Advance Data Mining - Analysis and forecasting of power factor for optimum electric consumption in a household

Analysis and Forecasting of Power Factor for
Optimum Electric Consumption in a Household
Manu Mishra Niraj Shah Punit Lohani Shrikant Samarth
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Group M Group M Group M Group M
M.Sc. Data Analytics M.Sc. Data Analytics M.Sc. Data Analytics M.Sc. Data Analytics
Advance Data Mining Advance Data Mining Advance Data Mining Advance Data Mining
Abstract— Household appliances operate on alternating current
circuits and consist of reactive load, which is a combination of
both capacitance and inductance. Due to presence of these kinds
of loads, there is an existence of phase difference between the
current and voltage. The cosine of phase angle between the
current and voltage, in such situations, is called Power Factor,
which is the ratio of the active and the apparent power.
Theoretically, its value must lie in the range of (0, 1). Lower
Power Factor affects the performance of electrical appliances.
Therefore, it is important to perform a check on its value. This
project focuses on the best short-term range of forecast for Power
Factor so as to achieve optimum energy consumption for a
household that can help in understanding the time series data in
terms of seasonal components. Techniques like ETS method,
Holt-Winters method and ARIMA model have been employed in
this research. The result shows that, for forecasting the time-
series data that contains seasonality Holt-Winters presented a
significant result. In addition to this, best short-term range of
forecast of Power Factor values have been achieved through
ARIMA model with 6 and 12 months forecast periods.
Keywords— Reactive load, capacitance, inductance,
alternating current, phase difference, power factor, ETS method,
Holt-Winters, ARIMA
I. INTRODUCTION
A. Background and Motivation
The consumption of electricity in a household is the total
combination of electrical energy consumed by the
household appliances. Household electrical appliances are
low rating electrical systems which operate on nominal
levels of voltage and current. The significance of power
factor can be understood in the case of AC circuits as they
consist of resistance, capacitance and inductance [1].
Household appliances such as kitchen equipment, washing
machine, light, air-conditioner etc. have a reactive load
mixture of both capacitance and inductance. Due to the
combined reactance offered by them, a phase difference
exists between the source voltage and current. A better
understanding of power factor can be given by the power
factor triangle given below:
Figure 1: Power Factor Triangle
This can also be represented as:
Cosine(Ø) =
𝐴𝑐𝑡𝑖𝑣𝑒 𝑃𝑜𝑤𝑒𝑟
𝐴𝑝𝑝𝑎𝑟𝑎𝑛𝑡 𝑃𝑜𝑤𝑒𝑟
where active power is the power consumed in an AC
(Alternating Current) circuit and the apparent power is the
total power across the element, given as the product of
voltage and current across it.
Theoretically, the value for power factor lies in the range
of (0, 1) and at all occasions, must be ideally close to 0.9 or
more. This condition is the requirement for optimum
performance of electrical equipment and transmission
systems. Lower values of power factor must be avoided
because it may lead to poor performance of equipment and
sometime, to damaging it as well. Therefore, it is a good
practice to keep a regular check on the value.
In practical situations, there can be variations in the value
of the power factor due to imbalance in reactive loads. With
the approach of machine learning methods, an attempt has
been made to analyze the power factor trend for a household
and forecast its power factor pattern so that best operating
conditions can be maintained.
The project aims to provide an application of machine
learning approach for power factor forecasting and can be
useful for audience intended to get insight into the usefulness
of power factor prediction and its implications.
B. Research Question
What can be the best short-term range of forecast for
power factor patterns so that optimum energy consumption
can be achieved for a household?
The objectives for this research are:
• To analyse the values of power factor for a household
using a variety of electrical appliances over a period
of time. This analysis will help in understanding the
time-series data in terms of its seasonal components
and other related parameters.
• To forecast the values of power factor using machine
learning approach and select the best short-term
forecasting range that can be used for referencing.
C. Structure of Paper

The paper has been divided into the following sub-
sections:
• Related Work: Discussion and review of literature and
work done in context to the project topic and research
question.
• Methodology: Implementation of CRISP-DM model in
implementation of data mining project.
• Result: Discussion of the results obtained in the
methodology.
• Conclusion and Future Work: Consideration of the final
outcome of the project and points for future work which
can be performed with the scope of the project.
II. RELATED WORK
A good approach for assessing the related work is by
reviewing the literature related to the field of study. Literature
review provides an exhaustive discussion on the past and
present attempts on the related topic, which helps in acquiring
a basis and overview of the concerned topic.
