consumption. Each moving average data point was granulated into one of finite granular intervals to reduce the resolution. By this step, the electricity consumption volumes that exhibited a slight variation were treated as the same.

Step 2-3: Clustering techniques were used to group the daily granulated time series that exhibited similar undulation curves into the same cluster. Each cluster represented a specific type of electricity consumption behavior pattern.

Stage 3: Forecasting Model Construction This stage comprised two parallel subtasks: intercluster behavior classification (Stage 3A) and intracluster consumption volume prediction (Stage 3B), which are detailed as follows:

Stage 3A: Intercluster Behavior Classification Model Construction

Step 3A-1: The day-dependent context features of the analyzed household building were collected over the analyzed time period.

Step 3A-2: Each cluster was treated as a behavior class and the days in the same class exhibited similar electricity consumption behavior patterns.

Step 3A-3: A classification model was constructed using the day sample’s behavior class label as output and the corresponding day-dependent context features as inputs.

Step 3A-4: A feature selection method was applied to rightsize the classification model and sieve out the significant context features that affected the daily electricity consumption behavior.

Stage 3B: Intracluster Consumption Volume Prediction Model Construction

Step 3B-1: The minute-dependent context features of the analyzed household building were collected over the analyzed time period.

Step 3B-2: An exclusive prediction model was constructed for each behavior class, using the electricity consumption volume at each time point (date-hour-minute) as output and the corresponding minute-dependent context features as inputs. The historical load data were also considered as inputs to the model.

Step 3B-3: A feature selection method was applied to rightsize the prediction model and sieve out the significant context features that caused the electricity consumption volume to vary at different time points within the same cluster.

Stage 4: Confirmation Test and Forecast Applications A separate data set was collected. The following steps were

used to conduct a confirmation test of the forecasting of the electricity consumption demand at a specific time point in a specific day:

Step 4-1: The intercluster behavior classification model was applied, which used the estimated day-dependent context features that corresponded to the specific day to identify its behavior pattern type.

Step 4-2: The intracluster consumption volume prediction model of the behavior pattern type identified in Step 4-1 was

Figure 2.1 The Proposed Load Modeling and Prediction Procedure



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applied and the estimated minute-dependent context features and historical load data that corresponded to the specific time point was used to predict the electricity consumption volume.

Step 4-3: A performance index was employed to evaluate the load forecasting error. If the results were unsatisfactory, the adequacy of the context features and constructed models in Stage 3 were checked; if the results were satisfactory, forecasting applications were initiated.

III. IMPLEMENTATION ON AN INDIVIDUAL HOUSEHOLD

A set of meter data obtained from an individual household located in Taipei, Taiwan was employed to illustrate the implementation of the proposed procedure.

Stage 1: Meter Data Collection and Preprocess The meter data were collected from October 31st, 2010 to

March 1st, 2012. For each day, time series of 96 data points was recorded, each of which recorded the cumulative electricity consumption over 15 min. After the incomplete and noisy data were cleaned, 400 days with complete data were implemented. Because the period of data collection was limited, 80% of the days in each month were randomly selected to form a dataset for constructing the model, and the remaining 20% of the days were used to form a dataset to confirm the effectiveness of the model. Fig. 3.1(a) displays three Tuesdays from varying seasons as an examples to reveal the typical load variations. High electricity demand frequently occurred from 6 pm to 11 pm, and the minimum demand typically occurred from 9 am to 5 pm. Additionally, it was observed that although the three example Tuesdays exhibited similar load patterns, the amount of consumption in summer was higher. This electricity consumption behavior was repeated on most working days for this household. Conversely, less common patterns were observed on nonworking days caused by the variety of schedules and activities. Fig. 3.1(b) displays the load variation of three Sundays in varying seasons. A higher load amount was also observed in summer. In addition to the above explanations regarding working and nonworking days, Tuesdays and Sundays, and seasons, various potential context features remained that affected the electricity consumption behavior and demand of this household, and this was the focus of this study.

