coasting point optimisation for mass rail transit lines using artificial neural networks and genetic...

172

& T

www.ietdl.org

Published in IET Electric Power ApplicationsReceived on 7th September 2007Revised on 6th December 2007doi: 10.1049/iet-epa:20070381

ISSN 1751-8660

Coasting point optimisation for mass railtransit lines using artificial neural networksand genetic algorithmsS. Acıkbas1 M.T. Soylemez21Istanbul Ulasim AS (IUAS), Ferhatpasa Metro Tesisleri, 34200, Esenler, Istanbul, Turkey2Electrical and Electronics Faculty, Istanbul Technical University, , 34469, Maslak, Istanbul, TurkeyE-mail: [email protected]

Abstract: Energy consumption of a rail transit system depends on many parameters. One of the most effectivemethods of reducing energy consumption in a rail transit system is optimising the speed profile of the trains alongthe route. A new efficient method will be presented for the optimisation of the coasting points for trains in aglobal manner. The proposed approach includes realistic system modelling using multi-train, multi-linesimulation software and application of artificial neural networks (ANN) and genetic algorithms (GA). Thesimulation software used can model regenerative braking and train performance at low voltages. Using ANNand GA together, optimal coasting points for long line sections covering five stations and two lines areachieved. Simulation software is used for creating training and test data for the ANN. These data are used fortraining of the ANN. Trained ANNs are then used for estimating energy consumption and travel time for newsets of coasting points. Finally, the outputs of the ANN are optimised to find optimal train coasting points. Forthis purpose, a fitness function with target travel time, energy consumption and weighting factors isproposed. An interesting observation is that the use of ANN increases the speed of optimisation. Theproposed method is used for optimising coasting points for minimum energy consumption for a given traveltime on the first 5 km section of Istanbul Aksaray–Airport metro line, where trains operate every 150 s. Thesection covers five passenger stations, which means four coasting points for each line. It has beendemonstrated that an eight input ANNs can be trained with acceptable error margins for such a system.

1 IntroductionMass transit systems around the world serve to the peoplewith high-energy efficiency. Although, the energy efficiencyis high, the energy demand from a large rail transitnetwork might be one of the biggest within the city itserves for. Therefore optimising the energy efficiency ofsuch networks is very important.

Traction energy is used for moving train sets on the lineand the consumption depends on many parametersincluding the following:

† Line geometry; gradients, curves, number of passengerstations and their locations, speed restrictions etc.

he Institution of Engineering and Technology 2008

† Vehicle characteristics; control logic, acceleration, weight,motor, auxiliary power system etc.

† Traction power system; transformer substation (SS)number, locations, equipment types, feeding conductorfeatures, feeding scheme, voltage level etc.

† Operation conditions; frequency of train dispatching(headway time – HT), train configuration, dwell time etc.

Total consumed traction energy for a givenmass transit systemcan be reduced by changing some of these parameters. Some ofthe methods that can be used for this purpose are given below:

† Reducing energy loss by catenary system paralleling [1].

IET Electr. Power Appl., 2008, Vol. 2, No. 3, pp. 172–182doi: 10.1049/iet-epa:20070381

IETdoi:

www.ietdl.org

† Increasing regenerated energy usage rate [2].

† Revising operation pattern. Shorter trains with higherfrequency are expected to reduce energy consumption [2].

† Re-arranging speed limits on the line.

† ‘Energy-wise’ driving approach.

In an earlier work of the authors, it had been found thatparalleling of the catenary systems can save up to 5% oftotal traction energy consumption [1]. After this study, theproposal for paralleling of the Istanbul Aksaray–Havalimani Metro Line catenary systems was put into reality.

In another paper [2], it was showed that frequent operationnot only improves passenger convenience, but also increasesenergy efficiency. Therefore using shorter trains with lowerHT can be suggested for maximising energy efficiency, aswell as passenger convenience. The parameters affecting theregenerated energy usage rate were examined in that paper.

