Short-Term Daily Peak Load Forecasting Using Fast Learning Neural Network

Gul Muhammad Khan,Shahid Khan

Department of Electrical Engineering

UET Peshawar

Pakistan

Email: gk502@nwfpuet.edu.pk,k shahid66@hotmail.com

Fahad Ullah

Department of Computer System Engineering,

UET Peshawar

Pakistan

Email: fahadullah@nwfpuet.edu.pk

Abstract—Load forecasting has been an inevitable issue inelectric power supply in past. It is always desired to predictthe load requirements in order to generate and supply electricpower efficiently. In this research, a neuro-evolutionary tech-nique known as Cartesian Genetic Algorithm evolved ArtificialNeural Network (CGPANN) has been deployed to develop apeak load forecasting model for the prediction of peak loads24 hours ahead. The proposed model presents the training of allthe parameters of Artificial Neural Network (ANN) including:weights, topology and functionality of individual nodes. Thenetwork is trained both on annual as well as quarterly bases,thus obtaining a unique model for each season.

Keywords-Short Term Load Forecasting, Artificial NeuralNetworks, Genetic Programming, Neuro-evolution.

I. INTRODUCTION

The price of electric unit and hence electricity itself

depends upon the efficient and optimal operation of an

electrical power generation plant. This efficiency means a

balance that must be achieved between the demand and the

generation of electric load. In order to achieve this balance,

there must be a forecasting system which can predict the

load requirement in future or any time for that matter.

The efficient operation of a power system needs proper

fuel scheduling and maintenance which can be achieved

by using a sophisticated forecasting system that determines

the electric load demand at any time in future. There are

a number of forecast techniques developed for electric load

forecasting. Some of these techniques are more conventional

and hence less favored. ANN based forecasting techniques

are amongst the modern approaches towards load forecast.

It is indeed a tedious job to find an optimal neural network

to efficiently predict the load requirements. Manual methods

are being used hitherto, to obtain optimized ANNs for elec-

tric load forecasting. Using evolutionary techniques would

make possible the generation of the optimized networks in

an automated way with better accuracy. Load forecasting is

categorized into three types: long term, medium term and

short term load forecasting. The long term load forecasting

deals with the forecast extending for duration longer than a

year. For short term the forecast time ranges from an hour to

a week. In this paper ANN based model has been developed

by using the evolutionary technique known as Cartesian

Genetic Programming evolved Artificial Neural Network

(CGPANN). It is intended to forecast daily peak loads with

load times of 1 to 7 days through the use of previous

ten days data history. Section II of the paper presents the

literature review with reflects on necessary concepts such

as load forecasting itself, Cartesian Genetic Programming,

Artificial Neural Networks and Neuro-Evolution. Section III

describes CGPANNs in detail. Section IV reflects on the

Application of CGPANN to load forecasting. This section

contains the Experimental setup as well as the Results and

Analysis. Section V shows the concluding remarks and the

future work.

II. LITERATURE REVIEW

A. Load Forecasting

Load forecasting, like any other forecasting model is

an efficient planning of supplying electricity from power

stations while keeping in mind the additional capacity as-

sociated with the load escalation in future. Load forecasting

is important for the reason that energy storage on large scale

either isn’t possible or undoubtedly problematic. Hence, it

is inevitable to implement a forecasting system so that the

production levels conform to the demand ones. A number

of techniques are adopted in order to efficiently forecast the

future load for power systems [11], [22], [14], [4], [1], [5],

[21]. Adaptive load forecasting [14] automatically sets the

system parameters when the load condition changes. In Au-

toregressive model [11] load is taken as a combination of the

previously used loads and hence the forecasting is achieved.

Autoregressive Moving Average (ARMA) model [4] and its

variant ARMA with Exogenous variable (ARMAX) model

[22] implements a non-linear regression algorithm approach

in load forecasting. Abbas and Arif used seven SVM models

for daily peak load demand [1]. Genetic algorithms were

used for the optimization of the parameters in this research.