Stage 2: Daily Electricity Consumption Behavior Pattern Extraction and Pattern Type Induction

At this stage, the one-hour moving average method was applied to the time series of daily electricity consumption to smooth the sporadic consumption sharp and impulse, and generate a macroscopic trend. After this step, 96 data points in a daily series were transferred to 93 moving averages. Taking the time series in Fig. 3.1(a) for example, their moving average series that displays the rough patterns of electricity consumption are shown in Fig. 3.2(a).

Next, to avoid acutely discriminating between two consumption behavior patterns that only exhibit a small difference and to extract the consumption behavior pattern trend while ignoring the consumption volume, the moving average data were granulated into finite granules with discrete intervals to normalize consumption and reduce the resolution. The granulization function is expressed in (3.1).

<

−=

>

−

=

..

.

..

,5.0

,0

,5.0

iiji

iij

iij

iiji

iij

ij

yyyy

yy

yyyy

g

σ

σ (3.1)

where ⋅ is a ceiling function; ⋅ is a floor function; ijy is the

jth 1-hour moving average value in day i and ijg is the

corresponding granulated value; and .iy and

iσ are the average

and standard deviation over 93 moving average data points of day i , respectively.

During the granulization process, the electricity consumption volumes that exhibited a slight variation were treated as the same as those that did not. This focused attention on the electricity consumption behavior patterns instead of on the small variations in consumption volumes. Fig. 3.2(b) shows an example of the granulated data series that was obtained from Fig. 3.2(2).

In the final step of this stage, a clustering technique was employed to group the daily series granulated data that exhibited similar undulations into the same cluster. Each cluster represented a specific type of electricity consumption behavior pattern. An agglomerative hierarchical cluster tree was used for the grouping because of the advantage that clustering criteria can be adjusted by adopting various similarity thresholds, which leads to flexible clustering results. In the clustering algorithm, the Ward’s linkage [33], which is frequently used to measure the distance between two clusters was merged with the proposed similarity evaluation method to more adaptively solve

1 10 20 30 40 50 60 70 80 90 960

0.2

0.42011.03.07 Spring Tuesday

1 10 20 30 40 50 60 70 80 90 960

0.2

0.42011.07.11 Summer Tuesday

1 10 20 30 40 50 60 70 80 90 960

0.2

0.4

Time Index (by 15 Minutes)

kWh

2011.10.31 Fall Tuesday

1 10 20 30 40 50 60 70 80 90 960

0.3

0.62011.04.09 Spring Sunday

1 10 20 30 40 50 60 70 80 90 960

0.3

0.6

2011.07.09 Summer Sunday

1 10 20 30 40 50 60 70 80 90 960

0.3

0.6

2011.11.15 Fall Sunday

Time Index (by 15 Minutes)

kWh

Figure 3.1 (a) Load variation of Tuesday (Working Day); (b) Load variation of Sunday (Nonworking Day)



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the clustering problems regarding the time series. The Ward’s linkage is defined as follows:

)(

2

2),(

2

sq

sq

sqsqnn

xxnnw

−

−= (3.2)

where 2

⋅ is the Euclidean distance; qn and

sn are the number

of samples in cluster q and cluster s , respectively; and qx and

sx are the centers of cluster q and cluster s , respectively.