It has also been demonstrated that choosing a higher-voltage level for the power feeding configuration makes animportant contribution to the traction energy saving.1500 V DC voltage level for a heavy metro line can savearound 10% traction energy compared with 750 V DCvoltage level [3].

1.1 Energy-efficient driving

In normal operation, a train can be accelerating, cruising at anallowed maximum speed, coasting or braking for a station or aspeed restriction.

Trains run along the line according to a timetable.Timetables define the travelling time for every train fromevery station to station. Timetables always include someslack time for an unexpected time loss, which could becaused by faulty equipment, but mostly by passengers.Slack times and station dwell times are very important forproviding a punctual service. Delays disturb the punctualoperation as well as reducing energy efficiency byconsuming the slack times, which can be used in normaloperation conditions for energy efficient driving.

Electr. Power Appl., 2008, Vol. 2, No. 3, pp. 172–18210.1049/iet-epa:20070381

A report prepared for Istanbul Mass Rail Transit operator,Istanbul Ulasim AS (IUAS), showed that lower accelerationrates (imposed by vehicle computer) and station entrancespeed limits (imposed by the signalling system) onAksaray–Airport Metro line cause almost 3 min longer tripcycle time [4]. This extra time is almost 5% of the totalcycle time.

IUAS is planning to increase the station entrance speedlimits on the line from 40 to 50 km/h. Possibilities forincreasing the allowed maximum acceleration rate from 0.7to 1.0 m/s2 have also been investigated.

1.2 Coasting schemes

A typical speed profile for a train that is allowed to coast isshown in Fig. 1. It is possible to consider the speedingregime of the train considered in Fig. 1 in differentregions. The train accelerates to gain speed in regionA. After reaching a predefined speed called coasting startspeed, VC, the train starts coasting (Regions C1 and C2).However, it is usually required that trains do not startcoasting before a predefined distance, which is denoted asSCS (Region C1). It is also not desirable that the trainsslow down too much during coasting, so a re-motoringspeed, VRM, is defined. The train is therefore forced toaccelerate again in re-motoring regions RM1 and RM2.We remark that the train decelerates for a speed limit inregion D1, cruises at a speed limit in region CR anddecelerates to stop at a station in region D2.

Chang and Sim [5] showed in their studies that geneticalgorithm (GA) is a very powerful heuristic tool to findoptimum points of coasting. Wong and Ho [6–8] studiedboth classical direct search methods and heuristic indirectsearch methods for finding optimum coasting points. Theystate that coasting only at one location (that is disallowingre-motoring) gives best results for mass transit system cases,where stations are located much closer compared with otherrailways.

One of the latest optimal coasting point determinationstudies has been carried out by Bocharnikov et al. [9]. Theyproposed finding an optimum coasting point takingaccount of the balance between acceleration and braking

Figure 1 Possible speed profile of a train between two stations

173

& The Institution of Engineering and Technology 2008

174&

www.ietdl.org

rates. They also examined the regenerative braking energycase with an assumption of full line receptivity, whichmeans that all the regenerated energy is assumed to beconsumed by other trains. A common feature of all thesestudies is that they all consider a single train running on asingle line between two given stations.

Global optimisation of coasting parameters for a whole lineagainst trip cycle time is a daunting job, since anexponentially growing number of alternatives needs to bestudied as it has also been stated in the previous literature.Coasting point optimisation for multiple trains running onmultiple lines and multiple stations that cover a section of arealistic railway has been attempted for the first time in thispaper.

The authors propose the use of artificial neural networks(ANN) and GAs for this purpose. The proposed approachincludes realistic system modelling by using multi-train,multi-line simulation software, ANN and GA. Thesimulation software used can model regenerative brakingand performance at low voltages of trains. By using ANNand GA together, optimal coasting points for long-linesections covering many stations and two lines can beachieved.