Considerable amount of work has been done with regard to
the forecasting and analysis of electrical load consumption. In
a research work by [2] an analysis was done on utilizing and
reducing the electricity consumption by analysing NILM at
appliance level. This paper aims at improving NILM using
load Division and Calibration (INDiC) that simpliﬁes NILM
by separating appliances over numerous instrument points
(meters/stages) and measured power was calibrated. The
proposed method was used with the Combinatorial
Optimization framework which shows signiﬁcant
improvement in disaggregation accuracy. [3] has created a
model which could accurately predict the future electricity
demand. It has assessed smart meter energy utilization data
from multiple houses and used autocorrelation to set up
decisive parameters for Gated Recurrent Unit (GRU) with the
help of recursive Deep Learning.
In a study by [4], an explanation has been provided as to
how time series approach, based on ARIMA (Auto Regressive
Moving average) model is useful for repairable system failure
analysis and forecasting. It has been suggested that for the
analysis of system failure, statistical methods can bridge the
gap in characterizing the failure process and found that the
ARIMA model shows promising results for such analysis.
Another work by [5] done in demand forecasting using time-
series approach shows how information of historical demand
can be used to create ARIMA models using time series. Based
on Akaike criterion, Schwarz Bayesian criterion, maximum
likelihood, and standard error performance criteria, a model
was selected which corresponds to ARIMA (1,0,1) and then it
was validated by another historical demand data. This research
proves that the model could be used in forecasting future
demands and can be a guideline for making decisions. Another
approach by [6], identifies of the issue of power demand
forecasting in residential micro-grids has been performed. In
the research work, comparison of performances of a few
methodologies utilizing ARMA models, support vector
machines, and neural systems that perform one-step ahead
predictions were extended to perform multi-step ahead
prediction error and error variance. As a result, they found out
that all machine learning approaches outperforms ARMA; but
the researchers suggest the adoption of hybrid approach by
using NAR (Nonlinear Auto-Regressive neural networks)
which displays the best forecasting accuracy for short term
forecasting, whereas SVM can be a potential choice for long
term intervals. The suggestion for SVM and PCA, as a
method, was suggested by [7] which analyses the electricity
usage by a single home. For this, K-Means clustering
algorithm was used for getting the ideal home utilization
electricity data points. The results of the study indicate that
Davis Boulden Index and Silhouette score obtains optimal, yet
detailed number of clusters in the K-means algorithm. It was
also been suggested that the house-hold power usage can be
analysed using other machine learning techniques such as PCA
and SVM algorithm. The literature on study involving the
application of machine learning algorithms in energy load
predictions can be further extended by considering the work of
[8] which found that different machine learning approaches
can be used to ensure the highest accuracy with the smallest
computational cost for different time scales in forecasting
electricity load. The performance-based metrics were
compared using Artificial Neutral Network (ANN), Support
Vector Regression (SVR), Random Forest Regression (RFR),
Extreme Gradient Boosting (XGB) and Flexible Neural Tree
(FNT) algorithms. A key point from the study shows how the
prediction accuracy decreases with the increase in the time
scale because of limitation of using all variables. Most of the
comparisons produced XGB model as the best performer.
It is difficult to forecast short term load prediction
accurately. Hence a model of hybrid ARIMA and SVM was
proposed by [9] to forecast daily load while correcting the
deviation of the previously forecasted values. The results show
that ARIMA-SVMs hybrid model further improves ARIMA in
simulation accuracy by declining 0.65% MAPE and 7.77MW
decline in RMSE which is far better than the SVM model
prediction. ARIMA and SARIMA (seasonal auto regressive
integrated moving average) models were used in another paper
by [10] for short term (i.e. at an hourly interval) load
forecasting. It was found that ARIMA and SARIMA model
outperforms other machine learning algorithms in predicting
short term load forecasting. Forecasting error was compared
and calculated by using multiplicative decomposition model
and SARIMA model as well by [11] and the results showed
that both of the time series model gives accurate prediction for
short term demand forecasting. [12] used numerous algorithms
including ARIMA and neural network as a bench marking
method for short term forecasting of household’s electricity
demand on different levels and timescale. The forecasting
horizon was considered from 15 minutes to 24 hours across
two datasets which had power usage statistics of households.