However, the similarity between two time series is always the outcome of simultaneously measuring the variations across all data points of the series. It has been commonly found that the same results of similarity measurement to a specific base point are obtained by two different time series even if they perform opposite and complementary to each other. In other words, it cannot be ensured that time series in the same cluster perform similarly in all time segments, and this results in the difficulty experienced in building a reliable prediction model. Therefore, the concept of desirability function was introduced to solve this problem. The task of similarity measurement between two time series was regarded as a multiobjective problem. Two time series were concluded as being similar only if all of the time segments on these two time series were sufficiently similar. Following the Ward’s linkage defined in (3.2), the proposed modification is as follows.

tt

isqsq idD

1

1),(),( ][

= ∏=

(3.3)

where t is the number of segments determined by users and

][),( id sq is the individual desirability function of segment i

( ti ...,,1= ), defined as follows:

=

<<

−−

=

=

][][,0

][][][,][][

][][

][][,1

][

),(2

),(2),(

2

),(2

),(

iUiw

iUiwiLiLiU

iwiU

iLiw

id

sq

sq

r

sq

sq

sq

(3.4)

where ][][

][][][][][

2

2),(

2

inin

ixixininiw

sq

sq

sqsq+

−⋅⋅= is the Ward’s linkage

between cluster q and cluster s in segment i ; r is a

user-specified parameter (here, 1>r is chosen because it places more emphasis on being close to the distance of 0); and ][ iU

and ][ iL are the upper and lower bounds of ][),(2 iw sq ,

respectively. Not limit to Ward’s linkage, the proposed modification method for similarity measurement between two time series can be easily imitated if other distance metrics else

are considered. In this study, a segment window of 10 data points with three overlaps was implemented. In other words, it generated 13 segments (13=t ) in each time series. The parameter 10=r was specified to put heavy emphasis on the expectation of two completely identical time series.

Additionally, a major challenge in clustering analysis is the estimation of the optimal number of clusters. In this study, the KL Index [34] was applied, which determines the appropriate number of clusters according to a decreasing amount of intracluster variation. The optimal number of clusters, k , was determined using (3.5).

)]([maxarg hKLkh

= (3.5)

where )1(

)()(

+=

hDIFF

hDIFFhKL

; h

ph

p WhWhhDIFF2

1

2

)1()( −−= −; p is

the number of dimensions; h is the number of clusters; and hW

is the within-cluster sum-of-square when h clusters. From (3.5), it was observed that the optimal number of

clusters, k , was determined in the experimental range of h . Not limit to Ward’s linkage, the proposed modification method for similarity measurement between two time series can be easily imitated if other distance metrics else are considered in advanced. This was easily implemented because the agglomerative hierarchical cluster tree was used. Fig. 3.3 shows that the classification accuracy decreased when the number of clusters increased, but was stable when the number of clusters was more than 13. That is, it was meaningless to analyze the cases that had been clustered into more than 13 types of electricity consumption behavior pattern. Therefore, the experimented range of h was set between two and 13, and the maximum KL index occurred when h was equal to seven. This meant that the electricity consumption behavior patterns were grouped into seven types for this individual household.

Stage 3: Forecasting Model Construction According to the analysis conducted in Stage 2, this

individual household exhibited 7 different types of electricity consumption pattern. Next, the focus was 1) intercluster behavior classification model construction used to determine the day-dependent context features that caused the daily schedule of this household to perform in this way; and 2) intracluster consumption volume prediction model construction used to model the relationship between the electricity consumption volume at a specific time point in a day and the corresponding minute-dependent features of each type of behavior pattern.

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0.62011.03.07 Spring Tuesday

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0.3

0.62011.07.11 Summer Tuesday

1 10 20 30 40 50 60 70 80 930

0.3

0.62011.10.31 Fall Tuesday

Moving Average Index

1-H

our

Mov

ing

Ave

rag

e (k

Wh)

1 10 20 30 40 50 60 70 80 93-7

0

72011.03.07 Spring Tuesday

1 10 20 30 40 50 60 70 80 93-7

0

72011.07.11 Summer Tuesday

1 10 20 30 40 50 60 70 80 93-7

0

7

Granulation Index

Gra

nula

ted

Val

ue

2011.10.31 Fall Tuesday

Figure 3.2 (a) The Moving Average Data; (b) The Granulated Data



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Stage 3A: Intercluster Behavior Classification Model Construction