The simulation software used in preparation of this paperis briefly described in the next section. Details of coastingpoint optimisation using ANN and GA will be describedin Section 3, then, optimisation of three passenger stationscase will be given in Section 4, which is followed byoptimisation of five passenger stations with two lines andmulti-trains case in Section 5. The last section summarisesthe conclusions.

2 DC fed rail system simulationsoftware: SimuXThe comparison studies for different energy efficiencyapproaches are done with a multi-line, multi-trainsimulator called SimuX [10, 11]. SimuX enables the usersto simulate DC fed rail systems in a user-friendlyenvironment. It takes the regenerative braking and under-voltage behaviour of the vehicles into consideration.

A traction power system simulation can be considered intwo parts: train movement simulation and solution of thepower network. Although some simulators isolate these twoparts, feedback of the power network solution is essential, ifthe performance limits of the system are to be properlyexamined as stated by Goodman et al. [12] and bySoylemez [13].

The simulator has been used in many major modificationprojects carried out for IUAS. It has also been used formany new line traction power system design works such asUskudar–Umraniye Metro, Sultanciftligi–Vezneciler–Topkapi

The Institution of Engineering and Technology 2008

Metro, Kirazli–Basaksehir–Olimpiyat Koyu Metro andlastly for Izmir Metro extension lines.

3 Coasting point optimisation byANN and GAsGA is a direct search method based on natural selection. Ittries to find the best values of variables, which minimisethe fitness function. To do this, the GA repeatedly changesa population of individual solutions. It eliminatesunsuitable solutions rapidly using natural selectiontechniques such as inheritance, crossover and mutation.These eliminations are done according to the value of afitness function. Finally, the population converges towardsa near global optimal solution [14].

The GA can be used in optimisation problems containingdiscontinuities and nonlinearities, which are not easily solvedby standard optimisation methods. GAs have been used inmany applications in mass rail transit systems for differentpurposes apart from coasting point optimisation. It hasbeen used to optimise train schedules for minimisingmaximum traction power demand by Chen et al. [15].Chuang et al. [16] used GA to find optimum inverter SSlocations for maximising regenerative braking energyrecuperation.

In all these studies, GAs are used together with asimulation tool. Carrying out simulations takes a longertime for realistic systems compared with simple systems. Itis stated in all existing studies that finding optimal coastingpoints for a complex system is an overwhelming job, evenfor GA. GA tool calls simulation software for a number of(population size � generation number) times duringoptimisation. This means that the simulation tool will becalled 10 000 times for a population size of 20 and 500generations. Hence, the required optimisation run time fora complex system would still be unacceptable even withexisting powerful CPUs.

Moreover, it is often required to redo the optimisation fordifferent target values and weights of parameters in multi-objective optimisation problems such as the onesconsidered in this paper. Therefore the problem ofcomputational complexity becomes more important, whenGAs are to be directly coupled to a simulation tool.

In this paper, the use of ANN instead of performingrepeated simulations is proposed to tackle this problem.Once ANNs are trained, they can produce outputs for anew set of inputs in only fractions of milliseconds. As aresult, the optimisation task is simplified significantly, andthe designer gains the ability to easily see the results ofoptimisation for varying parameters.

ANNs are composed of simple elements called neuronsimitating biological nervous systems. In fact, the output of


IETdoi

www.ietdl.org

ANN is determined largely by the connections between theseneurons. ANN can be trained to model complex functions.Training of ANN is done with training data sets. Neuralnetworks can be trained to solve nonlinear problems. Whenthe literature reviewed for ANN usage in mass rail transitpower system related studies, it was found that Gordonet al. [17] used ANN for estimation of low-voltageoccurrences on a traction power supply system. They statedthat the method was found to be successful and could beused to prevent sharp peaks in the power demand at SSs.

