Egede Project Final Correction
Egede Project Final Correction
Egede Project Final Correction
NEURAL NETWORK
BY
NWEKE EGEDE F.
PG/M.ENG/08/49172
UNIVERSITY OF NIGERIA,
NSUKKA.
JULY, 2012
i
SHORT-TERM ELECTRIC POWER FORECAST IN THE NIGERIAN
POWER SYSTEM USING ARTIFICIAL NEURAL NETWORK
BY
NWEKE EGEDE F.
PG/M.ENG/08/49172
July, 2012
i
APPROVAL PAGE
This is to certify that this research work was approved on behalf of the
BY
-----------------------------------------------
Student
Nweke Egede F.
------------------------------------------------
Supervisor
Ven. Engr. Prof T. C. Madueme
-----------------------------------------------------
H.O.D.
Engr. Dr. B. O. Anyaka
----------------------------------------------------
External Examiner
ii
CERTIFICATION
This is to certify that this thesis was written by Nweke Egede Friday, an M.Eng student of
number PG/M. Eng/2008/49172 in a partial fulfillment of the requirements for the award
of M.Eng.
The work embodied in this thesis is original and has not been submitted in part or full for
………………………………… Date………………………….
Student
Nweke Egede F.
………………………………... Date………………………….
Ven. Engr. Prof. T. C. Madueme
(Supervisor)
…………………………… Date…………………………
Engr. Dr. Anyaka B. O.
Head of Department
iii
Solely dedicated to
iv
ACKNOWLEDGEMENT
painstakingly reading this work between lines and effecting all the necessary
corrections on it and also for guiding me properly throughout this work. I am also
My thanks are also due to all the lecturers in the Department of Electrical
Engineering University of Nigeria especially, Dr. Ani for the warm treatment they
I also appreciate deeply the authorities of University of Nigeria Nsukka for giving
Finally my gratitude goes to my wife, Goodness, for being a wife that makes
v
vi
TABLE OF CONTENTS
Title page i
Approval page ii
Certification iii
Dedication iii
Acknowledgment iv
Table of contents v
List of figures ix
List of Tables x
List of Abbreviations xi
Abstract xii
vii
2.4.2 End-Use Method 15
3.0 Introduction 51
viii
CHAPTER FOUR: EXPERIMENTAL RESULTS AND DISCUSSIONS
4.0 Introduction 67
4.1 Selection of Network Architecture and Parametric Values 67
4.2 Choice of training algorithm 69
CHAPTER FIVE:
5.1 Conclusion 80
REFERENCES 83
APPENDIX 97
ix
LIST OF FIGURES
4.8 Test result for 7 days (Friday 25th- Thursday 31st March 2011) 77
x
LIST OF TABLES
4.3 Effect of time delay vector on model accuracy and training time 71
xi
LIST OF ABBREVIATIONS
xii
ABSTRACT
This thesis is a study of short-term electric power forecasting in the Nigerian power
system using artificial neural network model. The model is created in the form of a
simulation program written with MATLAB tool. The model, a multilayer time-
delayed feed-forward artificial neural network trained with error back propagation
algorithm, was made to study the pre-historical load pattern of a typical Nigerian
power system in a supervised training manner. After presenting the model with a
reasonable number of training samples, the model could forecast correctly electric
power supply in the Nigerian power system 24 hours in advance. An absolute mean
error of 4.27% was obtained when the trained neural network model was tested on
one week, daily hourly load data of a typical Nigerian power station. This result
xiii
CHAPTER ONE
INTRODUCTION
A great deal of effort is required to maintain an electric power supply within the
requirements of the various types of customers served. Some of the requirements for
power supply are readily recognized by most consumers, such as proper voltage,
on demand, we mean to say that power must be available to the consumer in any amount
that he may require from time to time. Stated yet in another way, motors may be started
or shut down, fans and lights may be turned on or off, without giving any advance
demographic and weather factors alongside econometric factors that has posed the
greatest challenges like the amount of energy to generate, the load (circuits) to switch on
or off at a point in time on the part of power utility company. Hence, a power system
must be well planned so as to ensure adequate and reliable power supply to meet the
The primary pre-requisite for system planning is to arrive at realistic estimates for
future demands of power. The foregoing concept is a part of load forecasting. Basically,
load forecast is no more than an intelligent projection of past and present demand patterns
to determine future ones with sufficient reliability [1]. The Nigerian power system today
is known for its epileptic, inadequate and unreliable nature [2]. Its performance will
1
improve if a system for accurate load forecasting is designed to aid its operation and
planning. Accurate load forecasting holds a great saving potential for electric utility
corporations. According to Bun and Farmer, [3] these savings are realized when load
forecasting is used to control operations and decisions such as economic load dispatch,
unit commitment, fuel allocation and off-line network analysis. The accuracy of load
and control of power systems may be quite sensitive to forecasting errors [4]. Haida et al,
[5] observed that both positive and negative forecasting errors resulted in increased
operating costs.
Load forecasting may be applied in the long, medium, short, and very short-term
time scale. Srinivasan and Lee, [6] classified load forecasting in terms of the planning
horizon’s duration: up to 1 day for short-term load forecasting (STLF), 1 day to 1 year for
medium-term load forecasting (MTLF), and 1-10 years for long-term load forecasting
(LTLF). Short-term load forecasting (STLF) aims at predicting electric loads for a period
of minutes, hours, days, or weeks [7]. STLF plays an important role in the real-time
control and the security functions of an energy management system. STLF applied to the
system security assessment problem, especially in the case of increased renewable energy
sources (RES) penetration in isolated power grids, can provide, in advance, valuable
information on the detection of vulnerable situations. Long- and medium- term forecasts
additions, along with the type of facilities required in transmission expansion planning,
annual hydro and thermal maintenance scheduling etc. [7] . Kalaitzakis et al, [7] noted
2
that short-term load forecast for a period of 1-24 h ahead is important for the daily
operations of a power utility since it is used for unit commitment, energy transfer
because electric load is determined largely by variables that involve “uncertainty” and
whose relation with the final load is not deduced directly [8]. Some of these variables or
factors include economic factors, time, day, season, weather and random effects.
Electricity usage may be, therefore, predicted using data from previous history of load,
temperature, humidity, luminosity, and wind speed among other factors. However,
accurate models of load forecasting that use all these factors increase modeling
complexity. Several methods, therefore, have been used to perform load forecasting each
with its inherent shortfalls. Time series analysis is a very effective method to create
mathematical models for solving a broad variety of complex problems [9]. These models
of observations. However, creating an accurate model for a time series that represents
non-linear processes or processes that have a wide variance is very difficult [9]. The trend
today, however, is to solve most problems of human using Artificial Intelligence Means
modeling of time series problems [10]. Artificial Neural Networks (ANNs) being one of
the artificial intelligence means have been successfully used to solve a broad variety of
systems, entailing linear and non-linear processes [9]. The application of ANNs in time
series prediction is presented in [11] and in [12]. The success in the application of ANNs
3
lies in the fact that when these networks are properly trained and configured, they are
capable of accurately approximating any measurable function. The neurons learn the
patterns hidden in data and make generalizations of these patterns even in the presence of
noise or missing information. Predictions are performed by the ANN based on the
observed data. Load forecasting is clearly a time series problem and an example of a time
series problem that can be solved with ANNs is electricity load forecasting.
computer programs which solve problems with “intuitive” or “best-guess” methods often
used by humans instead of the strictly quantitative methods usually used by computer
[13]. Expert systems, neural networks, fuzzy logic and support vector machines are some
of the AIs currently in use today. Programs for some problems such as image recognition,
speech recognition, weather forecasting, electric load forecasting, and three dimensional
such as 386/i486-based systems [13]. For applications such as these, new computer
architecture, modeled after the human brain and which is known as Artificial Neural
Hence, in this study a novel attempt is made to solve the problem of electric power
It is an established issue that the Nigerian power utility company is nowhere in the
energy business. The utility company, PHCN, as it is called today, is yet to meet the
people’s demand for electric energy satisfactorily for any known period of time. It is
4
evident that the generated power is inadequate and so, the utility company considers load
shedding and restricted demand as a way out just as the government of the federation is
insisting on privatization of the energy sector as the last resort. Worst still, even under
these conditions of load shedding and restricted demand, the integrity of the supplied
power has always been questioned. The irony of this development is that it is happening
The problem, therefore, is in spite of this inadequacy in generation, is there any way we
can manage what we have to satisfy our taste? Since economics is all about using limited
resources to address the endless human needs, there are ways. The issue now is, what are
Before we x-ray one way forward, we need ask: can prompt and proper decisions on unit
commitment, fuel allocation, energy transfer scheduling, and load dispatch be of any
help? Certainly, YES. Since short term load forecasting is necessary for such prompt and
proper decisions on unit commitment, fuel allocation, power wheeling arrangement, load
dispatch etc., knowledge of load forecasting in the Nigerian power system is one such
way forward. Better still, what if this load forecasting is performed by means of artificial
intelligence- Artificial Neural Network (ANN) means? In other words Man Machine
Interface (MMI) can be guaranteed. The problem is more than half-way solved since
So, this research is aimed at suggesting a solution to the ailing Nigerian power system by
proposing a model which can perform 24-hours-ahead load forecasting in the Nigerian
Although the objectives of the study can be inferred from the background to the study
outlined in the previous section, it can still be clearly and concisely stated that the
(a) To model artificial neural network which can forecast electric power supply for
(b) To train the model (using back propagation algorithm) with pre-historical load
data obtained from a sample of the Nigerian power company so that each input
(c) To Test the model to get the values of future power supplies in the Nigerian
(d) In the light of the above, make necessary recommendations and suggestions for
further research.
It will be clear from our objectives that even though the impetus for this study was
generated by the ‘sorry’ state of the Nigerian power system, the scope of this study has
been restricted to New Haven Enugu 132/33KV Transmission station. In addition, short-
term load forecasting model is being proposed in this work. This restriction has been
dictated by the need to attempt a reasonable depth of treatment of data collected within
the time available and on the other part due to some financial limitations.
during load forecasting, the ANN modeled for the purpose of this research will be trained
6
without such factors as inputs. This became necessary so as to avoid the unnecessary
model complexity that is usually associated with a model encompassing all or some of
such factors. The forecasting model being proposed here does not take into account
Temperature data have been omitted simply, because the prediction is concerned with
data corresponding to the territory of the whole country and since temperature changes a
lot in different regions of Nigeria, it would be difficult to adjust the proper value of
temperature for a particular day. Though load data from a sampled Nigerian power
station will be used to test the model, the model remains for the entire Nigerian utility.
From available literature still, it is primarily the behavior of low voltage consumers or
modeling and implementation problems limit the use of load forecasting models requiring
weather data, thus several works have appeared recently omitting weather data [7], [16],
[17], [18], [19], [20]. To support this stance further, we make the following case:
Adaptive Systems) had in the year 2001 organized a world-wide competition on methods
to accurately predict electricity load [9]. In the contest, the average temperature and load
data on half hourly basis for years 1997 and 1998 were provided. The objective of the
contest was to predict daily peak demands of electricity for January 1999 based on the
data from these previous years. The model proposed by Chang et al., [21] which in terms
7
of mean absolute percentage error (MAPE) obtained the first place in the competition
This shortfall is also due to non-readily availability of information on such factors at the
point of need.
The above restrictions notwithstanding, however, there are strong indications from
the available literature that any findings and conclusions will be generalizable to Nigerian
Power System at large even at a high degree of accuracy of the model results.
(i) To guide the operation and planning of the Nigerian Power System
(ii) To aid power system Engineers who may wish to design a power system newly
(iv) To help validate the results obtained by other leading researchers who might
8
CHAPTER TWO
LITERATURE REVIEW
may happen to a system in the next coming time periods. Chakrabarti and Halder, [23]
also defined load forecasting as a method to estimate the load for a future time point from
Vadhera, [1] seem, however, to have given a more comprehensive and acceptable
definition of load forecasting when he notes that load forecast is no more than an
intelligent projection of past and present demand patterns to determine future ones with
conglomeration of devices that taps energy from the power system network. Load is a
general term meaning either demand or energy, where demand is time rate of change of
energy.