Xu Tao et al. [21] implemented SVM to predict short-term

load. El-Attar et al. [5] proposed a hybrid approach that

used both support vector regression and local prediction

framework for load forecasting. A not very recent yet much

popular idea is the deployment of Artificial Neural Networks

(ANNs) for load forecasting [2], [19], [7], [6], [17], [12],

[18], [13], [10], [3]. Peng et al. [18] used neural networks,

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Table ICOMPARISON TABLE FOR PREVIOUS RESULTS

S/N Method MAPE Reference

1 Locally Linear Model Tree 1.98% [10]

2 Support Vector Machines- 1.93% [1]

Genetic Algorithm (SVM-GA )

3 Autonomous ANN 1.75% [6]

4 Floating Search + SVM 1.70% [21]

5 Prediction Framework + SVR 1.52% [5]

6 Feed-forward ANN 1.42% [17]

7 SOFNN + Bi-level Opt. 1.40% [12]

8 MLP-NN + Leve-Marq. 1.60% [3]

which have the capability of learning along with the ca-

pability to deal with the nonlinear relationships between

load and the factors affecting it directly from the historical

data and without the selection of a given model in advance.

Senjyu et al. [2] proposed short-term load forecasting using

a neural network that would produce a simple correction

value. They would add that value to the data associated with

a similar day; a day which exhibits the same load conditions

as of the forecast day. Pang Qingle et al. [19] proposed

load forecasting based on rough set and neural network.

Ghomi, Mohammad et al. [7] used ANN for peak load

forecasting without weather information. They evaluated two

popular algorithms of Multi Layer Perceptron (MLP) and

Radial Basis Function (RBF) and found that MLP bears

more favorable results in their forecasting system. Matsui et

al. [13] proposed peak load forecasting by using analyzable

structure ANN. Koushki et al. [10] presented neuro-fuzzy

model for short-term load forecasting. Ferreira et al. [6]

proposed two different procedures in a coupled way for the

solution of Neural Network structure and input selection for

short-term load forecasting. Daniel Ortiz-Arroyo et al. [17]

used a simple Artificial Neural Networks approach for load

forecasting with a well populated set of attributes. Huina

Mao et al. [12] presented a system for load forecasting

that combined both self-organizing fuzzy neural network

(SOFNN) and a bi-level optimization method. Amjaday

et al. [3] presented a hybrid model that used ANN, pre-

forecast mechanism and evolutionary algorithm to predict

the midterm peak load.

Table II-A shows the forecasting results for most of the

previous methods aforementioned with most of the methods

forecasting the load only for a month. In order to evaluate the

performance of the forecasting algorithm, Mean Absolute

Percentage Error (MAPE) is used to evaluate the prediction

accuracy. MAPE is widely used standard for measuring load

forecast performance. MAPE is given by:

MAPE(%) = 1

N

∑i=1toN

(|LF −LA|

LA

)x 100

Where LF is the forecasted load, LA is the actual load

and N is the number of season days.

B. Artificial Neural Networks

Artificial Neural network, a bio-inspired approach which

builds up from highly interconnected processing elements-

mimics a real neural network naturally present in any living

organism. “Self training and learning” are the key aspects

of an ANN. ANN is a layered model consisting of three

neural layers; input layer, hidden layer and output layer. A

connection between two neurons carries a weight; a specific

activation function belonging to each neuron generating

outputs based on given inputs.

Each unit in artificial neural network performs an ele-

mentary task i.e. to receive input from adjoining unit or

external sources and generate output based on the activation

function to other units. The network intrinsically behaves

in a parallel fashion meaning that many nodes do the

computation simultaneously. A unit in the network can fall

in any of the three categories: an input unit receiving data

from outside the network, an output unit sending data outside

ANN and finally the hidden unit connected to the units

inside the network. ANN can be classified into three types

each of which exhibit different behavior: Radial Basis Func-

tion Network (FBFN), Multi-Layered Perceptron Network

(MLP), and Recurrent Neural Network (RNN). MLPs are the

most popular neural networks. It is mandatory to perform a

sequence of steps before an ANN based model is available

for functioning. Among those steps training (or learning)

and testing are two vital steps essentially required before

making an ANN operational. Because of the fact that ANN

doesn’t rely on human experience and it is a self-adapted and

self-learnt system, it can be most certainly used to obtain

promising results in a changing environment.

