S.A.Kalogirou 1

Department of Mechanical and Marine Engineering,Higher Technical Institute,P.O.Box 20423,Nicosia,2152,Cyprus

Received 27March 1998;accepted 10December 1998

Abstract

Arti®cial neural networks are widely accepted as a technology o ering an alternative way to tackle complex and ill-de®ned problems.They can learn from examples,are fault tolerant in the sense that they are able to handle noisy and incomplete data,are able to deal with non-linear problems and,once trained,can perform prediction and generalisation at high speed.They have been used in diverse applications in control,robotics,pattern recognition,forecasting,medicine,power systems,manufacturing,optimisation,signal processing and social/psychological sciences.They are particularly useful in system modelling,such as in implementing complex mappings and system identi®cation.This paper presents various applications of neural networks in energy problems in a thematic rather than a chronological or any other order.Arti®cial neural networks have been used by the author in the ®eld of solar energy,for modelling the heat-up response of a solar steam-generating plant,for the estimation of a parabolic trough collector intercept factor,for the estimation of a parabolic trough collector local concentration ratio and for the design of a solar steam generation system.They have also been used for the estimation of heating loads of buildings.In all those models,a multiple hidden layer architecture has been used.Errors reported in these models are well within acceptable limits,which clearly suggest that arti®cial neural networks can be used for modelling in other ®elds of energy production and use.The work of other researchers in the ®eld of energy is also reported.This includes the use of arti®cial neural networks in heating,ventilating and air-conditioning systems,solar radiation,modelling and control of power generation systems,load forecasting and prediction,and refrigeration.#1999Elsevier Science Ltd.All rights reserved.

Keywords:Arti®cial neural networks;System modelling;System performance prediction

Energy Conversion &Management 40(1999)1073±1087

0196-04/99/$-see front matter #1999Elsevier Science Ltd.All rights reserved.PII:S 0196-04(99)00012-

6

1Tel.:+357-2-305030;fax:+357-2-494953

E-mail address:skalogir@spidernet.com.cy (S.A.Kalogirou)

1.Introduction

For estimation of the ¯ow of energy and the performance of systems,analytic computer codes are often used.The algorithms employed are usually complicated,involving the solution of complex di erential equations.These programs usually require large computer power and need a considerable amount of time to give accurate predictions.Instead of complex rules and mathematical routines,arti®cial neural networks are able to learn the key information patterns within a multidimensional information domain.In addition,neural networks are fault tolerant,robust and noise immune [1].Data from energy systems,being inherently noisy,are good candidate problems to be handled with neural networks.The objective of this paper is to present various applications of neural networks in energy problems.The problems are presented in a thematic rather than a chronological or any other order.This will show the capability of arti®cial neural networks as tools in energy prediction and modelling.

2.Arti®cial neural networks

The study of arti®cial neural networks (ANN)is one of the two major branches of arti®cial intelligence.The other one is expert systems.During the last ten years there has been a substantial increase in the interest on arti®cial neural networks.The ANNs are good for some tasks while lacking in some others.Speci®cally,they are good for tasks involving incomplete data sets,fuzzy or incomplete information and for highly complex and ill-de®ned problems,where humans usually decide on an intuitional basis.They can learn from examples and are able to deal with non-linear problems.Furthermore,they exhibit robustness and fault tolerance.The tasks that ANNs cannot handle e ectively are those requiring high accuracy and precision,as in logic and arithmetic.ANNs have been applied successfully in a number of applications.Some of the most important ones are:

(A)Classification .In pattern recognition..In sound and speech recognition..Analysis of electromyographs and other medical signatures..Identi®cation of military targets..Identi®cation of explosives in passenger suitcases.

(B)Forecasting .Weather and market trends..Predicting mineral exploration sites..Electrical and thermal load prediction.

(C)Control systems .In adaptive control..Robotic control.

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(D)Optimisation and decision-making .Engineering systems..Management.

2.1.Biological and arti®cial neurons

A biological neuron is shown in Fig.1.In the brain,there is a ¯ow of coded information (using electrochemical media,the so-called neurotransmitters)from the synapses towards the axon.The axon of each neuron transmits information to a number of other neurons.The neuron receives information at the synapses from a large number of other neurons.It is estimated that each neuron may receive stimuli from as many as 10,000other neurons.Groups of neurons are organised into subsystems and the integration of these subsystems forms the brain.It is estimated that the human brain has got around 100billion interconnected neurons.Fig.2shows a highly simpli®ed model of an arti®cial neuron,which may be used to simulate some important aspects of the real biological neuron.An ANN is a group of interconnected arti®cial neurons,interacting with one another in a concerted manner.In such a system,excitation is applied to the input of the network.Following some suitable operation,it results in a desired output.At the synapses,there is an accumulation of some potential,which in the case of the arti®cial neurons,is modelled as a connection weight.These weights are continuously modi®ed,based on suitable learning rules.