To cast the importance of load forecasting, Vadhera, [1] swiftly noted that good
Still on the justification of the need for load forecasting, Alfares and Nazeerudin, [4]
contended that load forecasting is a central and integral process in the planning and
operation of electric utilities. Alfares and Nazeerudin, [4] went further to note that load
forecasting involves the accurate prediction of both the magnitude and geographical
locations of electric load over the different periods (usually hours) of the planning
9
horizon. They went further to add that accurate load forecasting holds a great saving
potential for electric utility corporations. According to Bunn and Farmer, [3], these
savings are realized when load forecasting is used to control operations and decisions
such as dispatch, unit commitment, fuel allocation and off-line network analysis. Adepoju
et al, [24] shared the same view as Bunn and Farmer, [3] when they noted that load
forecasting being very essential to the operation of electricity companies enhances the
According to Adepoju et al, [24], the operation and planning of a power utility
company requires an adequate model for electric power load forecasting. Load
forecasting plays a key role in helping an electric utility to make important decisions on
development [24]. Feinberg et al, [25] was of the view that accurate models for electric
power load forecasting are essential to the operation and planning of a utility company.
Load forecasting helps an electric utility company to make important decisions including
decisions on purchasing and generating electric power, load switching, and infrastructure
development [25]. Those who can benefit from the knowledge of Load forecast include
energy suppliers, ISOs, financial institutions, and other participant in electric energy
Load forecasts can be divided into three categories: short-term forecasts which are
usually from one hour to one week, medium-term forecasts which are usually from a
week to a year, and long-term forecasts which are longer than a year [25], [4], [26], and
[24].
10
2.3: Problems of Load Forecasting
Load forecasting, however, is not an easy thing. This is because load is affected by
many physical factors such as weather, national economic health, popular TV programs,
public holidays, etc. [27]. This actually makes load forecasting a complex process
demanding experience and high analytical ability using probabilistic techniques including
neural networks.
Nicholson, [28] conducted an early survey of electric load forecasting techniques. Load
demand modeling and forecasting was also reviewed in the works of [3], [29], and [30].
Moghram and Rahman, [31] surveyed electric load forecasting techniques and in recent
times Alfares and Nazeerudin, [4] conducted a literature survey and classification of
review of newer papers on load forecasting techniques in general and load forecasting
using ANN in particular. An up-to-date brief verbal and mathematical description of each
Vadhera, [1] listed the methods normally used for load forecasting as:
• Extrapolation technique;
• Scheer’s method;
• Econometric models.
Chakrabarti and Halder, [23] Insisted that load forecasting might be done following any
i. Extrapolation;
ii. Correlation;
i. Multiple regression;
12
In addition to the above techniques Feinberg et al, [25] gave three additional
techniques named as (i) support vector machines (SVMs), (ii) Similar day approach, and
• Extrapolation Technique
• End-use method
• Scheer’s method
• Correlation method
on genetic algorithms
• Neural networks.
where applicable.
13
2.4.1: Extrapolation Technique
The extrapolation technique is based on curve fitting to previous load data available.
Then with a trend curve obtained from curve fitted, the load can be forecast at any future
point (t = δ +j) by calculating the trend curve function at that point (t = δ +j). This
method is very simple and it is found to be very reliable in some cases. The errors in data
available and errors in curve fitting are not accounted for, therefore, it is called a
deterministic extrapolation. Standard analytical functions used in trend cure fitting are;
• Straight line, d = α + β δ ,
• Parabola, d = α + β δ 2 ,
2 3
• S – curve, d = α + βδ + λδ + ηδ
• Exponential, d = ∂α + βδ
• Gompertz, d = In −1
(α + β l )
δ
The method of least squares is generally adopted for curve-fitting. If the accuracy of
the forecast available is tested using statistical measures such as mean and variance, the
basic technique becomes a probabilistic extrapolation. The best trend curve may be
obtained using regression analysis and the best estimate (to forecast the load at any future
time point) may be obtained using equation of that best trend cure. The main drawback of
entirely upon the past trend and sometimes, this may give erroneous results [1], [23].
14
2.4.2: End-Use Method
information on end use and end users, such as appliances, the customer use, their ages,
sizes of houses, and so on [25]. Statistical information about customers along with
dynamics of change is the basis for the forecast. End-use method is a modified form of
extrapolation [1]. In the method of extrapolation only the system yearly peak demand of
past years are plotted and future years demand is obtained by the trend curve of the past.
In the End-use method, the demands of different categories of loads are projected
separately.
commercial, and industrial sector. These models are based on the principle that electricity
demand is derived from customer’s demand for light, cooling, heating, refrigeration, etc.
Thus end-use models explain energy demand as a function of the number of appliances in
Ideally, this approach is very accurate. However, it is sensitive to the amount and
quality of end-use data. For example, in this method the distribution of equipment age is
important for particular types of appliances. End-use forecast requires less historical data
Scheer has studied the load growth pattern of the developing countries reporting to
United Nations [34], [35], [1]. His approach to the problem of load forecasting was
15
through the per-capita consumption of energy. The per capita consumption of energy in
all developing countries follows a unique pattern. Economic condition of the people,
policy of government, rainfall and mineral resources etc., in an area, are also responsible
for affecting the load growth pattern of the area. Scheer’s method of load forecasting
Where G= annual percentage growth in per capita consumption; U = annual Kwh usage
per person. C1, C2, C3, etc. are constants for population growth, growth of agriculture
K1,K2,.…,Kn are constants, assumed unity unless a very high or very low growth rate is
expected. If the rate of growth is higher than normal then their value is less than unity and
vice-versa.
in the past).
Using the value of G the total energy consumption in the area can be calculated for a year
knowing the per capita consumption of the previous year. If the load factor is known,
then from total energy value, the peak load demand can be calculated.
16
Load factor does not remain constant for all times. According to Scheer, the load
factor approaches its ultimate value of 65% in an asymptotic fashion cutting down the
difference by halves in every sixteen years. The load factor up to the 16th year from the
Where z is the base year load factor, Y is a multiplier whose value for different years
Year from 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
start
Values of Y 1.00 0.96 0.92 0.88 0.84 0.80 0.77 0.74 0.71 0.68 0.65 0.62 0.60 0.57 0.55 0.52 0.50
One problem with scheer’s model is the selection of the base year. For this
purpose, the best fit curve is drawn through the past growth of yearly peak load as well as
yearly energy consumption. Any point towards the end of the best fit curve may be taken
Multiple regression analysis for load forecasting uses the technique of weighted
least-squares estimation. Based on this analysis, the statistical relationship between total
load and weather conditions as well as the day type influences can be calculated. The
17
regression coefficients are computed by an equally or exponentially weighted least-
squares estimation using the defined amount of historical data. Mbamalu El-Hawary, [36]
Yt = Vtat + εt
Where t is sampling time, Yt measured system load, Vt vector of adapted variables such
as time, temperature, light intensity, wind speed, humidity, day type (workday, weekend,
holiday), etc., at transposed vector of regression coefficients, and εt model error at time, t.
The data analysis program allows the selection of the polynomial degree of
influence of the variables from 1 to 5. In most cases, linear dependency gives the best
results. Moghram and Rahman, [31] evaluated this model and compared it with other
models for a 24-h-ahead load forecast. Barakat et al, [37] used the regression model to fit
data and check seasonal variations. The model developed by Papalexopoulos and
Hesterberg, [38] produces an initial daily peak forecast and then uses this initial peak
forecast to produce initial hourly forecasts. In the next step, it uses the maximum of the
initial hourly forecast, the most recent initial peak forecast error, and exponentially
Haida and Muto, [5] presented a regression-based daily peak load forecasting
method with a transformation technique. Their method uses a regression model to predict
the nominal load and a learning method to predict the residual load. Haida et al, [39]
expanded this model by introducing two trend processing techniques designed to reduce
Hyde and Hodnett, [41] presented weather-load model to predict load demand for
the Irish electricity supply system. To include the effect of weather, the model was
developed using regression analysis of historical load and data. Hyde and Hodnett, [42]
later developed an adaptable regression model for 1-day-ahead forecasts, which identifies
to estimate the parameters of the two components. Nazarko, [43] used their new
regression based method, Nonlinear load Research Estimator (NLRE) to forecast load for
Eastern Saudi Arabia as a function of weather data, solar radiation, population and per
capita gross domestic product. Variable selection is carried out using the stepping
probability density function of the load and load effecting factors. The model produces
the forecast as a conditional expectation of the load given the time, weather and other
explanatory variables, such as the average of past actual loads and the size of the
neighbourhood.
Alfares and Nazeerudin, [4] presented a regression based daily peak load
forecasting method for a whole year including holidays. To forecast load precisely
throughout a year, different seasonal factors that affect load differently in different
19
seasons are considered. In the winter season, average wind chill factor is added as an
explanatory variable in addition to the explanatory variables used in the summer model.
In transitional seasons such as spring and fall, the transformation technique is used.
Finally for holiday, a holiday effect load is deducted from normal load to estimate the
Exponential smoothing is one of the classical methods used for load forecasting.
The approach is first to model the load based on previous data, then to use this model to
In exponential smoothing models used by [31], the load, y (t) at time, t is modeled
y(t) = β(t)Tf(t) + ε (t ) ,
where:
f(t) fitting function vector of the process, β(t) coefficient vector, ε (t ) white noise,
The Winter’s method is one of several exponential smoothing methods that can analyze
seasonal time series directly. This method is based on three smoothing constants for
stationary, trend and seasonality. Results of the analysis by [37] showed that the unique
pattern of energy and demand pertaining to fast growing areas was difficult to analyze
20
and predict by direct application of the Winter’s method. El-keib et al, [46] presented a
hybrid approach in which exponential smoothing was augmented with power spectrum
analysis and adaptive autoregressive modeling. A new trend removal technique by [47]
was based on optimal smoothing. This technique has been shown to compare favourably
reweighted least-squares to identify the model order and parameters. The method uses an
operator that controls one variable at a time. An optimal starting point is determined
using the operator. This method utilizes the autocorrelation function of the resulting
differenced past load data in identifying a sub-optimal model of the load dynamics.
The weighting function, the tuning constants and the weighted sum of the squared
residuals form a three way decision variable in identifying an optimal model and the
Y = ×β + ε ,
× 1 vector of random errors. Results are more accurate when the errors are not Guassian.
β can be obtained by iterative methods [48]. Given an initial β , one can also use the
21
Beaton-Turkey iterative reweighted least-squares algorithm (IRLS). In a similar work,
[36] proposed an interactive approach employing least-squares and the IRLS procedure
method was applied to predict load at the Nova Scotia Power Corporation.
In this context, forecasting is adaptive in the sense that the model parameters are
automatically corrected to keep track of the changing load conditions. Adaptive load
forecasting can be used as an on-line software package in the utilities control system.
Regression analysis based on the Kalman filter theory is used. The Kalman filter
normally uses the current prediction error and the current weather data acquisition
programs to estimate the next state vector. The total historical data set is analysed to
determine the state vector, not only most recent measured load and weather data. This
mode of operation allows switching between multiple and adaptive regression analysis.
The model used is the same as the one used in the multiple regression section as
Yt = Vt at + ε t
escalator structure as well as a lattice structure for joint processes. Their method used a
temperature. Their algorithm performed better than the commonly used RLS (Recursive
Least-Square) algorithm. Grady et al, [50] enhanced and applied the algorithm developed
22
by [49]. An improvement was obtained in the ability to forecast total system hourly load
Park et al, [52] developed a composite model for load prediction, composed of
three components: nominal load, type load and residual load. The nominal load is
modeled such that the Kalman filter can be used and the parameters of the model are
McDonald, [53] presented a real time implementation of weather adaptive short term load
Average ARMA model, whose parameters are estimated and updated on-line, using the
Paarman and Najar’s, [54] adaptive online load forecasting approach automatically
adjusts model parameters according to changing conditions based on time series analysis.