The difference or similarity between electricity consumption behavior patterns on various days was assumed to be the consequence of external factors that affected the individual household. These external factors are called context features. Various day-dependent context features were collected regarding the analyzed residential building over the analyzed time period from four sources: time, weather, calendar, and economic indicators. The day-dependent features are listed as follows: 1) Time: year (2010-2012), month (January-December), day

of the month (1st-31st), and day of the week (Sunday-Saturday);

2) Weather: temperature (Co ), precipitation (mm), relative humidity (%), wind speed (m/s), UV index (0-11), sunshine duration (h), typhoon (y/n), and earthquake (local intensity: 0-7). These data were obtained from the Data Bank for Atmospheric Research, National Science Council, Taiwan (http://dbar.ttfri.narl.org.tw);

3) Calendar: yesterday is a festival (y/n), today is a festival (y/n), tomorrow is a festival (y/n), yesterday is a holiday for work (y/n), today is a holiday for work (y/n), tomorrow is a holiday for work (y/n), yesterday is a holiday for school (y/n), today is a holiday for school (y/n), tomorrow is a holiday for school (y/n), and special local event (e.g. political parade) (y/n);

4) Economic Indicator: composite leading index, composite coincident index, composite lagging index, monitoring indicator, average rate of exchange to USD, economic growth rate, gross domestic product, gross national product, national income, unemployment rate, consumer price index, oil prices, prices of liquid petroleum gas, and average of the Taiwan stock exchange. These data were obtained from the Business Indicator Database, Council for Economic Planning and Development, Taiwan (http://index.cepd.gov.tw/).

Each of the seven clusters was then treated as a specific class of behavior and the days in the same cluster exhibited similar electricity consumption behavior patterns. The decision tree analysis method, C5.0, was then used to construct a classification model, using the day sample’s behavior class label as output and the corresponding day-dependent context features as inputs. By decision tree analysis, definite classification rules composed of significant context features were generated. The classification accuracy reached 91.3%, and the significant features were identified, including: 1) month; 2) the day of month; 3) the day of week; 4) today is a holiday

for work; 5) today is a holiday for school; 6) important local activity; 7) today is a festival; 8) tomorrow is a holiday for work; 9) temperature; 10) typhoon; 11) relative humidity; 12) wind speed; 13) consumer price index; 14) economic growth rate; 15) Taiwan average of stock exchange; 16) composite coincident index; and 17) oil prices. For future applications, once these significant context features are estimated, the most likely electricity consumption behavior pattern type for a specific day can be anticipated.

Stage 3B: Intracluster Consumption Volume Prediction Model Construction

Various days in the same cluster (the same class label) share common daily schedules and common electricity consumption behavior patterns. However, the discrepancies regarding consumption volumes were observed on the same time index of different days or different time points in a day. This can be ascribed to the effect of the minute-dependent context features. Furthermore, the electricity consumption was not timely independent data; therefore, the historical load data that with various time distances from the predicted time point were also considered. The back-propagation neural network (BPN) was applied to construct the estimation function of a time-point electricity consumption volume using minute-dependent context features and historical load data for each of the seven clusters. The neural network contained three layers, including the input layer, hidden layer, and output layer. The output layer exhibited one node of electricity consumption volume. The input layer included the nodes of time information, minute-dependent context features, and historical load data, listed as follows. 1) Time information: year (2010-2012), month

(January-December), day of the month (1st-31st), and day of the week (Sunday-Saturday);

2) Minute-dependent context features: time index (1-96), average consumption volume over various days within cluster at the time index, temperature at the time point ( Co ), relative humidity at the time point (%), wind speed at the time point (m/s), and UV index at the time point (1-11);

3) Historical load data: three different sets regarding time from the predicted time point were prepared for use in constructing the BPN model: a) Set 1 : the load 30 minutes ago and the average load of

the time interval from 12 hours to 30 minutes ago; b) Set 2: the load 2 hours ago and the average load of the

time interval from 12 hours to 2 hours ago; c) Set 3: the load of the same time index yesterday and

the average load yesterday.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 2270

75

80

85

90

95

100

Number of Clusters

Cla

ssifi

catio

n Acc

uracy

(%

)

Figure 3.3 The Number of Clusters vs. Classification Accuracy



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The use of set 1 limits the model to forecast the electricity demand ahead of 30 minutes; the use of set 2 limits the model to forecast the electricity demand ahead of 2 hours; the use of set 3 limits the model to forecast the electricity demand ahead of 1 day.