C. Cartesian Genetic Programming(CGP)

CGP is a specific type of genetic programming developed

by Thomson and Miller [15]. It is meant for the evolution

based design of the feed forward digital circuits. In CGP, A

genotype consists of genes representing nodes. Each node

has its inputs and a function that it performs on its inputs.

The outputs from the intermediary nodes can be the inputs

for the other nodes. The output of the system can be the

intermediary input i.e. the output from any other node or

even a system input itself. The genotype or also called

chromosome has a constant length and it is represented by a

stream or array of integers which represents the nodes (their

functions and inputs) as well as the outputs. The phenotype

is obtained by following the referenced links in the directed

graph meaning that those genes are selected which make the

path between the program inputs and outputs. The fitness

of each CGP program determines whether it should stay

in population and produce offspring or should be removed.

Offspring are obtained by mutating either node function or

the connection between nodes, or the output genes.

D. Neuro-Evolution

The use of artificial evolution with ANNs is known as

Neuro Evolution (NE). In NE every aspect of an ANN is

evolved including network topology, node function and con-

nection weights. A genetic algorithm is used with the ANN

844 2011 11th International Conference on Intelligent Systems Design and Applications

where the algorithm acts as the genotype and the network

as the corresponding phenotype. The genotypic evolution is

continued until the desired phenotypic behavior is obtained.

The encoded attributes in the genotype can affect the search

space of the solution. Sometimes only few parameters of the

system are evolved and at times, it is possible to evolve a

group of them. When only weights of the system are evolved

by keeping the topology fixed, the network solution space

is restricted. Hence, a new solution to the problem can’t

be achieved because of the fact that evolution has to work

in a more conservative environment. Topology and Weight

Evolved Artificial Neural Network (TWEANN) on the other

hand can evolve both weights and topology and hence can

boost the network efficiency [23]. A number of neuro-

evolutionary techniques are presented in the past with some

evolving weights, some topology and some evolving both

[23]. Xin, Yao further elaborated through experimentation

the fact that evolution of both topology and weight produces

much better results than evolution of weights or topology

alone. Symbiotic, Adaptive Neural Evolution (SANE) uses

the simultaneous evolution of neuron population along with

the network topologies representing the blue prints [16]. An

extension of SANE called Enforced Sub-Population (ESP)

evolves a subpopulation of hidden layer neurons rather one

population of neurons [8]. Neuroevolution of Augmenting

Topologies (NEAT) developed by Stanley solved three major

problems in neuroevolution including the tracking of genes

with historical markings that allow easy crossover between

different topologies, protecting innovation via speciation and

finally the starting from basic simple structure and “com-

plexifying” over time as the generations pass. NEAT had a

performance advantage over many previous NE algorithms

[20]. Cooperative Synapse Neuroevolution (CoSyNE) co-

evolves the synaptic weight. They have used multipoint

crossover and probabilistic mutation based on Cauchy dis-

tributed noise [8].

III. CARTESIAN GENETIC PROGRAMMING

EVOLVED ARTIFICIAL NEURAL NETWORK

(CGPANN)

CGPANN [9], a new Neuroevolutionary algorithm in-

troduced recently encode all the attributes of the neural

networks including weights, topology and node functions

in the genotype. It evolves all these parameters of the

network until best combination of them is achieved. This

paper implements the feed-forward CGPANN also called

FCGPANN. The results achieved in [9] reveal that this

algorithm learning rate is dramatically faster in contrast

to its contemporary NE techniques. CGPANN and hence

FCGPANN uses (1+λ) evolutionary strategy to generate the

population of next generation. The developed network in this

case has neurons that are not fully connected. Also, another

fact about CGPANN is that the program inputs are not

connected to every neuron in the input layer which makes

Figure 1. Representation of FCGPANN Node

Figure 2. (a) FCGPANN Genotype (b) Architecture of the Genotype

it peculiar in comparison to a conventional ANN. Such

features in this algorithm makes possible for it to generate

topologies that are more efficient in terms of hardware

implementation and time. An FCGPANN’s neuron (node)

includes inputs, weights, connections and function. Inputs

can be from the program or an intermediary input that is an

output from a node. Randomly generated weights are used

ranging from -1 to +1. Outputs can be from nodes or directly

from program inputs. For each node, inputs and weights

are multiplied and summed up. The sum is then forwarded

to an activation function. The output of a node can either

be an intermediary input or output of the program or it is

possible that it is never used leading to the formation of a

junk node. Figure 1 shows a FCGPANN based node with

I1 and I2 as its inputs and W1X and W2X being weights of

the connections. Whereas ’X’ represents the node number.