This approach has two unique features: autocorrelation optimization is used for handling
cyclic patterns and, in addition to updating model parameters, the structure and order of
time series is adaptable to new conditions. An important feature of the regression model
system is fully automated with a built-in procedure for updating the mdoel. Zheng et al,
[55] applied wavelet transform-Kalman filter method for load forecasting. Two models
are formed (weather sensitive and insensitive) in which the wavelet coefficients are
23
2.4.8: Stochastic time series
It has been observed that unique patterns of energy and demand pertaining to fast-
growing areas are difficult to analyze and predict by direct application of time-series
methods. However, these methods appear to be among the most popular approaches that
have been applied and are still being applied to STLF. Using the time-series approach, a
model is first developed based on the previous data then future load is predicted based on
this model. In other words, and as it was stated by Aggarwal, [56], we want to operate on
operations. Some of the time series models used for load forecasting will be discussed
here.
autoregressive (AR) model can be used to model the load profile, which is given by [57]
m
as: Lˆk = −∑ σ ik Lk −i + wk ...................... ( 3)
i =1
σ i , i = 1, 2,L, m are unknown coefficients, and (3) is the AR model of order m. the
unknown coefficients in (3) can be tuned on-line using the well-known least mean square
accuracy. Zhao et al., [59] developed two periodical autoregressive (PAR) models for
In the ARMA model the current value of the time series y(t) is expressed linearly
in terms of its values at previous periods [y(t-1), y (t-2),…] and in terms of previous
values of white noise [a(t-1), a(t-2),…]. For an ARMA of order (p, q), the model is
written as:
for load forecasting. In this method, the original time series of monthly peak demands are
decomposed into deterministic and stochastic load components, the latter determined by
ARMA model. Fan and McDonald, [53] used the weighted Recursive least squares
(WRLS) algorithm to update the parameters of their adaptive ARMA model. Chen, [61]
used an adaptive ARMA model for load forecasting, in which the available forecast
errors are used to update the model. Using minimum mean square error to derive error
25
• Autoregressive integrated moving average (ARIMA) model
form has to be done first. This transformation can be performed by the differencing
series that needs to be differenced d times and has orders p and q for the AR and MA
φ ( B ) ∇d y (t ) = θ ( B ) a (t )
--------------------------------------(5)
The procedure proposed by [62] used the trend component to forecast the growth
in the system load, the weather parameters to forecast the weather sensitive load
component, and the ARIMA model to produce the non-weather cyclic component of the
weekly peak load. Barakat, [37] used a seasonal ARIMA model on historical data to
predict the load with seasonal variations. Juberias, [63] developed a real time load
variable.
to identify the autoregressive moving average with exogenous variable (ARMAX) model
for load demand forecasts. By simulating natural evolutionary process, the algorithm
offers the capability of converging towards the global extremum of a complex error
surface. It is a global search technique that simulates the natural evolution process and
26
constitutes a stochastic optimization algorithm. Since the GA simultaneously evaluates
many points in the search space and need not assume the search space is differentiable or
The general scheme of the GA process is briefly described here. The integer or real
dimensional vector p for which a fitness f(p) is assigned. The initial population of k
parents vectors pi, i=1,2,….k, is generated from a randomly generated range in each
individuals are obtained. Of these, k individuals are selected randomly, with higher
probability of choosing those with the best fitness values, to become the new parents for
the next generation. This process is repeated until f is not improved or the maximum
Yang et al, [64] described the system load model in the following ARMAX form:
A(q)y(t)=B(q)u(t)+C(q)e(t),-------------------------------(6)
where
27
and A(q), B(q), and C(q) are parameters of the autoregressive (AR), exogenous (X), and
moving average (MA) parts, respectively. Yang et al, [64] chose the solution(s) with the
best fitness as the tentative model(s) that should further pass diagnostic checking for
future load forecasting. Yang and Huang, [65] presented a fuzzy autoregressive moving
average with exogenous variable (FARMAX) model for load demand forecasts. The
the forced mutation. Lee et al., [67] used genetic algorithms for long-term load
forecasting, assuming different functional forms and comparing results with regression.
machines, and automobiles are increasingly using fuzzy logic control circuits. Linking
the term fuzzy, which here means “not precisely defined,” with the term logic may seem
to create an oxymoron like “work party”, but the concept is very real. The original work
on fuzzy logic was done by Professor Lofti A. Zadeh at U. C. Berkeley in the mid-1960s,
but Japanese companies have been the main ones to patent the technology and implement
it in products.
A fuzzy logic controller is programmed with rules as is an expert system, but the
rules are very flexible. Figure 1 below shows the graphic method Professor Bart Kosko of
the University of Southern California uses to illustrate the difference between traditional
28
fixed value logic and fuzzy logic. Each corner of the cube represents one of the eight
{0,0,1}
{1,0,0}
{0,1,0}
Figure 1: Comparison of binary logic values and fuzzy logic values for a 3-input
function.
For this example, let’s assume that the function is true for the 010, 001and 100
combinations shown. In a traditional digital logic system the variables can only have
values of 0 or 1, so the only values that will produce a true output are these three. In a
fuzzy logic system the variables can have values other than 1 or 0, so the set of all the
possible values that will produce a true output is represented by the triangular plane
formed by the three points. One way to look at this is that traditional digital logic is just a
One advantage of fuzzy logic systems is that they can work with imprecise terms
such as cold, warm, hot, or near boiling that humans commonly use. In hardware terms
this means that a fuzzy logic system often doesn’t need precise A/D converters. The
29
Sanyo Fisher Corp. Model FVC-880 camcorder, for example, uses fuzzy logic to directly
process the outputs from six sensors and set the camera lens for best possible focusing
and exposure.
Fuzzy logic can provide very smooth control of mechanical systems. The fuzzy
standing riders do not use the hand straps during starts and stops.
Digital Fuzzy Processor chip. They have also developed a Fuzzy-C compiler which can
be used to write a program containing the rules and knowledge base for the processor.
It is well known that a fuzzy logic system with centroid defuzzification can
identify and approximate any unknown dynamic system (here load) on the compact set to
arbitrary accuracy. Liu et al., [57] observed that a fuzzy logic system has great capability
in drawing similarities from huge data. The similarities in input data (L-i -L0) can be
identified by different first order differences (Vk) and second-order differences (Ak),
The fuzzy logic-based forecaster works in two stages: training and on-line
forecasting. In the training stages, the metered historical load data are used to train a 2m-
input, 2n-output fuzzy-logic based forecaster to generate patterns database and a fuzzy
rule base by using first and second-order differences of the data. After enough training, it
will be linked with controller to predict the load change online. If a most probably
30
matching pattern with the highest possibility is found, then an output pattern will be
conditional statements. Hsu, [68] presented an expert system using fuzzy set theory for
STLF. The expert system was used to do the updating function. Short-term forecasting
was performed and evaluated on the Taiwan power system. Latter, Liang and Hsu, [69]
problem, representing uncertainties in forecast and input data using fuzzy set notation.
structural framework for the representation, manipulation and utilization of data and
information concerning the prediction of power commitments. Neural networks are used
Srinivasan et al., [71] used the hybrid fuzzy-neural technique to forecast load. This
technique combines the neural network modeling and techniques from fuzzy logic and
fuzzy set theory. The models were later enhanced by [72], [73]. This hybrid approach can
accurately forecast on weekdays, public holidays, and days before and after public
holidays. Based on the work of [71], [72] presented two fuzzy neural network (NN)
models capable of fuzzy classification of patterns. The first network uses the membership
values of the linguistic properties of the past load and weather parameters, where the
output of the network is defined as the fuzzy class membership values of the forecasted
load. The second network is based on the fact that any expert system can be represented
optimization model of STLF, whose objective is to minimize model errors. The search
for the optimum solution is performed by simulated annealing and the steepest descent
method. Dash et al., [75] used a hybrid scheme combining fuzzy logic with both neural
networks and expert systems for load forecasting. Fuzzy load values are inputs to the
neural network, and the output is corrected by a fuzzy rule inference mechanism.
planning problem of electric energy. Computer tests indicated that this approach out
Chow and Tram, [77] presented a fuzzy logic methodology for combining
information used in spatial load forecasting, which predicts both the magnitudes and
locations of future electric loads. The load growth in different locations depends on
multiple, conflicting factors, such as distance to highway, distance to electric poles, and
costs. Therefore, Chow et al., [78] applied a fuzzy, multi-objective model to spatial load
forecasting. The fuzzy logic approach proposed by [79] for next-day load forecasting
offers three advantages namely, the ability to (1) handle non-linear curves, (2) forecast
irrespective of day type and (3) provide accurate forecasts in hard-to-model situations.
Mori et al., [80] presented a fuzzy inference model for STLF in power systems.
Their method uses tabu search with supervised learning to optimize the inference
structure (i.e., number and location of fuzzy membership functions) to minimize forecast
errors. Wu and Lu, [81] proposed an alternative to the traditional trial and error method
32
for determining of fuzzy membership functions. Anautomatic model identification is
used, that utilizes analysis of variance, cluster estimation, and recursive least-squares.
Mastorocostas, [82] applied a two-phase STLF methodology that also uses orthogonal
fuzzy logic with neural networks in a technique that reduces both errors and
computational time. Srinivasan et al., [84] combined three techniques fuzzy logic, neural
networks and expert systems in a highly automated hybrid STLF approach with
unsupervised learning.
Probably the most developed area of AI at present is the area of expert systems.
An expert-system program consists of a large data base and a set of rules for searching
the data base to find the best solution for a particular type of problem. The data base and
rules are developed by questioning “experts” in that particular problem area. The data
base for a medical diagnosis expert system, for example, is built up by extensive
decision, expert system programs are designed to make a best guess, based on the
available data, just as a human expert would do. A medical diagnosis expert system, for
example, will indicate the illness that most likely corresponds to a given set of symptoms
and test data. To enable it to make a better guess, the system may suggest additional tests
to perform.
33
One advantage of a system such as this is that it can make the knowledge of many
experts readily available to a physician anywhere in the world via a modern connection.
Another advantage is that the data base and set of rules can be easily updated as new
research results and drugs become available. Other expert system programs are those
used to lay out PC boards and those used to lay out ICs.
Expert systems are new techniques that have emerged as a result of advances in
the field of artificial intelligence. An expert system is a computer program that has the
ability to reason, explain, and have its knowledge base expanded as new information
becomes available to it. To build the model, the ‘knowledge engineer’ extracts load
forecasting knowledge from an expert in the field by what is called the knowledge base
component of the expert system. This knowledge is represented as facts and IF-THEN
rules, and consists of the set of relationships between the changes in the system load and
changes in natural and forced condition factors that affect the use of electricity. This rule
base is used daily to generate the forecasts. Some of the rules do not change over time
The logical and syntactical relationships between weather load and the prevailing
daily load shapes have been widely examined to develop different rules for different
approaches. The typical variables in the process are the season under consideration, day
of the week, the temperature and the change in this temperature. Illustrations of this
method can be found in [85], [86], and [87]. The algorithms of [88] and [89] combine
features from knowledge-based and statistical techniques, using the pair-wise comparison
technique to prioritize categorical variables. Rahman and Hazim, [90] developed a site-
34
independent expert system for STLF. This system was tested using data from several sites
around the USA, and the errors were negligible. Brown et al., [91] used a knowledge
based load-forecasting approach that combines existing system knowledge, load growth
patterns, and horizon year data to develop multiple load growth scenarios.
approaches. Dash et al., [92], Dash et al., [75] combined fuzzy logic with expert systems.
Kim et al., [93] used a two-step approach in forecasting load for Korea Electric Power
Corporation. First, an ANN is trained to obtain an initial load prediction, then a fuzzy
expert system modifies the forecast to accommodate temperature changes and holidays.
Mohamad et al., [94] applied a combination of expert systems and NN for hourly load
forecasting in Egypt. Bataineh et al., [95] used neural networks and fuzzy logic for data
representation and manipulation to construct the expert system’s rule base. Chiu et al.,
[96] determined that a combined expert system-NN approach is faster and more accurate
than either one of the two methods alone. Chandrashekara et al., [98] applied a combined
expert system-NN procedure divided into three modules: location planning, forecasting
Support Vector Machines (SVMs) are a more recent powerful technique for
solving classification and regression problems. This approach was originated from
Vapnik’s, [99] statistical learning theory. Unlike neural networks which try to define
complex functions of the input feature space, support vector machines perform a
nonlinear mapping (by using the so-called kernel functions) of the data into a high
35
dimensional (feature) space. Then support vector machines use simple linear functions to
create linear decision boundaries in the new space. The problem of choosing architecture
for a neural network is replaced here by the problem of choosing a suitable kernel for the
Mohandes, [101] applied the method of support vector machines for short-term electrical
load forecasting. The author compares its performance with autoregressive method. The
results indicate that SVMs compare favourably against the autoregressive method. Chen
et al., [102] proposed a SVM model to predict daily load demand of a month. Their
program was the winning entry of the competition organized by EUNITE network. Li and
applications such as these, new computer architecture modeled after the human brain,
As you may remember from a general science class, the brain is composed of
billions of neurons. The output of each neuron is connected to the inputs of several
thousand other neurons by synapses. If the sum of the signals on the inputs of a neuron is
greater than a certain threshold value, the neuron “fires” and sends a signal to other
neurons. The simple op-amp circuit in Figure 2.2a may help you see how a neuron works.