There are many parameters to be determined and decisionsto be taken for creating, working ANN such as network type,training function, number of layers, number of neurons in thelayers and the transfer function of each layer. In this study,feed forward back propagation type networks were trainedwith the reduced memory Levenberg–Marquardt trainingfunction. The networks had one hidden layer betweeninput and output layers.

Simulation software is used for creating training and testdata for ANN. In these simulations for the training tests,there was only one varying parameter: the coasting point.All the rest of the parameters related to the operation, suchas headway or dwell times or train weights, accepted asunchanged. Therefore it should be noted that the role ofsimulation and of ANN are different, and ANN cannotreplace a detailed simulator, which can produce results fornumerous parameters.

Train and network discontinuities such as regenerativebraking are handled within the simulation itself, and theireffects are already included in the training data sets, whichare produced by the simulator. Since ANNs are trainedusing these data sets the results automatically reflect suchdiscontinuities.

Trained ANNs are then used for estimating energyconsumption and travel time for each new set of coastingpoints. Finally, using outputs of ANN, a fitness functionwith a target travel time and energy consumption, andweighting factors is optimised with the help of GAs todetermine the optimum coasting points. The fitnessfunction used in the optimisation is given below.

f ¼ EwE

ETarget

þ TwT

TTarget

(1)

where ETarget, E, TTarget and T are targeted and achievedvalues of energy consumption per vehicle � kilometre inkilowatt hour and travel time in seconds, respectively. Here,wE and wT represent weighting factors for energy andtravel time. Note that the fitness function defined in (1)consists of two parts: energy and time. It is required tominimise the fitness function so that both energyconsumption and travel time are minimised around giventarget values, which are usually chosen after observing theresults of a flat-out simulation. The balance between the

Electr. Power Appl., 2008, Vol. 2, No. 3, pp. 172–182: 10.1049/iet-epa:20070381

energy and the travel time is arranged using the weightingfactors (wE and wT). It should be remarked that the lowerthe weighting the higher the importance, since the fitnessfunction is minimised.

Travel time has more priority compared with energy savingfrom customer satisfaction point of view. Consequently, wT

is chosen considerably lower than wE to obtain optimumsolutions around the targeted travel time. To allowcomparisons, the weights are taken as wE ¼ 90 andwT ¼ 10 for all the tests given in this paper. It is obviouslypossible to achieve different results for different values ofwE and wT. The values taken here are obtained bycommunicating with an operator company (Istanbul UlasimAS) and after a few trials to achieve a ‘good’ balancebetween the energy saving and travel time. The best valuesof the weights and the target values of the travel time andthe energy consumption may change for different tracks,operator companies or even times of the day. For example,target travel times should be smaller when there is a highdemand from the line. The designer in real life wouldprobably try changing such parameters before making adecision. It should be noted that doing such trials is veryeasy with the proposed method since simulations are notrequired in the optimisation phase. Once ANNs are trainedfor a line’s characteristic operation, they can be used withGA for different parameter values of the fitness function toproduce fast results. The effect of changing weights of thefitness function is considered to be out of the scope of thispaper and is not further dealt with here. Optimisation ofthe coasting points on a single line with three passengerstations is considered in the next section.

4 Three passenger stations caseThe case of three and more stations is complicated andrequires investigation of wider solution space combinations.The test line, which is given in Fig. 2, is 2 km in lengthand has three stations at 51, 1000 and 1950 m (mid-points). Station wait time (dwell time) is taken as 20 s.There is a speed limit of 50 km/h when a train is enteringand leaving the stations. The catenary system resistance is6.02 � 1025 V/m. There is one transformer SS feedingthe line, at 1000 m, with 820 V DC no-load voltage.

The train set consists of four vehicles each of which is 23 min length and has a maximum of 0.7 m/s2 acceleration and1.1 m/s2 deceleration rate. The total weight of a vehiclewith passengers is assumed to be 45.2 tons. The maximumtractive effort produced by one vehicle is 50.5 kN up to thebase speed of 10 m/s; however, it reduces linearly withvoltage under 700 V DC.