Therefore, there were 12 input nodes and one output node in the network structure and the optimal network parameters including the number of hidden nodes, learning rate, and momentum was determined using trial-and-error experiments. The results showed that the mean absolute percentage errors (MAPEs) were 2.35%, 3.23%, and 3.96% regarding using the historical load data of Set 1, Set 2, and Set 3, respectively, in input nodes.

Stage 4: Confirmation Test and Forecast Applications During Stage 3, two models were constructed for the

individual household. The behavior classification model will be used first to predict the most likely behavior pattern type based on the estimated values of the 17 significant day-dependent context features for an approaching day. Once the behavior pattern class is known, the corresponding consumption volume prediction model will be employed to predict the electricity consumption at a given time point by using the four time information data, the estimated values of six minute-dependent context features, and the two historical load data. The estimation of context features was not dealt with for load forecast. Instead, they were obtained from some open estimation data reported by Taiwan government. The predicted weather data were from the Central Weather Bureau of Taiwan (http://www.cwb.gov.tw); the calendar data were collected from the Directorate-Central Personnel Administration of Taiwan (http://www.dgpa.gov.tw) and the local police department (http://www.tcpd.taipei.gov.tw); the data of predicted economic indicators were from the Council for Economic Planning and Development, Taiwan (http://index.cepd.gov.tw).

To verify the effectiveness of the proposed approach, the remaining 20% of the data which was not used in the

construction of the models were used as the confirming examples. In the same manner, the historical load data of Set 1, Set 2, and Set 3 were considered in the consumption volume prediction model. Finally, MAPEs of 3.17%, 4.52%, and 4.78% were obtained for Set 1, Set 2, and Set 3, respectively. This result was satisfactory, which indicated the forecasting ability of future applications for this individual household.

IV. OVERALL EXPERIMENT RESULTS AND COMPARISONS

The electricity consumption data were procured from 771 residential meters; 421 were located in Taipei City and 350 were located in Hsinchu City in Taiwan. The meter data were collected from October 31st, 2010 to March 1st, 2012. For a day, 96 data points, each of which recorded the cumulative electricity consumption over a period of 15 minutes were obtained. After the incomplete data and noisy data were cleaned, 213 of 771 residential meters that stored at least 200 days of complete data were used in this study. Because the proposed approach is for individual household, the analysis focused on one meter at a time. Furthermore, because of the limitation regarding the time period of the collected data, 80% of the days in each month were randomly selected to form a dataset for constructing the model, and the remaining 20% of the days were broken up into numerous time-point load data, which were used to form a dataset for confirming the effectiveness of the model. Totally, 471,735 individual time-point load data were used in verification test.

Several methods including BPN, linear regression (LR), support vector regression (SVR), SVR based on similar historical days (SVR2), random walk algorithm (RW), and autoregressive integrated moving average (ARIMA) were considered in comparison. Similar to that we have explained in Section III, three sets of historical load data with different time horizons were employed, respectively, as the predicted variables for constructing load forecasting models of various forecasting horizons. Regarding the methods of BPN, LR, and SVR, the day-dependent context features, minute-dependent