2.2.Arti®cial neural network principles

According to Haykin [2],a neural network is a massively parallel distributed processor that has a natural propensity for storing experiential knowledge and making it available for use.

It

Fig.1.A simpli®ed model of a biological neuron.

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resembles the human brain in two respects;the knowledge is acquired by the network through a learning process,and inter-neuron connection strengths known as synaptic weights are used to store the knowledge.Arti®cial neural network (ANN)models may be used as an alternative method in engineering analysis and predictions.ANNs mimic somewhat the learning process of a human brain.They operate like a ``black box''model,requiring no detailed information about the system.Instead,they learn the relationship between the input parameters and the controlled and uncontrolled variables by studying previously recorded data,similar to the way a non-linear regression might perform.Another advantage of using ANNs is their ability to handle large and complex systems with many interrelated parameters.They seem simply to ignore excess data that are of minimal signi®cance and concentrate instead on the more important

inputs.

Fig.2.A simpli®ed model of an arti®cial

neuron.

Fig.3.Schematic diagram of a multilayer feed forward neural network.

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A schematic diagram of a typical multilayer feedforward neural network architecture is shown in Fig.3.The network usually consists of an input layer,some hidden layers and an output layer.In its simple form,each single neuron is connected to other neurons of a previous layer through adaptable synaptic weights.Knowledge is usually stored as a set of connection weights (presumably corresponding to synapse e cacy in biological neural systems).Training is the process of modifying the connection weights in some orderly fashion using a suitable learning method.The network uses a learning mode,in which an input is presented to the network along with the desired output,and the weights are adjusted so that the network attempts to produce the desired output.The weights after training contain meaningful information,whereas before training,they are random and have no meaning.Fig.4illustrates how information is processed through a single node.The node receives weighted activation of other nodes through its incoming connections.First,these are added (summation).The result is then passed through an activation function,the outcome being activation of the node.For each of the outgoing connections,this activation value is multiplied with the speci®c weight and transferred to the next node.A training set is a group of matched input and output patterns used for training the network,usually by suitable adaptation of the synaptic weights.The outputs are the dependent variables that the network produces for the corresponding input.It is important that all the information the network needs to learn is supplied to the network as a data set.When each pattern is read,the network uses the input data to produce an output,which is then compared to the training pattern,i.e.the correct or desired output.If there is a di erence,the connection weights (usually but not always)are altered in such a direction that the error is decreased.After the network has run through all the input patterns,if the error is still greater than the maximum desired tolerance,the ANN runs again through all the input patterns repeatedly until all the errors are within the required tolerance.When the training reaches a satisfactory level,the network holds the weights constant and uses the trained network to make decisions,identify patterns,or de®ne associations in new input data sets not used to train it.The most popular learning algorithms are the back-propagation and its variants [1,3].The back-propagation (BP)algorithm is one of the most powerful learning algorithms in neural networks.The training of all patterns of a training data set is called an epoch.The training set has to be a representative collection of input±output examples.Back-propagation training is a gradient descent algorithm.It tries to improve the performance of the neural network

by

Fig.4.Information processing in a neural network unit.

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reducing the total error by changing the weights along its gradient.The error is expressed by the root-mean-square value (RMS),which can be calculated by:

E 124 p i

j t ip Ào ip j 251a 2 1 where E is the RMS error,t the network output (target)and o the desired output vectors over all pattern (p ).An error of zero would indicate that all the output patterns computed by the ANN perfectly match the expected values,and the network is well trained.In brief,back-propagation training is performed by initially assigning random values to the weight terms (w ij )2in all nodes.Each time a training pattern is presented to the ANN,the activation for each node,a pi ,is computed.After the output of the layer is computed the error term,d pi ,for each node is computed backwards through the network.This error term is the product of the error function,E ,and the derivative of the activation function and,hence,is a measure of the change in the network output produced by an incremental change in the node weight values.For the output layer nodes and for the case of the logistic-sigmoid activation,the error term is computed as:

d pi t pi Àa pi a pi 1Àa pi X

2 For a node in a hidden layer:

d pi a pi 1Àa pi

k d pk w kj X 3

In the latter expression,the k subscript indicates a summation over all nodes in the downstream layer (the layer in the direction of the output layer).The j subscript indicates the weight position in each node.Finally,the d and a terms for each node are used to compute an incremental change to each weight term via:

D w ij e d pi a pi mw ij old X 4 The term e is referred to as the learning rate and determines the size of the weight adjustments during each training iteration.The term m is called momentum factor.It is applied to the weight change used in the previous training iteration,w ij (old ).Both of these constant terms are speci®ed at the start of the training cycle and determine the speed and stability of the network.