36
Let’s assume the output of the comparator is initially low. If the sum of the input signals
to the adder produces an output voltage more negative than the comparator threshold
voltage, the output of the comparator will go high. This is analogous to the neuron firing.
The weight or relative influence of an input is determined by the value of the resistor on
that input. Figure 2.2b shows a symbol commonly used to represent a neuron in neural
network literature and Figure 2.2c shows a simple mathematical model of a neuron.
As with the neurons in the human brain, the neurons in a neural network are connected to
many other neurons. Figure 2.2d shows a simple three-layer neural network. This
network configuration is referred to as “feed forward”, because none of the output signals
some intermediate or final output signals are connected back to network inputs.
determine the one that works best for each type of application.
R5
2
U1
1
U2
R1
R2 to other
R3 R4
0 neurons
3
Vref
37
CONNECTIONS
INPUT 1 output
Transfer
INPUT 2 Sum function
INPUT 3
INPUT n
P1 w1
P2 w2 ∑ ∑ n f y
pn w n
w0
Neurodynamics
Summation function:
n=b*w0+ p1*w1+p2*w2+……+pn*wn
Transfer function:
f(x)=(1+e-x)-1
Output:
y=f(n)
38
NETWORK OUTPUT
OUTPUT
LAYER
HIDDEN
LAYER
INPUT
LAYER
DATA INPUT
Neural networks based computing can be implemented in several ways. One way is to
use a dedicated processor for each neuron. The large number of neurons usually makes
this impractical, and most applications don’t need the speed capability. An alternative
approach is to use a single processor and simulate neurons with lookup tables. The
lookup table for each neuron contains the connections, input weight values, and output
markets neural net simulation programs for both PC and Macintosh type computers.
These packages can be used to learn about neural nets or develop actual applications
39
which do not have to operate in real time. Another interesting neutral network program is
Neural network computers are not programmed in the way that digital computers
are, rather, they are trained. Instead of being programmed with a set of rules the way a
classic expert system is, a neural network computer learns the desired behavior. The
In the supervised method a set of input conditions and the expected output
conditions are applied to the network. The network learns by adjusting or “adapting” the
weights of the interconnections until the output is correct. Another input-output is then
applied, and the network is allowed to learn this set. After a few sets the network will
have learned or generalized its response so that it can give the correct response to most
The scheme used to adapt the network is called the learning rule. As an example,
one of the simplest learning rules that can be used is the Hebbean learning law. This law
decrees that each time the input of a neuron contributes to the firing, its weight should be
increased, and each time an input does not contribute, its weight should be decreased.
human behavior modification. In the case of the network, the result is that these
40
The major advantages of neural networks are these:
1: They do not need to be programmed: they can simply be taught the desired response.
2. They can improve their response by learning. A neural network designed to evaluate
loan applications, for example, can automatically adapt its criteria based on loan-failure
feedback data.
3. Input data does not have to be precise, because the network works with the sum of the
inputs. A neural network image-recognition system, for example, can recognize a person
even though he or she has a somewhat different hairstyle than when the “learning” image
words spoken by different people. Traditional digital techniques have a very hard time
4. Information is not stored in a specific memory location the way it is in a normal digital
result of this is that the “death” of a few neurons will usually not seriously degrade the
forecasting the weather or the stock market. For real time applications such as image
recognition and speech recognition, the software methods are obviously not fast enough.
University researchers and companies such as TRW and Texas Instruments are working
on ICs which implement neural networks in hardware. In the not-too-distant future these
ICs should allow you to talk to your computer instead of using a mouse, allow your
41
computer to read typed messages to you, and allow your car to drive itself down the
freeway. And so it is today, as at the time of compiling this report the first two
Neural networks (ANN) have very wide applications because of their ability to
learn. According to Damborg et al., [104], neural networks offer the potential to
overcome the reliance on a functional form of a forecasting model. There are many types
are multiple hidden layers in the network. In each hidden layer there are many neurons.
Inputs are multiplied by weights and are added to a threshold θ to form an inner product
number called the net function. The net function NET used by Ho et al., [105], for
example, is put through the activation function y, to produce the unit’s final output,
y(NET).
The main advantage here is that most of the forecasting methods seen in the
literature do not require a load model. However, training usually takes a lot of time. Here
we describe the method discussed by Liu et al., [57], using fully connected feed-forward
type neural networks. The network outputs are linear functions of the weights that
connect inputs and hidden units to output units. Therefore, linear equations can be solved
for these output weights. In each iteration through the training data (epoch), the output
hidden unit weights, then solves linear equations for the output weights using the
42
Srinivasan and Lee, [6] surveyed hybrid fuzzy neural approaches to load
forecasting. Park and Osama, [106] used a NN approach for forecasting which, compared
to regression methods gave more flexible relations between temperature and load
patterns. Extending this work, [107] presented a NN algorithm that combines time series
and regression approaches. Park et al., [107] proposed an improved training procedure for
training the ANN. Atlas et al., [108] earlier compared a similar technique with other
regression methods. Hsu and Yang, [109] estimated the load pattern of the day under
study by averaging the load patterns of several past days, which are of the same day type
(ANN being used for the classification). To predict the daily peak load, a feed-forward
appropriate historical pattern of load and temperature weights to be used to find the
network weights. They also proposed an improved algorithm that combined linear and
non-linear terms to map past load and temperature inputs to the load forecast output. This
work was an extension to a strategy byPeng et al., [111] which was applied on daily load.
The major difference lies in the alternate method for the selection of the training cases.
Later, Peng et al., [112] applied a neural network approach to one-week ahead load
Ho and Hsu, [113] designed a multilayer ANN with a new adaptive learning
algorithm for short term load forecasting. In this algorithm the momentum is
automatically adapted in the training process. Lee and Park, [114] proposed a non-linear
load model and several structures of ANNs were tested. Inputs to the ANN include past
43
load values, and the output is the forecast for a given day. Lee and Park, [114]
demonstrated that the ANN could be successfully used in STLF with accepted accuracy.
Chen et al., [115] presented an ANN, which is not fully connected, to forecast weather
sensitive loads for a week. Their model could differentiate between the weekday loads
learning concept and historical relationship between the load and temperature for a given
season, day type and hour of the day. They used this algorithm to forecast hourly electric
load with a lead time of 24h.Papalexopoulos et al., [118] developed and implemented the
ANN based model for the energy control centre of the Pacific Gas and Electric Company.
Attention was paid to accurately model special events, such as holidays, heat waves, cold
snaps and other conditions that disturb the normal pattern of the load. Ho et al., [105]
Srinivasan et al., [120] used an ANN based on Back propagation for forecasting,
and showed its superiority to traditional methods. Liu et al., [121] compared an
econometric model and a neural network model, through a case study on electricity
consumption forecasting in Singapore. Their results show that a fully trained NN model
with a good fitting performance for the past may not give a good forecasting performance
44
for the future. Kalra et al., [122] demonstrated how present methods for solving such
Azzam-Ul-assar and McDonald, [123] trained a family of ANNs and then used
them in line with a supervisory expert system to form an expert network. They also
investigated the effectiveness of the ANN approach to short term load forecasting, where
the networks were trained on actual load data using back-propagation. Al Anbuky et al.,
[70] presented fuzzy logic based neural networks for load forecasting. Dash et al., [72],
Dash et al., [73], and Dash et al., [75] also used fuzzy logic in combination with neural
networks for load forecasting. Their work has been discussed in the previous section.
Chen et al., [124] applied a supervisory functional ANN technique to forecast load
for three substations in Taiwan. To enhance forecasting accuracy, the load was correlated
humidity effects in an ANN approach for STLF in Kuwait. Vermaak and Botha, [126]
proposed a recurrent NN to model the STLF of the South African utility. They utilized
the inherent non-linear dynamic nature of NN to represent the load as the output of some
used non-linear least-squares to estimate parameters, and simple statistics such as MAPE
ANN approach, involving the prediction of load curve peaks and valleys and mapping
45
them to forecasted peak values. Dash et al., [129] presented a fuzzy NN load forecasting
system that accounts for seasonal and daily changes, as well as holidays and special
situation. An adaptive mechanism is used to train the system on line, providing accurate
results when tested with actual data of the Virginia Utility. Another adaptive NN
technique, employing genetic algorithms in the design and training phase, was used by
ANNs have been integrated with several other techniques to improve their
accuracy. Chow and Leung, [131] for example, combined ANN with stochastic time-
series methods, in the form of non-linear autoregressive integrated (NARI) Model. They
electric load in Hong Kong. Choueiki et al., [132] used weighted least-squares procedure
in the training phase of developing an ANN for load forecasting. Several other hybrid
methods involving ANNs in combination with fuzzy logic and expert systems are also on
record. It is very hard to keep track of all publications on load forecasting using NN,
which is currently a very active area of research. Neibur, [133] and,Dorizzi and
Germond, [134] surveyed methods and applications of electrical load forecasting with
ANNs.
power system commercial load using a wavelet neural network. Their results showed that
[136] presented a new ANN-based technique for STLF. The technique implemented
supervised adaptive NN to perform STLF for a large power system. They used the self-
supervised network to extract correlation feature from temperature and load data. Their
results showed low forecasting errors. Kandil et al., [138] used multilayer perception
(MLP) type ANN for STLF using real load and weather data. Leyan and Chen, [139]
used variable learning rate method combined with quasi Newton method to expedite the
Nazarko and Styczynski., [140] presented load-modeling methods useful for long
term planning of power distribution systems using statistical clustering and NN approach.
Ijumba and Hunsley.,[141] applied ANN model to predict hourly peak demands of loads
in a newly electrified area. Sinha and Mandal.,[142] presented an ANN-based model for
bus-load prediction and dynamic state estimation in power systems. Drezga and Rahman,
temperature and cycle variables, into ANN-based STLF. Drezga and Rahman, [144]
applied another ANN-based technique that features the following characteristics: (1)
selection of training data by the K-nearest neighbours concept, (2) pilot simulation to
determine the number of ANN units and (3) iterative forecasting by simple moving
Bakirtzis et al., [145] developed an ANN based short-term load forecasting model
for the Energy Control Centre of the Greek Public Power Corporation. In the
development they used a fully connected three-layer feed-forward ANN and back
propagation algorithm was used for the training. Input variables included historical
47
hourly load data, temperature, and the day of the week. The model could forecast load
profiles from one to seven days. Kalaitzakis et al., [7] implemented a 24-hr-ahead load
prediction using ANN model that was capable of parallel processing of data. In their
approach, n-neural blocks with a single output were implemented and trained separately
to provide the n hourly ahead load forecasts. According to this procedure, the requested
load for each specific hour is forecasted, not only using the load time-series for this
specific hour from the previous days, but also using the forecasted load data of the closer
previous time steps for the same day. Bassi and Olivares, [8] performed medium term
load forecasting using a time lagged feed-forward neural network (TLFN). Adepoju et
al., [24] implemented neural network based short-term (one hour ahead) electric load
forecasting and applied the model to the Nigerian power system for one hour in advance
load prediction. The load of the previous hour, the load of the previous day, the load of
the previous week, the day of the week, and the hour of the day all formed the inputs to
the models proposed by [24]. Sarangi et al., [22] performed short term load forecasting
using artificial neural network and compared the result with one obtained using genetic
algorithm based neural network to implement the same problem. They model was tested
with the daily load demand of Delhi state. The model performed wonderfully well.
Arroyo et al., [9] performed electricity load forecasting using a feed-forward artificial
neural network. They model was trained and tested with the load data used during
[9]’s model would have ranked second in the competition. Outside the EUNITE
48
competition, [146] proposed a method to forecast electrical load using weather ensemble
nodes in the input layer, 10 nodes in the single hidden layer, and 1 node in the output
layer. The input layer nodes were the 7 different days of a week and 3 weather variables.