Overall results showed that MAPE (Mean Absolute Percentage
Error) varied between 5 to less than 100% which can be
further improved. Similar study on energy demand forecasting

by [13], in his research work on New Zealand, compared six
forecasting models, i.e. Logistic, ARIMA, combined, Harvey
Logistic, Harvey and Val models. The comparison of accuracy
was done for goodness-of-fit and showed that ARIMA is the
best performing model for short term forecasting demand.
Studies on India, Pakistan and Serbia by [14] and [15] [16]
used metabolic grey model (MGM), ARIMA, MGM-ARIMA
and back-propagation neural network and concluded that all
models gave high accuracy i.e. above 95%.
In recent years, power factor improvement has been a point
of attention for both customers and power generation
organizations for efficient energy usage and consumption.
Case studies on impact of power factor correction for the
economies of Kuwait by [17] and Uganda by [18] pointed out
that the value of power factor should be optimized in the range
of 0.9 to 0.95 so that an improved performance of the
electrical supply system can be achieved. Improvement in
power factor may lead to reduction in overloading of
transmission lines, high-voltage electrical equipment and
other related household equipment which are served through
the supply lines. A periodic measurement of power factor
among the electricity consumers may lead to finding cases of
low power factor and proper measures can be taken at the
correct time to improve the situations. [19] discusses that If a
case of low power factor is being encountered in electrical
distribution system, the same can be remediated using shunt
capacitor of appropriate value. A method of power factor
correction, as provided by [20], can be implemented by using
Integrated Circuits and microcontrollers. If the measurement
of power factor falls below 0.85, the setup using
microcontroller will cause triggering of relay which will then
add the capacitors to the circuit, in order to correct the case of
low power factor.
The main concerns related to low power factor values is of
prime concern for discussion. According to [21] and [22],
lower values of power factor increase the level of current in
distribution system. This surge in current will directly lead to
large line losses or copper losses, as per the formula:
Power Loss = I2
× R; where I is the current and R, resistance
In addition to this, conductor of large cross-section is
required for flow of high current. High level of current flow
through the conductor leads to large voltage drop. This is the
cause of for poor voltage regulation. Machines operating on
low power factor require higher kVA ratings and higher kVA
ratings directly increase the cost of machines. Therefore, cost
of machinery can be controlled by managing the level of
power factor.
The above discussion in terms of literature review provides
enough background for the problem being analysed in the
project to find out the best short-term range of forecast for
power factor patterns so that optimum energy consumption can
be achieved for a household.
III.METHODOLOGY
Cross-Industry Standard Process for Data Mining, or in
short, CRISP-DM [23] has been employed as the reference
methodology for the data mining project. The selection for this
methodology for the project has been made in accordance to
the discussion that CRISP-DM channelizes the operation of
data mining project into six phases which makes it easier to
apply the concept of data mining in real-life scenarios and
bring out the business outcomes from the same. Since the
project approach is to scrutinize and forecast the power factor
for households, therefore it stands out as the best model for
this project.
There are six stages for CRISP-DM model, which are as
follows:
• Business Understanding
• Data Understanding
• Data Preparation
• Modeling
• Evaluation
• Deployment
A. Business Understanding
The business objective for the project deals with the
analysis and forecasting of power factor values for a
household. This objective has been dealt in detail in the
Research Question section. R has been used in this project
for exploratory data analysis and model implementation. An
attempt has been made in the project to produce accurate
forecasting of power factor values, based on the dataset of 2
million electrical measurements. All the efforts have been
made so that the results obtained from the forecasting and
analysis can be useful in terms of business perspective.
B. Data Understanding
Data for the project has been sourced from UCI machine
learning repository1
. This dataset contains the electrical
power consumption of an individual household located in
Sceaux, which is seven kilometers from Paris, France. The
time-series dataset contains measurements in the range of
December 2006 to November 2010 and has approximately 2
million measurements, as a combination of following
indicators:
Figure 2: Description of variables in dataset
1
https://archive.ics.uci.edu/ml/datasets/individual+household+electric+power+
consumption

Sub-metering 1refers to energy consumption in kitchen,
sub-metering 2 is the measurement of energy consumed in
laundry room while the measurement for electric water
heater and air-conditioner is captured by sub-metering 3.
The variables included in the dataset provide enough
indicators to calculate and analyze the power factor and its
prediction. Size of the dataset is pertinent enough for a data
mining project to bring out useful insights related to the
business requirements. The data quality in terms of missing
values and other related parameters has been dealt in the
stage for data preparation.