3.Applications in energy systems

ANNs have been used by various researchers and by the author for modelling and predictions in the ®eld of energy engineering systems.This paper presents various such 2The j subscript refers to a summation of all nodes in the previous layer of nodes and the i subscript refers to the node position in the present layer S.A.Kalogirou /Energy Conversion &Management 40(1999)1073±1087

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applications in a thematic rather than a chronological or any other order.More details are given on the most recent work of the author in the area.

3.1.Modelling of a solar steam generator

ANNs have been applied to model various aspects of a solar steam generator.The system employs a parabolic trough collector,a¯ash vessel,a high pressure circulating pump and the associated pipework as shown in Fig.5.Some of the work done on this system is described here below:

3.1.1.Intercept factor

A comparative study of various methods employed in order to estimate the collector intercept factor is detailed by Kalogirou et al.[4].The intercept factor is de®ned as the ratio of the energy absorbed by the receiver to the energy incident on the concentrator aperture.From the intercept factor,the collector optical e ciency can be determined.This is a very important parameter in the determination of the overall e ectiveness of solar concentrating collectors. ANNs have been able to calculate the intercept factor with a di erence con®ned to less than 0.4%,as compared to the much more complex estimation of the energy deposition(EDEP) computer code.

3.1.2.Local concentration ratios

The radiation pro®le on the receiver of the collector has a``bell''type shape.This is represented in terms of the local concentration ratios at108intervals on the periphery of the receiver.It is very important to be able to measure this pro®le,because in this way,the

Fig.5.The steam generation system.collector optical e ciency can be determined.This measurement must be carried out at various incidence angles and also at normal incidence angle(y=08).This is usually very di cult to perform due to the size of the collector.ANNs have been used to learn the radiation pro®le from readings at angles that experiments could be performed and make prediction for the other angles including the normal incidence angle[5].The predictions of the ANN,as compared to the actual experimental values,have a maximum di erence of3.2%,which is considered satisfactory.

3.1.3.Starting-up the solar steam generating plant

ANNs have been used also to model the starting-up of the system stated above[6].It is very important to the designer of such systems to be able to make such predictions because the energy spent during starting-up in the morning has a signi®cant e ect on the system performance.It should be noted that this energy is lost due to the diurnal cycle of the sun and the resulting cooling of the system during the night.This problem is very di cult to handle with analytic methods,as the system operates under transient conditions.ANNs could predict the pro®le of the temperatures at various points of the system,as shown in Table1,to within 3.9%,which is considered adequate for design purposes.From the pro®les of two sets of¯ash vessel top and bottom temperatures versus time,the energy invested during the heat-up period can be easily estimated.

3.1.

4.Mean and monthly average steam production

An important parameter required for the design of such systems is the mean monthly average steam production of the system.A network was trained with performance values for a number of collector sizes ranging from3.5to2160m2and was able to make predictions both within and outside the training range[7].A neural network was able to predict the mean monthly average steam production of the system as shown in Fig.6with a maximum di erence con®ned to less than5.1%,as compared to simulated values,which is considered acceptable.The matching of the predicted and actual values in each case is excellent.In fact, the pairs of two lines,shown in Fig.6,are almost indistinguishable.

Table1

Statistical analysis of program predictions and resulting maximum percentage error

Temperature Correlation coe cient R2-value Maximum%error

Collector outlet0.9990.9987 3.9

Collector inlet 1.0000.9996 1.3

Flash vessel bottom 1.0000.9992 2.3

Flash vessel top 1.0000.9992 3.3

3.2.Heating,ventilating and air conditioning (HVAC)systems

3.2.1.Building thermal load ANNs were also used for the estimation of building heating loads using a minimum of input data [8].A number of cases were used to train a suitable network by using only some basic building areas and a di erentiation of the various elements according to their structure.It should be noted that no actual U -values were used as input parameters for the di erent building materials but indicative values (i.e.1for single wall,2for double wall etc.).When trained,the network was able to give predictions to within 9%as shown in Table 2.This apparently large error does not have any e ect on the actual radiator size selected for the particular room.This is so because the sizes of commercial radiators which are available vary in steps of 0.1m and 0.2m,which correspond to a di erence in heating load of about 220kcal/h and 450kcal/h,respectively.The errors of the test runs presented in Table 2are well within the above

values.