Table 4.1 Experiment and Comparison Results

Forecast for Individual Forecast for Aggregation

Set 1 30 minutes-ahead

forecast

Set 2 2 hours-ahead

forecast

Set 3 1 day-ahead

forecast

Set 1 30 minutes-ahead

Forecast

Set 2 2 hours-ahead

Forecast

Set 3 1 day-ahead

Forecast

Ave. MAPE

Ave. MASE

Ave. MAPE

Ave. MASE

Ave. MAPE

Ave. MASE

MAPE MAPE MAPE

Proposed Approach 3.23% 0.22 3.52% 0.15 4.34% 0.16 2.44% 3.10% 4.12%

w/o Cluster Linkage Modification 4.18% 0.27 - - - - - - -

BPN 5.76% 0.34 6.21% 0.26 6.32% 0.21 5.52% 5.44% 7.13%

LR 8.34% 0.55 8.85% 0.36 10.12% 0.33 7.65% 7.94% 9.68%

SVR 4.05% 0.26 5.20% 0.20 5.95% 0.20 3.53% 4.72% 6.32%

SVR2 3.96% 0.25 4.68% 0.17 5.64% 0.19 3.20% 3.93% 4.88%

RW 15.58% 1.00 24.72% 1.00 30.35% 1.00 11.15% 18.21% 13.77%

ARIMA 15 minutes-ahead forecast

Ave. MAPE

8.81% Ave.

MASE 0.81 MAPE 8.34%



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context features, and historical load data were used as the predicted variables to construct the forecasting model that focused on the time-point electricity demand. These three methods excluded the analysis and induction of the daily schedule and daily electricity consumption behavior patterns, which was the emphasis of our proposed approach. The parameters of BPN containing learning rate, momentum, and the number of hidden nodes were determined by trial-and-error approach to find the combination with minimum root mean square error. LIBSVM [35] was used to implement SVR. LIBSVM provides an efficient parameter selection tool using cross validation via parallel grid search under the kernel of the radial basis function type. The SVR2 is a method of applying SVR based on similar historical days. The SVR2 was implemented by selecting historical days with similar day-dependent context features to form a forecasting pattern-base. Then SVR model was constructed only using the historical days in the base. This concept has been widely used in the time series prediction or load forecasting applications in literature [8, 10, 12, 21, 27, 28]. The RW adopted one-step forecast which regards the last observation as the forecasting solution. The ARIMA was performed based on the historical load data of 2 days and the forecast horizon was 15 minutes. The Box-Jenkins methodology was used to select polynominal function orders for autoregressive and moving average terms.

The results are listed in Table 4.1. In this comparison experiment, an individual household obtained a forecast MAPE and mean absolute scaled error (MASE) over all time-point forecast results in all confirmation examples. To assess MASE, the absolute forecasting errors were scaled based on the mean absolute error (MAE) from RW. The “Ave. MAPE” and “Ave. MASE” are the average of MAPE and MASE, respectively over 213 individual households. The forecasting results indicated that our proposed approach obtained lower average MAPEs and lower average MASEs over all of experiments when compared with other methods, which included the method of the proposed approach using the original Ward’s linkage in the behavior pattern clustering process. The cluster linkage modification for time series data improved the recognition of similar electricity consumption behaviors and consequently improved the load forecasting performance; the average MAPE decreased from 4.18% to 3.23% and the average MASE decreased from 0.27 to 0.22. The one-step RW performed worst among all compared forecasting methods and with apparently high average MAPEs and MASEs. This may be because that the most recently historical load datum was the only information relied by the RW for forecasting the load demand in the future. When the forecasting horizon is longer,