From the 7 nodes, 6 were used to represent different days in the week, and the last one
was used for the second week of the industrial closure in the summer. The 3 weather
variables employed were the effective temperature, cooling power of the wind, and
effective illumination. Four different methods were modeled and tested to determine what
influence the weather had on forecasting accuracy. The three methods based on neural
networks, which used weather data showed better prediction results when compared to
the one that did not use weather data. Ringwood et al., [147] modeled electricity load
forecasting using neural networks at three different time scales: hourly, weekly and
yearly. Using data from the national electricity demand in Ireland, ANN-based models
were supplied with parameters obtained from previous experiences with linear modeling
techniques and from manual forecasting methods. The last two approaches described in
the works of [146] and [147] show that including data from other sources may improve
the models more complex [9]. Yi et al., [10] implemented a neural network based
electricity load forecasting model. In their model, only pre-historical load data were used
as well as post process the load data. Their model showed a high forecasting accuracy.
Mosalman [148] proposed artificial neural network based model for a one-day-ahead load
49
forecasting. Their model was trained using hourly historical load data, and daily historical
max/min temperature and humidity data. The results of testing the system on data from
From the above literature, it can be seen that much have been done on electric load
forecasting with the current trend being to use artificial intelligence means to predict
electric load. It can also be said that artificial neural network model is predominantly
being used to forecast electric load today. This notwithstanding, this research proposal
remains a novel attempt to treat electric load forecasting using artificial neuronal network
in the context of the Nigerian power system. Although the work of [24] was on electric
load forecasting by means of artificial neuronal network in the Nigerian power system,
this particular model is a clear variant in the following senses: input variable
homogeneity and model simplicity. The neural networks with non-homogeneous input
sets, mixing analogue and digital variables with very different ranges of values and
meaning, face weight adaptation problem over the training process [15].The network
architecture and training methods for both models are also different.
50
CHAPTER THREE
RESEARCH DESIGN/METHODOLOGY
3.0. Introduction
This chapter is focused on the simulation design which includes (a) Research Data
minimum number of patterns, (e) Selection of input variables (f) model training and
The data that was used in training and testing of the model proposed in this
research are the daily Electric power supplied to Enugu state of Nigeria as contained in
the National Electric power authority New Haven, Enugu 132/33kV Transmission station
daily hourly load reading sheets for the months of February and March 2011. A month’s
data could do for the purpose of short-term electric forecasting [24, 22] and hence for this
research the load profile for the month of March 2011 was actually used. The essence of
Although in theory all ANNs have arbitrary mapping capacities between sets of
variables, it is convenient to normalize the data before carrying out the training to
compensate for the inevitable scaling and variability differences between the variables
51
[8]. Neural network training can be made more efficient if certain preprocessing steps are
Data pre-processing was in two stages: the first action on the load data was to find
replacement for missing load values. The case of missing load values arose either due to
system collapse, earth fault, transformers being on soak, feeder opened for the purpose of
maintenance operation etc,. In cases like the above, load information for the same hour,
weekday, and week of the preceding month would always be used to refill the missing
gap. Calendar, however, showed that the months of February and March 2011 were the
most compatible months for the purpose of this data doctoring. This is because the 1st
days of both months were coincidentally on the same day of the week, namely Tuesday.
The second operation on the data was performed to put the input values in the same scale.
The approach here was to normalize the mean and standard deviation of the training set.
This would be implemented using the matlab code ‘prestd’. This code normalizes the
network inputs and targets so that they will have zero mean and unity standard deviation.
Several neural network paradigms have been implemented such as radial basis
back propagation network, etc., but none has shown better forecasting accuracy than a
feed-forward input-delay back propagation network which was used for this application.
52
One special feature of the input-delayed feed-forward network is that it combines
generalizes the short term structures of memory, based on delays and recurrences. This
scheme allows smaller adjustments without requiring changes in the general network
structure.
configuration mainly depends on the number of hidden layers, number of neurons in each
hidden layer and the selection of activation function. Although there is no clear cut
guideline on how to select the architecture of ANN, [149] suggest that for a three layer
ANN, the number of hidden neurons can be selected by one of the following thumb rules:
c) For every 5 input neurons, 8 hidden neurons can be taken. This is developed
seeing the performance of a network with 5 inputs, 8 hidden and 1 output neuron;
f) P/i neurons where ‘i’ is the input neurons and ‘p’ represents number of training
samples.
53
Determining the number of hidden nodes in the ANN, and the number of epochs
to Gowri and Reedy, [149] heuristic or simple rule of thumb approach to solving this
architecture and parameter settings that would give better prediction results. In each
evaluated using mean absolute percentage error, MAPE, defined as: MAPE (%)
|
|
= ∑
∗ 100 3.1
Where ℎ
, ℎ
, and N denote forecast load at hth hour, actual load for the
Gowri and Reedy, [149] suggest that the minimum numbers of patterns required
are half the number of input neurons and the maximum is equal to the product of number
of input neurons and number of hidden neurons or five times the number of input
performance of configurations is studied with eight numbers of training patterns and three
In this research the idea is to use a total number of 31 days load data grouped into
24 input data sets which in turn are divided into two subsets- the training and test subsets.
54
The training set shall consist of first 17 data sets and the test set shall consist of last 7
data sets.
Papalexopoulos et al., [118] stated that there is no general rule for the selection of
and is carried out almost entirely on trial and error basis. The importance of the factors
may vary for different consumers. According to Wang and Tsoukalas, [150] for most
consumers, historical data (such as weather data, weekend load and previous load data) is
most important for predicting demand in short term load forecasting (STLF). In practice,
it is neither necessary nor useful to include all the historical data as input. Autocorrelation
helps to identify the most important historical data. Theimportance of recent daily loads
Table 3.1: Importance of recent daily loads in daily load prediction based on correlation
analysis.
Factors X1 X2 X3 X4 X5 X6 X7
importance 1 2 3 5 7 6 4
55
The first row of the table shows the recent daily load history.
X represents the load consumed and its subscripts show the time index, i.e., 1
means yesterday (one day ago), 2 means the day before yesterday (2 days ago), 7 means
the same day of last week (7 days ago). In the second row, the rank or importance of the
load is described. 1 means the most important and 7 means the least important.
These information and results guided the decision of input factors in this work.
According to table 3.1, when daily load prediction is performed, one should include X1,
X2, X3, X7, as the inputs. Here in this work, use was made of X1 and X7, as the input
variables (i.e., the day before and the same day last week load data).
This choice of input variables left us with a total of 24 data sets for both training and
Once created, the network shall be trained with samples of the research data so it
can recognize the latent pattern in all the utility load data.
Two training styles exist namely:- Incremental training in which the weights and biases
of the network are updated each time an input is presented to the network, and batch
training wherein the weights and biases are updated only after all of the inputs are
presented to the network [151]. The choice of training style can be primarily influenced
by the network model, which can be either a static or dynamic network, and partly by the
56
input data structure which in turn can be presented to the network as either a set of
The neural network proposed in this paper namely a feed-forward neural network with
tap delay lines (NEWFFTD) is a dynamic network and was trained using the batch mode
style of training. This was implemented using the matlab code train. This being because
train has access to more efficient matlab training algorithms [152]. The input although by
its nature is a sequence, was presented to the network model as though a concurrent
vector. This nonetheless, the presence of the tap delay lines on the network input ports
readily makes the model see the input data as though sequential.
Several training algorithms are known and used in training feed-forward networks
which are basically back-propagation networks. Some of the training algorithms suffer
the problem of slow rate of convergence and will not be considered for the purpose of
this work. Among the faster training algorithms are: variable learning rate back-
The second category of fast algorithms uses standard numerical optimization techniques.
Three types of numerical optimization techniques for neural network training are:
algorithm although rated the fastest training algorithm requires too much computer
memory especially, when the number of biases and weights in the network increase, and
57
so was not considered in this experiment [153]. Reduced memory Levenberg-Marquardt
was designed to offset this drawback. But even with reduced memory Levenberg-
Marquardt, the algorithm will always compute the approximate Hessian matrix, and if the
network is very large, then out of memory problem may still exist [151].
In spite of the above, during the experiment trial was given to the under listed algorithms
From available literature, however, it was almost clear that conjugate gradient algorithms
propagation algorithm viz, gradient descent algorithm. Back-propagation is the basis for
the Widrow-Hoff learning rule to multiple layer networks and non-linear differentiable
transfer functions [151]. The algorithm consists of a forward and backward passes. The
data used as inputs is transmitted through the network, layer by layer, and up to the
output layer where a set of outputs is obtained. During this first forward pass, the weights
of the network are set. The obtained outputs are compared with the desired outputs values
58
and, as backward pass, the difference between the desired outputs and the calculated
outputs (error) is used to adjust the synaptic weights of the net in order to reduce the level
of error [10].
This is an iterative process, which continues until an acceptable level of errors will be
obtained. Each time the network processes the whole set of data (both a forward and a
backward pass) is called an epoch. The network is in this way trained and the error is
reduced by every epoch until an acceptable level of error will be gained. So, learning is
just reduced to the minimization of the Euclidean error measure over the entire learning
set. This method is called error back back-propagation training algorithm and the most
effective learning approach applies gradient information and uses second order
various intermediate values and error terms are explained with the help of the figure 3.1
below.
59
Input
Wij
Hidden layer
Output
The output from neuron i, Oi, is connected to input of neuron j through the
interconnection weight Wij. Unless neuron k is one of the input neurons, the state of
neuron k is:
= ∑
3.2
1⁄1 +
is commonly used at all layers but the output layer, and the sum is over all
Let the target state of the output neuron be, t, thus the error at the output neuron can be
defined as:
! = # −
" 3.3
"
( ) ( ) ( -,
∆& ∝ − =− 3.4
( *+, ( -, ( *+,
( )
.& = − 3.5
( -,
With some manipulations, we can get the following general delta rule:
Where, ɛ, is the adaptation gain. .& is computed based on whether or not neuron j is in the
.& = # − 0
& 11 − & 2 3.7
∆& 3 + 1
= ɛ.& + 4∆& 3
3.9
Some other variants of gradient descent algorithm introduce in addition to the momentum
61
Where η is the learning rate parameter, α is the momentum term which ranges from 0 to
1, and δ is the negative derivative of the total square error in respect to neuron’s output.
The objective here is the minimization of the following error cost function over time t,
7;+<=>
!7879: = ∑7 ! #
3.11
All of the conjugate gradient algorithms start out by searching in the steepest descent
A line search is then performed to determine the optimal distance to move along the
BC = B + 4 3.13
Then the next search direction is determined so that it is conjugate to previous search
directions.
The general procedure for determining the new search direction is to combine the new
= −A + D 3.14
The various versions of conjugate gradient algorithms are distinguished by the manner in
EFG EF
D = G E 3.15
EFHI FHI
62
This is the ratio of the norm squared of the current gradient to the norm squared of the
This is the inner product of the previous change in the gradient with the current gradient
For all conjugate gradient algorithms, the search direction will be periodically reset to the
negative of the gradient. The standard reset point occurs when the number of iterations is
equal to the number of network parameters (weights and biases), but there are other reset
methods that can improve the efficiency of training. One such method was proposed by
Powell, based on an earlier version proposed by Beale. For this technique we will restart
if there is very little orthogonality left between the current and the previous gradient. This
If this condition is satisfied, the search direction is reset to the negative of the gradient.
For any chosen training algorithm, the training approach to be adapted in this research
shall be to present the training data which constitutes of 17 input/target sets one set at a
time to the model until the last set is presented to the network model when the entire
training data set shall be presented to the model all at a time. The model will then adapt
its weights and biases to suit the trend of all the data set that ever participated in the
63
training exercise. The network response to the test data sets which are input sets that
never participated in the training exercise was then simulated. During this testing time,
the expected targets were not submitted to the model. Both the network response and the
desired target were plotted on the same figure window for comparison. The model
One of the major problems that occur during neural network training is called
over-fitting or problem of generalization. The error on the training set is driven to a very
small value, but when new data is presented to the network, the error is large. The
network has memorized the training examples, but it has not learned to generalize to new
Use a network that is just large enough to provide an adequate fit. The problem
with this approach however is that it is difficult to know beforehand how large a
Collect more data and increase the size of the training set and so eliminate entirely
the problem of over fitting[153]. This is true since if the number of parameters in
the network is much smaller than the total number of points in the training set,
then there is little or no chance of over fitting. This is tedious especially in the
Nigerian power system where the required data was too raw and available only in
subsets. The first subset is the training set, which is used for computing the
gradient and updating the network weights and biases. The second subset is the
the training process. The validation error will normally decrease during the initial
phase of the training, as does the training set error. However, when the network
begins to over fit the data, the error on the validation set will typically begin to
increase. When the validation error increases for a specified number of iterations,
the training is stopped, and the weights and biases at the minimum of the
validation error are returned. The problem with this technique is sizing the subsets
properly.