Fig.6.Comparison of predicted and actual (simulated)results for di erent collector areas.

Table 2Typical test results for the heating load estimation project

Room No

Actual load (kcal/h)ANN predicted load (kcal/h)%di erence 1454447À1.529179+4.9332073491+8.9436293724+2.6527012598À3.8621202107À0.6

Kreider and Wang[9]have applied ANNs to predict energy use in commercial buildings.In particular,the authors have applied the method as part of their work on the application of expert systems to HVAC diagnostics in commercial buildings.They have used ANNs to determine with good accuracy the energy use of chillers by using hourly averaged data collected from the system.

3.2.3.Energy consumption optimisation

Curtiss et al.[10]demonstrated how ANNs can be used to optimise the energy consumption in a commercial scale HVAC system.For this study,information from an actual system has been used to train a network in an attempt to optimise the energy consumption without sacri®cing comfort and by considering all the physical limitations of the system.Subsequently, the ANN based energy management system was successfully used to perform on-line set-point resets in an actual HVAC control system.The network was able to predict energy use better than the conventional regression techniques,and the energy management system was able to maintain comfort and use less energy than either a®xed set-point or basic temperature reset algorithm.

3.2.

4.Bus air conditioning

Kah et al.[11]applied a modular network using a multilayer perceptron to control the temperature of the air conditioning system of a bus.The input parameters used for training the network were the temperature,number of passengers and time of day.A®nal data fusion module was used for decision making to set the system to an optimum state of operation such that the passengers feel comfortable.The authors claimed that the system o ered fast learning with good accuracy.

3.2.5.Evaluation of building energy consumption

Kajl et al.[12]proposed a fuzzy-neural assistant which can®ll the gap between simpli®ed and detailed estimation methods of building energy consumption.The fuzzy-neural assistant allows the user to determine the impact of eleven building parameters on the annual and monthly energy consumption and demand.The neural network training and testing data set and fuzzy rules used by the system were based on simulation results of numerous o ce buildings carried out with the DOE-2software program.Comparisons presented showed that the fuzzy-neural assistant predictions are quite comparable with those obtained from DOE-2 simulations.It is claimed by the authors that the proposed method retains all the advantages of the simple steady state methods(degree-day and bin),and additionally,it gives certain advantages of the detailed dynamic methods,as for example,the interaction between the envelope and the HVAC systems of the building.

3.2.6.Model of room storage heater

Roberge et al.[13]used ANNs to model room storage heaters.The input data to the network were the immediate past brick temperature,the room temperature,the electric power input and the on/o activation function of the fan.The energy released and the current brick temperature were the neural network outputs.A dynamic model was developed by the authorsusing results obtained from tests performed in a calorimetric chamber.The model was veri®ed against the results obtained during®ve di erent charge±discharge test periods.The presented ANN model results are quite comparable(within5%)to the results obtained from the dynamic model.

3.3.Solar radiation

3.3.1.Determination of solar irradiance

Negnevitsky and Le[14]combined an expert system and an ANN for the evaluation of the thermal rating and temperature rise of overhead power lines.The ANN has been used to determine the hourly solar irradiance depending on astronomic and meteoroclimatic conditions.

3.4.Modelling and control in power generation systems

3.4.1.Incineration process

Muller and Keller[15]used ANNs to model the combustion process of incineration plants with the objective to optimise the reduction of toxic emissions.Waste incineration is a dynamic process with strong inherent non-linearities and large time lags.As outlined by the authors, analytic models fail due to the complexity of the process.A fully autonomous simulation of waste incineration using ANNs has been presented which simulates e ectively the process parameters for predictive control strategies.

3.4.2.Heating coil

Anderson et al.[16],used simulated performance values to train an ANN to predict the steady state output of a PI controller.The neural network was trained to minimise the n-step ahead error between the coil output and the set point and a reinforcement learning agent was trained to minimise the sum squared error over time.The result was an improved performance with respect to tracking the temperature set point of a simulated heating coil.

3.4.3.Thermal plant

Milanic and Karba[17]used ANNs for the predictive control of a thermal plant.The plant consisted of a heat exchanger through which steam from an electrically heated steam generator continuously circulated in contra¯ow to the water circuit.They found that ANN models are suitable for the control of the steam plant by using the steam¯ow as the control input,and that simple network structures are preferable to complex ones because on-line predictions of plant behaviour can be faster.