the merit of historical data for forecasting load demand will become weaker and this leads the RW model performs worse. The BPN, LR, and SVR achieved a lower forecasting accuracy than our proposed approach did because they ignored the importance of behavior pattern analysis, which was reckoned critical in this study. The predicted variables used for constructing the BPN, LR and SVR were identical to those of our proposed approach. Therefore, the better performance of our proposed approach indicated that considering household behaviors is a helpful strategy for forecasting. Besides, the average MAPEs and MASEs of LR were apparently higher than BPN and SVR and the average MAPEs were almost reached to 10%. This revealed the lack of ability for LR to consider the non-linear relationship among variables in forecast model construction. The SVR2 performed the lowest average MAPEs and MASEs in this comparison except the proposed approach. The most critical advantage of SVR2 is that the forecasting model was constructed using the pattern-base formed by historical days characterized by high similar context features with the predicted day, which was a widely used strategy in previous studies. This pattern-base filtering process facilitated improving the forecasting accuracy, and this was reflected by the evidence that SVR2 performed better than SVR. However, the performance gap between SVR2 and the proposed approach was observed. In the proposed approach, the construction of a pattern-base did not begin with selecting the relevant historical days according to their similarity to the predicted day regarding the context features. Conversely, the proposed approach emphasized understanding the user behavior pattern first, and then obtaining the common context features that caused the individual household to exhibit a specific type of behavior pattern. The greatest advantage was that more and correct information was included in the pattern-base. A household might exhibit similar daily schedules and similar daily electricity consumption patterns under various conditions of context features. Or, under similar conditions of context features, a household might exhibit dissimilar daily schedules and daily electricity consumption patterns. In this case, if the pattern-base was constructed only considering the similarity of context features, certain days that also exhibited similar behaviors were excluded and certain days that exhibited dissimilar behaviors were included. This reduces the extensibility and correctness of the constructed forecasting model. Finally, the comparisons with ARIMA and other methods were inadequate in this experiment because the ARIMA was implemented on the basis of forecasting horizon of 15 minutes which is different from other methods. However,

Table 4.2 Wilcoxon Signed Ranks Test for Pairwise Comparisons

Comparison Set 1 Set 2 Set 3

Wilcoxon Statistic p-value Wilcoxon Statistic p-value Wilcoxon Statistic p-value

Proposed Approach vs. BPN 5.52084E+09 0.000 6.78582E+09 0.000 1.11212E+10 0.000

vs. LR 286163261.0 0.000 866419336.0 0.000 116267418.0 0.000

vs. SVR 3.07397E+10 0.000 2.29672E+10 0.000 1.47901E+10 0.000

vs. SVR2 4.47832E+10 0.000 3.39978E+10 0.000 3.14649E+10 0.000 Test for 471,735 time-point forecasts



9

the unsatisfied results of 8.81% for average MAPE provided a reference that the ARIMA analysis, a conventional statistical time series method, was not sufficient to solve the load forecasting problem in this case.

On the other hand, regarding the historical load data, using Set 1 generated a more favorable prediction ability across all methods than using Sets 2 and 3, and Set 2 was more favorable than Set 3. This provided evidence that the historical load data played a critical role in forecasting the load, and near historical data exerted a stronger effect on forecasting accuracy, and the effect decreased with the passage of time.

Table 4.2 presents the results of Wilcoxon signed rank test for the pairwise comparisons concerning our proposed method. The comparison with RW was opted to omit for simplicity because the RW were apparently poorer than others, shown as Table 4.1. Turning to the more sophisticated methods, as the p-value equaling to 0.000 states, our proposed method shows a significant improvement over BPN, LR, SVR, and SVR2 no mater for 30 minutes-ahead forecasts (Set 1), 2 hours-ahead forecasts (Set 2), or 1 day-ahead forecasts (Set 3).

Regarding the performance of the aggregate load demand forecast, the actual load demand of each individual household was summed to be the actual aggregate load demand at each time point. Also, the forecasted load demand of each individual household was summed to be the forecast aggregate load demand at each time point. The absolute percentage error at each time point was then obtained, and the average across all time points was calculated to obtain the MAPE. The results are provided in Table 4.1. The results confirmed that the phenomenon of risk pooling provides an error offset, and consequently, revealed a higher forecasting accuracy regarding the demand at the aggregation level. This revealed that calculating the electricity demand of individual households is more challenging than calculating the forecasts concerning large spatial regions, which has been solved in previous research.