The last technique is called regularization method. This involves modifying the
network errors on the training set. A typical performance function that is used for
training a feed-forward neural network is the mean sum of the squares of the
network errors.
P = QR = ∑ "
= ∑# − S
"
3.18
a term that consists of the mean of the sum of the squares of the network weights and
QRTA = γQR + 1 − γ
QRU 3.19
65
Where γ is the performance ratio, and
QRU = ∑@& U&" 3.20
@
Using this performance function will cause the network to have smaller weights and
biases, and this will force the network response to be smoother and less likely to over fit.
The problem with regularization is that it is difficult to determine the optimum value for
One approach to this process of determining the optimum value of the performance ratio
automated regularization has been implemented using the matlab code trainbr.
regularization technique. However, rather than use the Bayesian regularization approach
to determine the optimal value of the performance ratio parameter, it was done by
experimentation instead. The default value of performance ratio in matlab toolbox is 0.5,
so this value was increased or decreased until optimum value in terms of the model
forecasting accuracy was achieved. Such optimum value was then considered for this
experiment.
66
CHAPTER FOUR
4.0. Introduction
Forecast results and statistical properties obtained from the application of the
developed Short Term Load Forecasting (STLF) ANN model on the load data of New
Haven Enugu transmission station, a typical Nigerian power system are presented and
The STLF results for the utility of New Haven Enugu, Nigeria produced by the ANN
structure proposed by this research were analyzed on the basis of the well-known
statistical index, mean absolute percentage error (MAPE) stated in equation 3.1 and
repeated below:
|
|
MAPE(%) = ∑
∗ 100 4.1
The errors have been calculated separately for the learning and testing data. Here we will
present only the testing errors related to the data not taking part in the learning /training
process since this information is the most important from the practical point of view.
terms of MAPE, on the test data set, when other network parameters were fixed, were
67
Table 4.1: Tested network architectures and their performances in terms of MAPE.
architecture 1 2 3 4 5 6 7 Average
MAPE
68
DISCUSSION: From table 4.1, it can be seen that the model architecture that gave
optimal performance in terms of forecast error is 28-38-1 architecture, i.e., a three layered
ANN model with 28 neurons in the input /first layer, 38 neurons in the second/hidden
It can be observed from table 4.1 that increasing or decreasing the number of neurons in a
layer by one or few neurons does not necessarily affect the model performance
significantly.
Different architectures could give the same results as is the case with 30-48-1 and 35-45-
1 architectures in our experiment. These architectures gave the same forecasting error of
The time elapsed in training and testing the optimal network architecture as well
as the model performance with different training algorithms and for common conditions
of other model parameters was experimented with and documented, and partly presented
DISCUSSION: From table 4.2 it can be seen that scaled conjugate gradient algorithm
performed fastest during this work, but in terms of model performance conjugate gradient
algorithm which uses Polak-Ribiere restart technique or the one which uses Fletcher-
Reeves restart technique was the best. Since the difference in the time taken for the
training of this model using conjugate gradient algorithm which uses Polak-Ribiererestart
69
technique is not much when compared to the fastest training algorithm, namely scaled
conjugate gradient algorithm, choice of the former as the training algorithm for this
model made.
Table 4.2:Various training algorithms and their performances when used with our
model
When the length of the tap delay vector was varied during the experiment, the
effect on the network model performance was noted to be increased time of training
without significant improvement on the model performance. Table 4.3 below shows the
time elapsed and the model performance for varying lengths of time delay vector.
70
Table 4.3: Effect of time delay vector on model accuracy and training time
Sec Performance
MAPE (%)
1 1 1 15.42 18.10
2 0 1 138.72 4.88
3 [0 1] 2 118.69 4.88
Epoch: The epoch was set to a high initial value, 10,000 in this case, and the network
performance was monitored. Particularly the number of epoch during which training
stopped was observed, and with this as a guide the number of epoch was tuned down
problem of over fitting was solved by regularization technique just as the optimal value
of the performance ratio parameter was achieved by trial and error. Table 6 below shows
the effect of choice of performance ratio parameter on our model accuracy. From table 6,
it can be seen that the model forecasting accuracy was best with the value of performance
71
Table 4.4: Variation in performance ratio parameter with model accuracy
γ MAPE (%)
0.5 5.24
0.2 5.15
0.1 5.03
0.09 5.03
0.6 5.23
0.01 4.88
0.9 7.20
0.001 10.49
0.05 5.01
Results: Table 4.5 below shows the optimal values of various model parameters used in
this research while the test results when the trained model was tested on the 24-hourly
load curves of New Haven Enugu for the days of Friday 25th March 2011 through
Thursday, 31st March the same are depicted in figures 4.1 through 4.8. The results
obtained from testing the trained neural network on new data that never participated in
the training exercise for 24 hours of a day over a one week period are presented below in
graphical form (figures 4.1-4.8). Each graph shows a plot of both the actual and forecast
72
Table 4.5: Optimal values of our model parameters
Architecture/Structure-------------------- 28-38-1
Epochs--------------------------------------- 3000
tolerance
73
plot of actual and predicted load values against time in hours
90
rh- predicted values
80 bd-- actual values
70
60
load in Megawatt
50
40
30
20
10
0
0 5 10 15 20 25
time in hours
70
60
load in Megawatt
50
40
30
20
10
0
0 5 10 15 20 25
time in hours
74
plot of actual and predicted load values against time in hours
90
rh- predicted values
80 bd-- actual values
70
60
load in Megawatt
50
40
30
20
10
0
0 5 10 15 20 25
time in hours
70
60
load in Megawatt
50
40
30
20
10
0
0 5 10 15 20 25
time in hours
70
60
load in Megawatt
50
40
30
20
10
0
0 5 10 15 20 25
time in hours
70
60
load in Megawatt
50
40
30
20
10
0
0 5 10 15 20 25
time in hours
76
plot of actual and predicted load values against time in hours
90
rh- predicted values
80 bd-- actual values
70
60
load in Megawatt
50
40
30
20
10
0
0 5 10 15 20 25
time in hours
70
60
load in Megawatt
50
40
30
20
10
0
0 20 40 60 80 100 120 140 160
time in hours
Figure 4.8: Test result for 7 days (Friday, 25th –Thursday, 31st March 2011
77
The percentage absolute mean error of this model on the test sets have been calculated
DISCUSSION: From table 4.6 above, it can be seen that the neural network showed
higher forecasting error in the days when people have specific start-up activities such as
With the aid of figure 4.8 the average MAPE for this model can be obtained as
4.27%.This connotes a high degree of forecasting accuracy for this model in spite of its
simplicity both in architecture and input variables. It is proper to note that forecasting
errors reported for various ANN load forecasting models in some literatures are in the
varied range of 12.8%-1.18%. The accuracy of the model presented in this paper seems
78
not to be the overall best so far. There is, however, no basis for direct comparison of
models results especially when it is noted that data used for the various experiments are
So, it is reported for this short term load forecasting model, namely, a feed-forward
artificial neural network with input delay, trained using error back-propagation algorithm,
an average forecasting error of 4.27% when the model was trained and tested using one
month hourly load data obtained from New-Haven Enugu 132/33KV transmission station
79
CHAPTER FIVE
5.1 Conclusion
This work and its results show that the ANN represents a powerful tool for
The result of the feed-forward time-delay (NewFFTD) network model used for one day
ahead short term load forecast for New Haven Enugu transmission station, a typical
Nigerian Power System, shows that NewFFTD, which is a multilayer feed forward
network with time delay, has a good performance, and reasonable prediction accuracy
Its forecasting reliabilities were evaluated by computing the mean absolute error between
the exact and predicted values. The results suggest that ANN model with the developed
structure can perform good prediction with least error and finally, this neural network
could be an important tool for short term load forecasting. Our experimental results also
show that a simple ANN-based prediction model appropriately tuned can outperform
We conclude therefore by saying that this research is a novel attempt to deal with load
forecasting in the Nigerian power system by means of Artificial Neural Network with
forecasting accuracy.
80
5.2 Suggestions for Further Research
In spite of the delimitations of this work and the observations made on the course
of the experiment proper, we make the following suggestions for further studies:
The neural network typically shows higher error in the days when people have
specific start-up activities such as Friday (for example on day 1 of the test set in
table 4.6), or variant activities such as during Sundays which are like holidays in
the Eastern part of the country (for example, on day 3 of the test set in table 4.6).
In order to have more accurate results, one may need to have more sophisticated
topology for the neural network which can discriminate start-up days from other
days. In other words, a model with special holiday encoding may perform this task
better.
So, a hybrid approach may be necessary to this effect. Use of genetic algorithms or
Due to time constraint and financial limitations we narrowed our work to New-
the model is tested on load data obtained from a larger part of the Nigerian Power
system.