Figure 2(a) shows the genotype of a FCGPANN with three

nodes having corresponding inputs, weights and functions.

The final square represents the output of the system. The

dotted boundary of the first node reveals that it doesn’t take

part in the circuit and hence it is a junk node. Figure 2(b)

shows the phenotype of the genotype in Figure 2 (a).

2011 11th International Conference on Intelligent Systems Design and Applications 845

IV. APPLICATION OF CGPANN TO LOAD

FORECASTING

A. Experimental Setup

The proposed load forecasting model is based on the past

daily peak loads (historical consumption data) as the only

input variable. The training is performed by dividing the

training data into four types, one for each of the four seasons

i.e. winter, spring, summer and autumn. The whole year data

has also been used for training the corresponding model. The

load at a particular instant can get affected by many factors

but here we are using only the loads of previous ten days as

the inputs to the model. This data is used to predict the peak

load of the eleventh day and onwards. A random population

of ten CGPANN networks is generated at the start of the

process. The activation functions used is log-sigmoid. The

number of inputs per node is 5. Mutation rate used in this

case is 10%. The number of CGPANN rows in this case is

one, thus the number of columns are equal to the number of

nodes. Input(s) are applied and the MAPE value is measured

for each of the ten Networks. These MAPE values are

compared with each other and the network with best MAPE

value is selected for promotion to the next generation. This

very network is then used to produce nine other networks

by mutation of parent’s genotype. This process continues

until the maximum number of generations has arrived or

the MAPE has reduced to zero. In this case, all experiments

are run for two million generations during its training phase.

B. Results And Analysis

In order to evaluate the performance of algorithm the

data is obtained from the United Kingdom national grid in

the form of hourly load from which peak load data was

extracted on daily bases1. Each year data has been divided

into four seasons along with the whole year data for a period

of four years. Out of four years data only the first year data

(2006) is used for training of algorithm and the rest of the

data is used for testing and validation. MAPE is used as

a performance criterion. We have trained the network for

every individual season and for the whole year. A separate

model is obtained for each seasonal and annual data. At the

end the best obtained genotype is transformed to phenotype

and tested on the data of 2007, 2008 and 2009 for all the

seasons and complete year. For both training and testing

purposes, various morphological alterations have been made

for different experiments in order to obtain an optimum

network that can achieve the best of forecasting results.