C. Data Preparation and Transformation
According to the analysis in previous section, the
discussed data is suitable and has been taken up for the
project. The description of the dataset, at the source, claims
that the data contains missing values. Upon inspecting the
same using R, it has been found that about 26,000 entries or
1.25% of the data has missing values. These values have
been removed as their share is quite small as compared to the
size of the dataset. Since the main motive of the analysis
employs the use of power factor, in reference to the electrical
measurements, therefore, a new column for power factor has
been introduced. The formula for calculating the power
factor is as follows:
Root Mean Square Voltage, Vrms=1.11× voltage ………. (1)
Apparent Power = Vrms × current …………….………….. (2)
Power Factor = Active Power ÷ Apparent Power …..…... (3)
The value of voltage in equation (2) and current, as
global_intensity in equation (3) has been provided in the
parent dataset.
Another data pre-processing has been carried out in terms
of the range of value of power factor. The value of power
factor is theoretically always in the range [0,1] and
practically, less than 1. The value of power factor as unity
means that the referenced load is purely resistive, and 100%
power is consumed. Since the data in reference has
household appliances, which are reactive in nature i.e.
inductive or capacitive, therefore there must be some power
loss. Thus, the value of power factor can never be unity, and
in this case, it must be less than one.
Therefore, a check has been performed to know the
number of measurements having the value of power factor
greater than 1. On analysis, 34,000 entries or 1.6% of the
data have this anomaly. Owing to their share, they have been
removed to produce the analysis-ready dataset.
The considered data for the analysis is a time-series data
as the project deals with time-series forecasting of power
factor. There is a possibility that the time series dataset may
contain seasonal component. The seasonal data may iterate
itself over time-range of day, week, month or year and this
may interfere with the predictions given by the models.
Time-series data has been segregated in terms of four
seasons: Autumn, Spring, Summer and Winter. From figure
3, it can be observed that the aggregated values of power
factor, as per the seasons, are not same. This confirms the
presence of seasonality component in the reference data.
Figure 3: Power Factor Averaged by Seasons
The value of monthly averaged power factor is shown in
figure 4, which shows that how aggregated value of power
factor varies over months in a year, for the reference time
period of 2007-2010. This variation in the values depicts that
in addition to seasonal variation, the time series data has
variation in terms of monthly intervals.
Figure 4: Power Factor Averaged by Months
Usage of energy for the household can be described
in terms of the measurements from the three meters.
Figure 5 shows that the sub-meter 1 and 2 have
approximately same energy usage over the years 2007 to
2010 while the measurements of sub-meter 3 have the
highest value.
Figure 5: Total Energy Usage by Year, as per different sub-meters

The same trend can be seen in figure 6 where it can be
interpreted that the sub-meter 3 has the highest proportion of
energy consumption for the three years, as compared to sub-
meter 1 and 2.
Figure 6: Proportion of Total Yearly Energy Consumption, as per
different sub-meters
The appliances measured by sub-meter-1 are
dishwasher, oven and microwave. Sub-meter-2 measures
washing machine, refrigerator and light while consumption
of electric water heater and air-conditioner is measured by
sub-meter 3. According to the above description, the load
mix for sub-meter-1and sub-meter-2 is somewhat resistive
while it is a mixture of resistive and inductive load for sub-
meter-3. This information is represented in order to explain
that the overall household load is not completely resistive in
nature and hence, the value of power factor at any given
instance of time-series should not be equal to unity.
D. Modelling
A study by [24] shows the importance of data
granularity. Breaking the data into the smallest possible and
realistic levels or granules provides the opportunity to study
and analyze the data at the micro level. Therefore, the
reference time series has been broken down into daily,
weekly and monthly levels so as to study the nature of data
at each of the granular level.
Since the data has been divided in the possible levels in
terms of day, week and month, the evaluation of randomness
can be an added factor of study because this can provide the
level at which the time series data can be fed to the
forecasting models to get optimum results.
Figure 7 shows the randomness for the three levels of
granularity i.e. day, month and week. The lowest value has
been obtained for monthly granularity which means that
time-series data, aggregated on monthly basis, possess lack
of pattern and predictability in terms of prediction of power
factor. Therefore, monthly aggregated data has been
provided to the models, which has been discussed in detail.