3.4.4.Turbulent combustion modelling

Christo et al.[18]applied ANNs successfully to model the chemical reactions in turbulent combustion simulations.Chemical reactions are highly non-linear functions of temperature and concentrations.Input data used for training the network are the mixture fraction and molar abundances of CO2,H,and H2O,whereas the output represents the change in composition of the reactive scalars,CO2,H,and H2O,over a certain reaction time.The network showed goodability in capturing the general behaviour of chemical reactions.Reasonable accuracy was obtained except for a few samples,which constituted less than10%of the sample space.

3.4.5.Analysis of power system harmonics

Keerthipala et al.[19]applied neural networks for the analysis of harmonic distortion.This is necessary in order to improve the quality of power distributed.The trained network was tested,and it was found that it was able to predict the magnitude and phase angle of each harmonic component to within5%.The network was also shown to be noise tolerant.

3.5.Forecasting and prediction

3.5.1.Load forecasting

Czernichow et al.[20]used a fully connected recurrent network for load forecasting.The learning database consisted of70,000patterns with high degree of diversity.The accuracy of the system was found to be at least as good,for one day ahead forecasting,as the complex model used at the utility and better for longer predictions.

3.5.2.Tari forecasting and energy management

Wezenbers and Dewe[21]applied ANNs to predict local power tari rates and energy use with the intent of cost-e ectively utilising electric power to heat the water in a domestic hot water cylinder.The data used for the training of the network were the tari rates,hot water demand(calculated every30mins),ambient temperature,humidity,day of the week,month of the year and special days(e.g.holidays).The objective of the method was to turn the heating element on only when the rates were low and hot water was needed in the next three-hour period.The authors claimed that the system could be applied to similar large-scale industrial applications.

3.5.3.Short-term electric power forecasting

Mandal et al.[22]applied neural networks for short term load forecasting in electric power systems.The inputs to the network consisted of the past load data only.No weather variables (temperature,humidity,etc.)were used.The output of the ANN was the next hour load forecast.The average error obtained for both the training and testing data sets was con®ned to less than2%.

3.5.

4.Power system load forecaster

Khotanzad et al.[23]used a recurrent neural network(RNN)load forecaster for hourly prediction of power system loads.The hours of the day were divided into four categories and a di erent set of load and temperature input variables were de®ned for the RNN of each category.The performance of the system was tested on one year of real data from two di erent electric utilities with excellent results.

3.5.5.Electrical load prediction in supermarkets

Datta and Tassou[24]used multi-layered perceptron(MLP)and radial basis function(RBF) networks for prediction of the electrical load in supermarkets.Electrical load prediction in

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half-hour time intervals is important in energy management of supermarkets as the maximum demand is charged on this time period.It is shown that the simple MLP network performed better than the RBF.The maximum error reported is4.6%in the®rst case and7.1%in the latter.In another paper[25]the authors presented a similar problem where a number of networks were compared,with the objective of identifying the important inputs to the network which will facilitate on-line prediction and thereby implement refrigeration and HVAC system diagnostics,process control,optimisation and energy management in retail stores.The network showed a superior performance compared to traditional multiple regression techniques.

3.6.Refrigeration

3.6.1.Frost prediction on evaporator coils

Datta et al.[26]employed an arti®cial neural network in order to model the amount of frost on the coil and propose a demand defrost method based on it which should overcome the disadvantages of other demand defrost approaches.The usually applied methods of timed defrost cause a number of unnecessary defrost cycles,and this reduces the energy e ciency of refrigeration systems(by consuming electrical energy)as well as the accuracy of temperature control of the refrigerated cases.From the results presented,it was proved that ANNs can be used to estimate the amount of frost formation on the coil in terms of the amount of condensate obtained after defrost,based on space temperature,relative humidity and hours of cooling.

4.Conclusions

From the above system descriptions,one can see that ANNs have been applied in a wide range of®elds for modelling and prediction in energy engineering systems.What is required for setting up such ANN systems is data that represents the past history and performance of the real system and a suitable selection of a neural network model.The selection of this model is done empirically and after testing various alternative solutions.The performance of the selected models is tested with the data of the past history and performance of the real system. Surely,the number of applications presented here is neither complete nor exhaustive but merely a sample of applications that demonstrate the usefulness of arti®cial neural networks. Arti®cial neural networks like all other approximation techniques have relative advantages and disadvantages.There are no rules as to when this particular technique is more or less suitable for an application.Based on the work presented here,it is believed that ANNs o er an alternative method which should not be underestimated.

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