Two aspects concerning the proposed approach must be discussed. First, the forecasting accuracy was governed by the information richness of the context features in this study. The proposed approach assumed that the context features affected an individual household’s daily schedule, which was revealed in the electricity consumption behaviors. Therefore, the context features were used as the leading predictors to anticipate electricity consumption behaviors. To render the forecasting model effective and reliable, it was crucial to consider as many domain sources of context features as possible. However, restricted by the availability of sources and privacy issues, insufficient context features were acquired. For example, the exact location, demographic structure, building size, and personal schedule or calendar of each household were unavailable; however, this information was expected to be helpful for use in load forecasting. This depressed the forecasting accuracy. However, although the forecasting accuracy was satisfactory when using the context features available, the accuracy would have been improved if more context features could have been obtained from more sources. Second, the data size was relatively small and the data period was relatively short. This is a severe problem in all data mining

applications, particularly for time series analysis, not only decreasing the robustness of a forecasting model but missing the opportunities of analyzing the trend and cyclical effect. In this study, one and a half years’ worth of data were obtained, but it was not sufficient to reveal the trend and cyclical effect. Therefore, to ensure the robustness of the forecasting model, the training and test data split strategy was implemented regarding each month. This made the model endeavor to learn the characteristics from every month of a year. Therefore, the training and test processes were forced to dodges the effects of trend and cycle properties, and was unable to observe the long-term load. Thus, the constructed model was only able to be used to conduct STLF and VSTLF. According to the experiment results, although the forecasting accuracy was satisfactory for real applications, improvement is possible if additional data that contained information concerning trend and cyclical properties were collected.

V. CONCLUSION

A novel approach to modeling the electricity demand of individual households based on context information and daily schedule patterns was proposed. First, at the application level, this approach focused on investigating the problem of load forecasting for individual households rather than for a large spatial region (which has been widely discussed and successfully solved in previous research). Accurately forecasting the electricity demand for individual households is crucial for the implementation of personalized auto demand response in a smart grid, which leads to effective electricity deployment. Second, at the methodology level, this study indicated that a household’s daily schedule was affected by various context features and was revealed by daily electricity consumption behavior. Therefore, this approach emphasized understanding and inducing the type of pattern exhibited regarding the daily electricity consumption behavior of individual households. The relationship between the context features and daily electricity consumption behavior pattern types was modeled. Application and methodology seemed to be lacking in previous research and were therefore demonstrated in this study.

A VSTLF problem for individual households in Taiwan was implemented using the proposed approach, and the test results revealed a more favorable forecasting accuracy when compared with other methods. Furthermore, the effects of including historical load data as the predicted variables in the forecasting model and the accuracy of forecasting the aggregate electricity demand were studied in the numerical experiments. The results provided evidence that recent load data is valuable in conducting electricity demand forecasts. Additionally, as expected, the forecasting accuracy of the aggregate electricity demand was significnatly higher than that of individual households. This illustrated the disadvantage of an absence of risk pooling and error offsets in forecasting the electricity demand of individual households, but little has been discussed regarding this concern in previous research.

The methods of this study are promising for practical applications, and it is necessary to emphasize that the approach presented is applicable to any demand forecasting problem in



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which the products are uninventoriable and consumers’ consumption behavior is affected by external contextual features.

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Yu-Hsiang Hsiao received the Ph.D. degree in industrial engineering and engineering management from the National Tsing Hua University, Taiwan, in 2009. From 2009 to 2012, he was with the Information and Communications Research Laboratories, Industrial Technology Research Institute, Taiwan.

He is currently an Assistant Professor with the Department of Business Administration, National Taipei University, Taiwan. His research interests include quality engineering and management, data mining, statistical methods, and soft computing.

household electricity demand forecast based on context information and user daily schedule analysis...

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