Figure 7: Randomness for the declared granularity (day, month and year)
For the purpose of forecasting and getting the result, below
mentioned techniques have been used:
• ETS Method
Exponential smoothing method helps in the smart
forecasting by taking the weighted average of the past
values into consideration and assigning the higher weights to
the recent values [25].
As a part of this project, ets() in R, has been used in the
ETS method.
• Holt-winters method
Double exponential smoothing type of method has been
used as part of the Holt-winters method. The Holt-Winters
method is basically employed for forecasting the data which
consist of correlation in terms of seasons, change in trends
and seasonality [26].
• ARIMA model
ARIMA model has been used for forecasting the result
and it consists of three parameters i.e. (p,d,q) which is
represented as ARIMA(p,d,q). The AR part of the model is
based on the concept that the current estimate of the series xt,
which is explained as p, where p represents the total number
of past steps needed to forecast the present value. Level of
differencing required by the original time series to transform
to stationary is represented by d. q represents the order of the
moving average model.
Here, Auto ARIMA has been implemented using
auto.arima() in R, that helps in obtaining the best ARIMA
model which is performed in reference to single variable i.e.
Power factor [27].

E. Evaluation
For the evaluation of the forecasted model, three metrics
have been taken into consideration and they are:
• Mean absolute percentage error (MAPE)
• Root mean square error (RMSE)
• Mean absolute error (MAE)
If the value of MAPE falls in the bracket of 10%-20%
then the model will be categorized as an acceptable model
while the value of less than 10% shows that the model has
performed well [28]. The mean absolute error is an average
of errors in the measurement. Moreover, lower value of the
RMSE signifies that the model is good enough.
Below are the results obtained:
1) ETS Method
The performance metrics for ETS method is represented
below:
Figure 8: Table for accuracy statistics for ETS method
The forecast of the power factor for the next 12 months
from the ETS method is depicted below:
Figure 9: Forecast curve for ETS method
2) Holt-Winters Method
The performance metrics for Holt-Winters method is
represented below:
Figure 10: Table for accuracy statistics for Holt-Winters method
from the Holt-winters method is depicted below:
Figure 10: Forecast curve for Holt-Winters method
3) ARIMA Model
The performance metrics for ARIMA model is
represented below:
Figure 11: Table for accuracy statistics for ARIMA Model
from the ARIMA (1, 0, 0) is depicted below:
Figure 12: Forecast curve for ARIMA Model
On evaluating the results, for forecasting the data that
contains seasonality, Holt-winters presented a good result
with the RMSE value of 0.014. In addition, the ARIMA
model with 6 and 12 months forecasts period proved to be an
effective model for predicting the power factor usage for
achieving the optimum energy consumption of households
with acceptable values of MAPE, RMSE and MAE
respectively. Further, the forecast months and the values of
respective RMSE, MAPE and MAE are represented below in
the tabular format:

Figure 13: Evaluation Statistics for different forecasting months of
ARIMA
F. Deployment
In the phase of deployment of the project, the results
derived from the evaluation section can be employed to
provide insights regarding the business objectives outlined.
The report of the project is a complete discussion of the
implementation of solution of research question, and thus,
can be referred as a handy documentation by the intended
audience.
IV. RESULT
The evaluation phase of the CRISP-DM methodology
deals with assessment of the various methods applied to the
data set, i.e. ETS method, Holt-Winters method and ARIMA
model, in order to get useful results with reference to the
research question. For forecasting the time-series which
contains seasonality, Holt-Winters presented a good result
with the RMSE value of 0.014.The best short-term range of
forecast for power factor values and its patterns has been
achieved through ARIMA model with 6-months and 12-
months forecasting period.
V. CONCLUSION & FUTURE WORK
The best short-term range of forecasts for power factor
patterns and values has been achieved for 6 months and 12
months duration, using ARIMA model. Satisfactory result
has been achieved using Holts-Winters method as well.
These results can help the organizations which deal with
power factor measurement so that the overall power quality
of the electrical distribution and transmission systems can be
maintained. The scope of this project can be further extended
by application of hybrid model for enhancing the
performance and accuracy of the forecasts. The
forecastHybrid package in R provides hybridModel function
which fits multiple models from the auto.arima (), ets (),
thetaf (), nnetar (), stlm () and tbats () functions using either
equal weights or weights based on in-sample errors [28].
A different approach of using various combinations of
resistive and reactive load can be used for checking the
ability of ARIMA and hybrid model for forecasting the
power factor patterns of households.
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