The morphology of the network is altered by changing

the principle aspect of the network; the number of nodes

constituting the whole network itself. By varying the number

of nodes in the network, the corresponding size of network

varies and thus affecting the possible types of network

morphologies that can be developed. A number of runs

1http://www.tutiempo.net

Table IITRAINING RESULTS FOR DIFFERENT COMBINATIONS OF NODES

MAPE for Different Number of Nodes

Model 50 100 150 200 250 300

Winter 3.11 3.11 3.14 3.13 3.13 3.11

Spring 3.44 3.31 3.43 3.44 3.50 3.47

Summer 2.37 2.26 2.53 2.50 2.36 2.57

Autumn 1.44 1.38 1.45 1.54 1.55 1.52

Annual 3.55 3.38 3.58 3.54 3.58 3.38

Table IIITESTING RESULTS FOR DIFFERENT COMBINATION OF NODES

MAPE for Different Number of Nodes

Model Year 50 100 150 200 250 300

Winter

2007 3.32 3.34 3.39 3.48 3.48 3.28

2008 4.43 4.43 4.47 4.50 4.50 4.39

2009 3.74 3.77 3.81 3.94 3.94 3.49

Spring

2007 3.96 4.00 3.77 3.96 3.79 4.03

2008 3.24 3.18 3.28 3.24 3.33 3.30

2009 4.05 4.14 3.69 4.06 3.74 4.16

Summer

2007 2.23 2.19 2.39 2.35 2.26 2.47

2008 2.82 2.72 2.99 2.94 2.78 3.02

2009 3.39 2.95 3.86 3.59 3.37 3.63

Autumn

2007 1.78 1.71 1.80 1.83 1.84 1.82

2008 2.31 2.16 2.35 2.46 2.46 2.43

2009 1.78 1.49 1.83 1.93 1.97 1.91

Annual

2007 3.36 3.16 3.40 3.38 3.40 3.16

2008 3.85 3.61 3.91 3.85 3.92 3.63

2009 3.74 3.52 3.82 3.76 3.81 3.54

of the training and testing experiments are performed on

the network sizes ranging from 50 to 300 nodes i.e. 50,

100, 150, 200, 250, 300. It is worth mentioning that the

ultimate phenotype will not necessarily use all the nodes of

the network, and statistics showed that only 5 to 10 percent

of nodes are used to produce ultimate phenotype [9].

Table IV-B and IV-B summarize the results for both train-

ing and testing respectively. The MAPE has been calculated

for different experiments in each of which the number of

nodes in the network is varying. As the weather in UK

is relatively stable in autumn, the forecasting accuracy is

far better as clear from the table IV-B. As the results

suggest, with 100 nodes constituting the network the MAPE

values are favorable. The forecasting error for 200 and 250

node networks reveal the poor performance of the networks.

Figure 3 shows the variation in the best estimated and actual

load for all the combinations, clearly demonstrating the

capabilities of CGPANN to predict peak load accurately.

Figure 3 depict the best cases of forecasting for a number

of different combinations of nodes respectively for autumn

seasons. In winters, and particularly in 2008, the forecasting

accuracy is the poorest and hence MAPE values higher.

Table IV-B shows the seasonal and annual MAPE values

obtained by testing the corresponding models. From the table

it is evident that the results are best for the autumn 2009

being less variation in peak load.

Figure 4 represents the corresponding curves for both

actual and estimated peak load for autumn season, 2009.

Both the curves exhibits close resemblance which shows the

index to which the prediction has been successful. Figure 5

and 6 shows corresponding frequency plots of the peak load

for the estimated and actual load respectively. The frequency

spectrum of both the graphs reveals the extent to which

the forecasting has been successful. Another important fact

846 2011 11th International Conference on Intelligent Systems Design and Applications

Figure 3. Peak load variation graphs showing the best estimations against the Actual peak load for various number of nodes (a) 50, (b) 100, (c) 150, (d)200, (e) 250, (f) 300

Figure 4. Comparison curve for actual and estimated load for autumn2009

Figure 5. Frequency distribution of the estimated peak load for autumn2009

about the data in Table IV-B is that the forecasting in

this case is based on 10 days that is the daily forecast

is made for next 50 days based on the previous 10 days

actual load. Because load forecasting intrinsically depends

on the geography and hence the weather conditions of an

area, the results are better for autumn because the weather

is steadier in that season in United Kingdom. A straight

forward comparison isn’t possible with Table II-A because

Figure 6. Frequency distribution of the estimated peak load for autumn2009

Figure 7. Comparison curve for actual and estimated load through thewinter 2008

the results in Table IV-B follow a different approach yet the

performance can be analyzed. Figure 7 shows both actual

and forecasted peak load for winter 2008 (4 months). The

results are based on the load data from UK national grid

and as obvious from the curve, the load prediction is poor

in winter due to the whimsical and unpredictable nature of

weather in Great Britain in that particular season. Winter

2008 shows the worst case of results-MAPE obtained is

2011 11th International Conference on Intelligent Systems Design and Applications 847

4.50% -as shown in Table IV-B.

V. CONCLUSION AND FUTURE WORK

In this paper a novel Neuro-evolutionary technique called

CGPANN has been used for the daily peak load forecasting.

Electric Load data of different durations is used to train the

ANN on both quarterly and annual basis and then the testing

is done for the peak load forecasting. The results obtained in

all autumn seasons are generally better. The results, as from

Table IV-B show the efficiency of this approach in steadier

weather conditions as weather parameters aren’t taken into

account in this research. The various curves reveals the

forecasting accuracy in both time and frequency domains.

As this approach only use the peak load as an input to the

artificial neural network and doesn’t take into account other

relevant parameters like atmospheric temperature, humidity,

rain and pressure, thus, there is a potential research to be

conducted highlighting the effect of these parameters on load

forecasting systems in future.

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