81
Finally, since the effects of exogenous variables on models accuracy is still in
historical load data, can take as input some other exogenous variables as input data
82
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APPENDIX
MATLAB CODE
clc;clear ALL;
tic
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%the
daily load data for the month of March is read into the system using a
%three lettered variable names plus 2-digit numbers interpreted thus:
%the first two letters represent the day of the week; the third letter the
%month;the digits the date. Example,tum01 means tuesday march 1st etc
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%time=[1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.0 11.0 12.0 1.00 2.00 3.00 4.00
5.00 6.00 7.00 8.00 9.00 10.0 11.0 12.0];
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
tum01=[42.5 38.8 30.5 39.1 58.0 64.7 82.0 78.8 61.2 60.2 56.4 55.6 48.1 47.8 53.0 56.5
58.8 63.7 70.5 72.3 78.6 68.7 50.9 48.8];
wem02=[40.4 34.2 29.5 36.5 54.0 58.7 78.3 74.2 69.9 56.1 54.5 52.3 42.4 40.1 46.2 50.2
53.1 59.8 65.2 70.8 80.3 71.1 58.2 48.3];
thm03=[49.3 41.9 36.4 43.7 58.3 65.2 85.0 71.5 70.1 69.5 52.2 50.4 46.3 44.9 51.0 54.7
57.3 66.1 69.3 74.6 77.4 62.3 57.4 55.2];
frm04=[41.1 37.4 33.3 41.1 49.1 55.1 77.2 74.9 71.0 69.4 62.3 56.0 49.7 43.9 57.0 61.0
65.2 66.9 71.5 75.6 79.5 70.3 51.4 43.5];
sam05=[38.2 33.3 30.3 38.8 55.4 62.7 75.9 71.6 65.6 60.2 46.7 44.2 41.9 38.7 55.1 65.3
67.5 69.4 73.3 74.7 76.6 62.6 53.8 49.3];
sum06=[35.3 30.8 26.2 35.6 43.6 68.6 56.6 54.2 52.2 50.1 48.9 50.2 52.2 54.1 55.9 58.7
59.3 61.0 63.9 67.6 69.3 65.7 48.7 43.2];
mom07=[45.4 44.7 35.0 39.9 45.5 57.7 86.7 71.9 68.5 65.2 58.5 53.8 52.6 50.2 58.6 59.6
66.1 69.5 69.8 70.9 81.1 77.3 52.2 50.1];
tum08=[43.1 39.7 31.1 34.3 39.8 44.2 63.3 78.7 70.0 51.3 46.5 41.2 40.9 40.6 42.4 46.8
55.1 58.2 66.4 68.9 72.3 72.4 69.3 57.4];
wem09=[50.2 47.2 35.5 38.9 41.7 68.1 79.8 74.4 68.3 65.1 61.5 57.6 58.8 50.9 54.2 63.9
66.1 67.2 70.8 76.2 78.2 67.4 58.4 55.3];
thm10=[41.9 38.9 34.7 45.7 47.7 51.8 86.1 79.5 71.2 65.2 61.7 58.5 54.2 52.9 59.2 62.1
63.2 64.4 72.1 75.4 79.1 73.1 69.4 53.4];
frm11=[40.4 30.6 28.9 39.5 38.4 49.1 79.7 78.3 74.4 68.8 61.9 59.5 51.3 50.9 58.2 60.6
69.4 70.9 75.8 77.0 83.9 80.7 65.7 45.2];
sam12=[32.3 28.0 21.5 33.3 42.5 51.7 73.6 72.4 71.6 64.6 59.5 58.4 53.5 50.9 57.3 59.5
63.7 65.3 68.5 74.2 77.4 60.5 48.9 33.6];
sum13=[35.4 31.2 24.3 29.1 40.7 59.4 53.0 50.0 48.3 45.4 43.7 40.8 47.1 52.6 55.0 58.4
65.1 68.6 69.5 69.4 71.2 66.3 55.1 41.4];
mom14=[47.9 35.5 31.4 33.7 43.3 57.6 80.6 77.6 71.7 61.3 55.2 52.8 52.3 50.5 52.9 55.7
61.7 65.9 69.3 71.4 75.1 70.2 62.3 59.5];
97
tum15=[43.6 41.2 33.1 38.6 44.4 48.3 70.0 73.4 71.5 60.1 53.5 46.1 39.1 33.1 38.1 46.0
66.9 68.9 69.7 70.5 72.8 62.5 52.6 50.6];
wem16=[45.5 42.5 32.5 47.8 55.8 60.5 79.1 76.1 73.2 65.8 61.9 56.1 48.6 46.9 57.8 58.9
63.7 68.7 69.1 73.7 79.9 73.4 60.1 55.5];
thm17=[48.7 44.1 34.1 44.1 52.2 64.0 84.5 80.8 77.6 72.6 63.4 60.7 53.4 52.8 54.6 66.9
65.7 69.8 70.3 74.4 82.7 76.5 58.8 53.2];
frm18=[47.2 46.8 35.6 38.9 49.6 72.9 86.9 79.6 71.7 64.5 49.3 47.4 45.7 45.4 50.7 55.1
59.1 62.3 69.8 74.3 77.6 73.6 57.6 56.4];
sam19=[43.4 32.3 30.7 46.3 54.3 66.8 75.7 74.2 71.4 66.6 58.8 54.6 52.3 49.3 53.4 54.4
66.3 68.4 70.2 74.3 81.8 63.8 59.1 49.2];
sum20=[33.1 31.4 29.6 32.3 45.4 63.2 60.0 59.8 55.6 54.9 47.8 51.4 55.0 57.5 57.7 58.2
61.6 67.3 69.4 72.2 72.0 68.1 45.3 33.2];
mom21=[44.5 40.5 32.5 34.3 39.7 52.1 63.5 75.4 74.4 69.7 65.4 63.3 60.7 51.8 64.5 68.8
69.4 70.2 70.2 76.3 80.1 71.3 63.1 46.3];
tum22=[44.2 40.9 37.9 37.9 38.3 48.7 68.3 66.8 61.2 59.4 58.3 55.6 50.4 44.2 50.1 56.4
65.5 72.5 77.4 79.9 80.7 70.8 50.3 41.7];
wem23=[40.4 38.2 31.1 39.1 45.9 46.9 83.2 77.6 72.4 65.4 61.5 53.2 49.2 46.1 56.4 57.2
59.4 64.9 69.4 70.1 74.6 72.3 52.5 46.9];
thm24=[45.3 39.6 32.4 43.7 49.6 59.9 70.2 69.2 68.6 67.6 58.4 52.1 49.2 46.8 47.7 51.7
55.8 59.6 61.1 75.1 78.8 72.5 66.4 50.5];
frm25=[42.9 41.3 36.2 37.1 48.3 63.5 73.3 70.8 61.5 58.8 52.0 50.4 46.9 45.6 51.2 53.4
60.3 63.4 66.7 70.8 73.6 67.1 59.2 46.8];
sam26=[47.7 37.2 40.1 41.3 51.5 54.6 69.5 67.3 63.8 60.9 57.8 56.5 51.3 52.2 57.1 59.8
63.2 66.8 70.6 72.1 76.2 69.8 52.7 49.9];
sum27=[38.2 35.6 33.0 41.9 48.2 57.3 59.5 58.0 53.9 50.3 47.9 52.3 55.0 59.4 59.9 60.6
61.6 63.5 65.3 66.0 72.1 57.6 44.1 41.9];
mom28=[45.1 42.3 35.7 38.1 46.8 50.6 65.3 69.7 65.2 66.3 62.9 60.1 57.5 53.9 60.2 63.7
64.2 67.2 67.7 69.1 75.9 63.8 56.1 46.3];
tum29=[43.7 40.2 38.0 40.7 42.7 53.5 67.1 64.2 62.7 60.2 58.4 56.0 54.0 50.9 53.8 56.3
61.7 66.9 70.8 74.0 75.4 64.1 54.7 45.4];
wem30=[44.5 40.0 37.0 42.0 43.3 48.9 73.5 68.6 70.1 66.3 63.4 52.3 50.5 49.1 50.7 52.1
60.1 67.3 69.6 72.6 73.2 67.1 51.1 48.9];
thm31=[48.0 38.8 35.9 44.9 47.6 56.4 70.9 66.8 66.3 64.6 53.9 50.7 49.8 48.0 46.5 49.2
54.9 63.6 66.2 70.3 72.7 65.2 56.9 52.5];
%single variable with variable name march_load is now created to capture
%the entire working data
march_load=[tum01;wem02;thm03;frm04;sam05;sum06;mom07;tum08;wem09;thm10;fr
m11;sam12;sum13;mom14;tum15;....
wem16;thm17;frm18;sam19;sum20;mom21;tum22;wem23;thm24;frm25;sam26;sum27;
mom28;tum29;wem30;thm31];
%%
%%
98
data=[march_load];
p1=[data(1,:); data(7,:)];t1= [data(8,:)];
p2=[data(2,:); data(8,:)];t2= [data(9,:)];
p3=[data(3,:); data(9,:)];t3= [data(10,:)];
p4=[data(4,:); data(10,:)];t4=[data(11,:)];
p5=[data(5,:); data(11,:)];t5=[data(12,:)];
p6=[data(6,:); data(12,:)];t6=[data(13,:)];
p7=[data(7,:); data(13,:)];t7=[data(14,:)];
p8=[data(8,:); data(14,:)];t8=[data(15,:)];
p9=[data(9,:); data(15,:)];t9=[data(16,:)];
p10=[data(10,:); data(16,:)];t10=[data(17,:)];
p11=[data(11,:); data(17,:)];t11=[data(18,:)];
p12=[data(12,:); data(18,:)];t12=[data(19,:)];
p13=[data(13,:); data(19,:)];t13=[data(20,:)];
p14=[data(14,:); data(20,:)];t14=[data(21,:)];
p15=[data(15,:); data(21,:)];t15=[data(22,:)];
p16=[data(16,:); data(22,:)];t16=[data(23,:)];
p17=[data(17,:); data(23,:)];t17=[data(24,:)];
p18=[data(18,:); data(24,:)];t18=[data(25,:)];
p19=[data(19,:); data(25,:)];t19=[data(26,:)];
p20=[data(20,:); data(26,:)];t20=[data(27,:)];
p21=[data(21,:); data(27,:)];t21=[data(28,:)];
p22=[data(22,:); data(28,:)];t22=[data(29,:)];
p23=[data(23,:); data(29,:)];t23=[data(30,:)];
p24=[data(24,:); data(30,:)];t24=[data(31,:)];
% we define the following submatrices which will be needed to forecast the
% loads of the days (i.e., the inputs to the neural network) and the corresponding days
which such data will be used
% to forecast (i.e., the targets)
%%
xx=1;yy=7;zz=8;hr=1:24;
% we present the training data set all at ago to the network by means of
% the loop below
forjj=1:25
p=[data(xx,:); data(yy,:)];t=[data(zz,:)];
ifjj==18
p=[p1 p2 p3 p4 p5 p6 p7 p8 p9 p10 p11 p12 p13 p14 p15 p16 p17];
t=[t1 t2 t3 t4 t5 t6 t7 t8 t9 t10 t11 t12 t13 t14 t15 t16 t17];
net.trainParam.passes=100;
else
ifjj>=19
break
end
99
end
%the input sets and targets are preprocessed and normalised thus:
[pn,meanp,stdp,tn,meant,stdt] = prestd(p,t);
%we create the network thus
net=newfftd(minmax(pn),[0 1],[28 38 1],{'tansig' 'tansig' 'purelin' },'traincgp');
% net=newelm(minmax(pn),[25 28 1],{'tansig' 'tansig' 'purelin'},'traincgb')
% net=newff(minmax(pn),[35 45 1],{'tansig' 'tansig' 'purelin' },'trains')
% we tune the network parameters below
net.biasConnect=[1;1;1];
net.performFcn='msereg'
% net.layersConnect=[1 0 0;1 1 0;0 1 0];
net.layerWeights{2,1}.delays=[0 1];
net.layerWeights{3,2}.delays=[0 1];
net.trainParam.passes=100;
net.performParam.ratio=0.01;
lp.lr=0.001;
lp.mc=0.75;
net.inputWeights{1,1}.learnFcn='learngdm'
net.layerWeights{2,1}.learnFcn='learngdm'
net.layerWeights{3,2}.learnFcn='learngdm'
net.trainParam.goal=1.0e-5;
net.trainParam.epochs=3000;
net.trainParam.show=100;
[net,tr]=train(net,pn,tn);
an=sim(net,pn);
a=poststd(an,meant,stdt);
error=(t-a)./t;
disp([t' a' error'])
perf=mae(error,net)
% figure(xx)
%plot(hr,a,'gd-',hr,t,'mp--');axis([0,25,0,90]);
xx=xx+1;yy=yy+1;zz=zz+1;
end
% the trained network is tested with new data set
xx=18;yy=24;zz=25;
forll=1:8
pnew=[data(xx,:);data(yy,:)];y=1:24;
ifll==8
break
end
pnewn=trastd(pnew,meanp,stdp);anewn=sim(net,pnewn);
anew=poststd(anewn,meant,stdt);
t=[data(zz,:)];
100
error=(t-anew);
e=(error)./t;
dd=abs(e);
figure(ll)
plot(y,anew,'rh-',y,t,'bd--'); axis([0,25,0,90]);
grid on
ylabel('load in Megawatt')
xlabel('time in hours')
title('plot of actual and predicted load values against time in hours')
legend('rh- predicted values','bd-- actual values','bl')
print -dtiffogbagu
disp([t' anew' error' e' dd']);disp([xx yyzz]);
perf=mae(e,net)
xx=xx+1;yy=yy+1;zz=zz+1;
% a simulink equivalent of the model is generated by the code below
end
pnew=[p18 p19 p20 p21 p22 p23 p24];
pnewn=trastd(pnew,meanp,stdp);anewn=sim(net,pnewn);
anew=poststd(anewn,meant,stdt);
t=[t18 t19 t20 t21 t22 t23 t24];
y=1:168;
error=(t-anew);
e=(error)./t;
dd=abs(e);
figure(ll)
plot(y,anew,'rh-',y,t,'bd--'); axis([0,170,0,90]);grid on
ylabel('load in Megawatt')
xlabel('time in hours')
title('plot of actual and predicted load values against time in hours')
legend('rh- predicted values','bd-- actual values','bl')
print -dtiffogbagu
disp([t' anew' error' e' dd']);disp([xx yyzz]);
perf=mae(e,net)
xx=xx+1;yy=yy+1;zz=zz+1;
toc
gensim(net,1)
101
THE RESEARCH DATA
Table 1: Daily-hourly load for the month of February, 2011
Hr/Day Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat Sun Mon
01 02 03 04 05 06 07 08 09 10 11 12 13 14
01.00 40.20 35.80 39.10 45.50 30.70 33.00 42.50 37.30 48.50 33.50 37.20 38.80 35.40 43.10
02.00 36.40 30.20 34.40 41.80 29.30 30.20 40.60 32.10 43.40 30.80 36.00 33.50 31.20 40.00
03.00 31.30 28.10 30.20 38.60 25.50 30.20 40.00 30.00 37.20 28.90 34.70 32.20 24.30 39.60
04.00 30.90 40.40 45.60 35.90 38.10 34.50 49.20 27.60 37.90 41.20 31.40 32.00 29.10 42.00
05.00 44.60 47.30 48.10 51.40 40.30 56.10 60.40 44.90 55.60 46.30 50.70 45.60 40.70 56.80
06.00 59.10 52.00 50.90 63.20 45.60 77.90 65.00 58.10 52.00 51.70 56.40 60.40 59.40 62.50
07.00 70.70 80.50 67.40 82.30 67.70 73.80 85.60 64.30 70.90 83.50 78.30 62.70 53.00 63.90
08.00 70.00 76.20 77.90 80.40 71.20 64.30 81.00 60.20 68.60 73.10 62.20 74.00 50.00 78.00
09.00 67.50 72.50 75.20 70.10 70.30 60.30 74.90 58.40 64.10 66.80 60.00 73.20 48.30 76.10
10.00 61.60 68.10 72.20 67.90 55.40 58.10 53.70 57.00 62.60 65.70 52.90 66.70 45.40 64.80
11.00 60.20 62.90 70.00 65.00 51.50 53.90 50.30 56.10 60.00 63.20 46.30 62.40 43.70 60.30
12.00 57.80 55.80 68.10 62.50 49.30 50.20 48.50 52.30 58.20 60.40 40.60 56.30 40.80 58.30
13.00 53.60 51.40 63.30 57.40 42.80 59.30 45.40 50.50 53.40 55.90 38.70 54.00 47.10 52.00
14.00 48.70 50.70 59.40 55.30 40.10 61.00 41.30 48.20 50.90 52.40 35.80 50.90 52.60 48.30
15.00 **** 55.90 56.10 48.80 45.00 60.40 51.90 45.70 55.10 40.20 44.60 57.30 55.00 46.60
16.00 **** 59.20 61.50 51.00 49.20 67.30 58.90 57.30 60.30 58.70 52.30 59.50 58.40 53.40
17.00 **** 61.10 66.20 58.30 57.60 70.00 63.30 64.00 66.20 67.00 58.00 63.70 65.10 66.20
18.00 **** 65.30 67.30 61.50 64.40 71.50 66.10 68.20 72.70 69.10 61.50 65.30 68.60 60.80
19.00 **** 71.70 67.10 64.70 70.50 74.90 69.00 73.40 78.10 69.00 68.90 68.50 72.20 69.40
20.00 **** 73.60 70.40 68.90 70.00 76.30 74.10 78.20 78.40 73.50 76.00 74.20 76.70 71.20
21.00 **** 78.90 85.30 72.10 73.80 69.20 76.50 81.30 79.00 64.40 70.20 77.40 61.50 66.70
22.00 45.20 56.30 80.00 60.20 58.00 65.60 51.40 72.40 65.60 44.90 48.10 60.50 40.00 54.00
23.00 43.70 43.30 50.70 47.40 42.90 38.70 50.00 46.20 53.50 40.80 42.70 48.90 40.00 51.20
24.00 36.40 38.70 41.40 46.20 32.30 35.20 40.60 43.10 50.30 38.40 40.00 33.60 33.10 42.80
102
Table 1 contd.
Hr/Day Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat Sun Mon
15 16 17 18 19 20 21 22 23 24 25 26 27 28
01.00 31.20 45.50 28.90 40.70 34.60 41.70 46.90 40.20 36.40 42.30 45.90 39.70 31.20 47.10
02.00 25.40 40.80 26.30 40.00 34.20 38.00 43.20 37.90 33.10 37.60 42.40 37.00 30.30 40.10
03.00 20.90 32.70 23.20 33.30 34.20 27.80 41.00 34.10 31.80 36.20 40.20 32.80 27.70 36.50
04.00 18.50 34.40 25.90 56.70 46.90 22.00 48.10 39.00 39.10 41.30 45.00 36.80 36.20 43.50
05.00 27.70 48.90 34.10 52.80 49.00 38.60 52.60 44.70 45.90 43.30 46.20 48.70 39.10 49.40
06.00 47.80 55.60 61.30 54.00 52.70 59.00 59.00 46.20 52.40 63.50 48.30 52.60 65.30 51.80
07.00 69.00 80.10 77.20 65.90 58.30 51.40 77.00 71.40 60.70 76.10 66.10 72.30 52.60 81.60
08.00 58.10 78.40 70.90 68.20 61.40 50.00 72.00 70.30 74.30 65.30 73.40 70.10 45.20 73.40
09.00 53.20 64.30 70.30 66.40 73.10 47.60 70.50 68.50 65.20 61.30 70.40 67.40 42.60 68.00
10.00 50.60 61.20 70.00 64.10 66.50 41.30 65.40 64.30 61.20 55.30 66.40 62.70 40.10 65.10
11.00 50.00 57.90 64.20 60.80 59.10 38.00 62.20 62.10 58.40 52.70 50.90 57.80 47.90 62.60
12.00 46.30 53.60 60.10 56.20 48.40 35.60 60.10 57.30 56.90 50.10 45.30 56.50 52.30 57.30
13.00 41.90 50.10 59.20 52.30 50.80 47.30 54.30 53.20 50.40 44.50 48.50 51.30 55.00 54.10
14.00 40.70 48.30 55.60 50.00 49.70 53.20 53.60 49.10 43.20 40.90 44.20 52.20 59.40 49.70
15.00 47.80 49.00 50.40 45.30 56.20 58.90 48.40 53.40 45.10 51.00 49.40 57.10 59.90 58.10
16.00 55.20 53.50 62.70 49.10 59.00 64.70 51.70 55.20 47.80 56.30 53.20 59.80 60.60 60.30
17.00 59.20 56.10 65.00 54.90 63.40 66.30 58.20 61.40 53.20 59.50 62.10 63.20 61.60 63.40
18.00 61.50 58.90 68.30 57.20 66.10 61.50 65.10 66.30 60.40 65.30 69.70 66.80 61.10 66.00
19.00 67.30 64.00 71.90 61.00 70.80 68.20 66.80 69.00 64.10 67.60 72.30 70.60 66.00 71.30
20.00 69.40 72.20 76.70 66.20 73.10 68.00 70.50 74.60 69.30 72.40 78.10 72.10 69.30 72.50
21.00 72.60 81.30 78.20 69.10 65.90 70.20 82.70 75.30 70.40 83.60 79.20 75.90 66.40 83.60
22.00 62.50 60.70 50.30 56.20 51.30 40.60 63.00 68.30 51.70 65.30 72.50 63.40 60.30 70.30
23.00 52.60 49.30 44.10 47.90 50.00 37.30 49.20 56.10 50.30 61.80 65.30 47.80 50.20 65.40
24.00 50.60 47.20 35.00 40.10 39.70 32.20 48.70 50.40 47.60 50.30 48.70 42.60 37.70 53.20
103
09.00 61.20 69.90 70.10 71.00 65.60 52.20 68.50 70.00 68.30 71.20 74.40 71.60 **** 71.70 71.50 73.200
10.00 60.20 56.10 69.50 69.40 60.20 50.10 65.20 51.30 65.10 65.20 68.80 64.60 **** 61.30 60.10 65.80
11.00 56.40 54.50 52.20 62.30 46.70 48.90 58.50 46.50 61.50 61.70 61.90 59.50 **** 55.20 53.50 61.90
12.00 55.60 52.30 50.40 56.00 44.20 50.20 53.80 41.20 57.60 58.50 59.50 58.40 **** 52.80 46.10 56.10
13.00 48.10 42.40 46.30 49.70 41.90 52.20 52.60 40.90 58.80 54.20 51.30 53.50 **** 52.30 39.10 48.60
14.00 47.80 40.10 44.90 43.90 38.70 54.10 50.20 40.60 **** 52.90 50.90 **** **** 50.50 33.10 46.90
15.00 53.00 46.20 51.00 57.00 55.10 55.90 58.60 42.40 54.20 59.20 58.20 **** **** 52.90 38.10 57.80
16.00 56.50 50.20 54.70 61.00 65.30 58.70 59.60 48.80 63.90 62.10 60.60 **** **** 55.70 46.00 58.90
17.00 58.80 53.10 57.30 65.20 67.50 59.30 66.10 55.10 66.10 63.20 69.40 **** **** 61.70 66.90 63.70
18.00 63.70 59.80 66.10 66.90 69.40 61.00 69.50 58.20 67.20 64.40 70.90 **** **** 65.90 68.90 68.70
19.00 70.50 65.20 69.30 71.50 73.30 63.90 69.80 66.40 70.80 72.10 75.80 **** 69.50 69.30 69.70 69.10
20.00 72.30 70.80 74.60 75.60 74.70 67.60 70.90 68.90 76.20 75.40 77.00 **** 69.40 71.40 70.50 73.70
21.00 78.60 80.30 77.40 79.50 76.60 69.30 81.10 72.30 78.20 79.10 83.90 **** 71.20 75.10 72.80 79.90
22.00 68.70 71.10 62.30 70.30 62.60 65.70 77.30 72.40 67.40 73.10 80.70 **** 66.30 70.20 **** 73.40
23.00 50.90 58.20 57.40 51.40 53.80 48.70 52.20 69.30 58.40 69.40 65.70 **** 55.10 62.30 **** 60.10
24.00 48.80 48.30 55.20 43.50 49.30 43.20 50.10 57.40 55.30 53.40 45.20 **** 41.40 59.50 **** 55.50
104
Table 2 contd.
Hr/Day Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu
17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
01.00 48.70 47.20 43.40 33.10 44.50 44.20 40.40 45.30 42.90 47.70 38.20 45.10 43.70 44.50 48.00
02.00 44.10 46.80 32.30 31.40 40.50 40.90 38.20 39.60 41.30 37.20 35.60 42.30 40.20 40.00 38.80
03.00 34.10 35.60 30.70 29.60 32.50 37.90 31.10 32.40 36.20 40.10 33.00 35.70 38.00 37.00 35.90
04.00 44.10 38.90 46.30 32.30 34.30 37.90 **** 43.70 37.10 41.30 41.90 38.10 40.70 42.00 44.90
05.00 52.20 49.60 54.30 45.40 39.70 38.30 **** 49.60 48.30 51.50 48.20 46.80 42.70 43.30 47.60
06.00 64.00 72.90 66.80 63.20 52.10 48.70 46.90 59.90 63.50 54.60 57.30 50.60 53.50 48.90 56.40
07.00 84.50 86.90 75.70 60.00 63.50 68.30 83.20 70.20 73.30 69.50 59.50 65.30 67.10 73.50 70.90
08.00 80.80 79.60 74.20 59.80 75.40 66.80 77.60 69.20 70.80 67.30 58.00 69.70 64.20 68.60 66.80
09.00 77.60 71.70 71.40 55.60 74.40 61.20 72.40 68.60 61.50 63.80 53.90 65.20 62.70 70.10 66.30
10.00 72.60 64.50 66.60 54.90 69.70 59.40 65.40 67.60 58.80 60.90 50.30 66.30 60.20 66.30 64.60
11.00 63.40 49.30 58.80 47.80 65.40 58.30 61.50 58.40 52.00 **** **** 62.90 58.40 63.40 53.90
12.00 60.70 47.40 54.60 51.40 63.30 55.60 53.20 52.10 50.40 **** **** 60.10 56.00 52.30 50.70
13.00 53.40 45.70 52.30 55.00 60.70 50.40 49.20 49.20 46.90 **** **** 57.50 54.00 50.50 49.80
14.00 52.80 45.40 49.30 57.50 51.80 44.20 46.10 46.80 45.60 **** **** 53.90 50.90 49.10 48.00
15.00 54.60 50.70 53.40 57.70 64.50 50.10 56.40 47.70 51.20 **** **** 60.20 53.80 50.70 46.50
16.00 66.90 55.10 54.40 58.20 68.80 56.40 57.20 51.70 53.40 **** **** 63.70 56.30 52.10 49.20
17.00 65.70 59.10 66.30 61.60 69.40 65.50 59.40 55.80 60.30 **** **** 64.20 61.70 60.10 54.90
18.00 69.80 62.30 68.40 67.30 70.20 72.50 64.90 59.60 63.40 **** 63.50 67.20 66.90 67.30 63.60
19.00 70.30 69.80 70.20 69.40 70.20 77.40 69.40 61.10 66.70 **** 65.30 67.70 70.80 69.60 66.20
20.00 74.40 74.30 74.30 72.20 76.30 79.90 70.10 75.10 70.80 **** 66.00 69.10 74.00 72.60 70.30
21.00 82.70 77.60 81.80 72.00 80.10 80.70 74.60 78.80 73.60 76.20 72.10 75.90 75.40 73.20 72.70
22.00 76.50 73.60 63.80 68.10 71.30 70.80 72.30 72.50 67.10 69.80 57.60 63.80 64.10 67.10 65.20
23.00 58.80 57.60 59.10 45.30 63.10 50.30 52.50 66.40 59.20 52.70 44.10 56.10 54.70 51.10 56.90
24.00 53.20 56.40 49.20 33.20 46.30 41.70 46.90 50.50 46.80 49.90 41.90 46.30 45.40 48.90 52.50
105