Line alignment is chosen as flat, that is, there is nogradient. Firstly, a flat-out (no coasting) run was simulatedand the travel time between the first and last station was(Tmin) found to be 166 s and the energy consumption forthis run (Emax) was calculated as 5.7 kWh/vehicle/km.

175


176

& T

www.ietdl.org

Figure 2 Line with three stations

These two values were used as a basis for comparison with thecoasting case results.

Two hundred random coasting start points were createdand simulated in SimuX. Coasting cannot start within thebraking areas for stations left outside for coasting start, sothe maximum locations are limited to 800 and 1750 m,respectively, for the first and second coasting start locations(X1 and X2). The train is not allowed to start coastingbefore reaching 50 km/h; that is Vc ¼ 50 km/h. There-motoring speed is chosen as VRM ¼ 1 km/h to producehigh fitness function costs (as the result of extendedjourney times) in the case of multiple coasting between twostations. Sample data are given in Table 1.

It took the simulation software to complete 200 differentthree-station cases approximately 110 s in a 1.86 GHz IntelCore Duo computer with 1 GB RAM.

4.1 ANN training

Two hundred data sets are used for training ANN. At first, atwo input two output neural network (see Fig. 3a) was testedfor training to predict the energy and time at the same time.However, training was not satisfactory (error level was .3%for many sets of test data) for this case even with multiplehidden layers and increased neuron numbers. Therefore itwas decided to use two different neural networks for energy(E) and travel time (T ). The two input, one output neuralnetwork with 15 neurons (2-15-1 ANN) shown in Fig. 3bis used for predicting energy, E. A similar neural network(with 32 neurons) is also used to predict travel time, T.

The performance of the ANN in Fig. 3b after 1000 epochswas very satisfactory. Trained ANN must be tested and theirresults must be validated with a second set of data, which arenot used in the training. To do thorough testing for this

Table 1 Sample data from 200 data sets

Sampleno.

X1, m X2, m E, kWh/vehicle/km

T, s

1 599.76 1404.70 3.0407 170.00

2 367.25 1467.55 3.1093 175.00

3 771.07 1514.42 2.9215 167.00

4 104.97 1508.01 2.9614 182.00

5 269.70 1009.67 2.8212 198.00


comparably simple case, the first coasting point is changedbetween 51 and 800 m with 15 m steps, and the secondcoasting point is changed between 1015 and 1750 m with15 m steps and the resulting 2550 different combinationsare simulated with SimuX. The results of these simulationswere compared with the results obtained from the trainedANN. Errors in output, which is the difference betweenenergy value for this test and validation data, are given inFig. 4a as a graph and in Fig. 4b as a distributionhistogram. It is seen from this figure that the maximumerror level is around 0.08 kWh, which is equal to 2% of theactual value. However, the majority of the errors areobserved to be below 1%. These values are considered to beacceptable from a practical point of view.

It should be remarked that training a 2-15-1 network doesnot give satisfactory results for estimating the travel time (T ).After a few trials, it has been found out that a 2-32-1 networkgives acceptable results (i.e. standard deviation in the errorbeing ,3% of the actual values) for this case.

The performance of the ANN depends on the number ofdata sets used for training and the number of the neurons inthe hidden layers. However, the details of such relations arethought to be out of this article’s scope and left for furtherstudies.

4.2 Optimisation with GA

Matlab GATool was used for finding the optimum coastingpoints with GA. To increase the speed of optimisation,restrictions on the coasting points, Xmin and Xmax, wereintroduced. These restrictions are necessary to omitlocations where the train is supposed to decelerate forstations or cannot reach 50 km/h. Values of the restrictionsare determined by looking at the velocity against locationprofile of a flat-out run. For this test case, they wereassigned as Xmin ¼ [300 1300] Xmax ¼ [800 1800]. That isX1 and X2 were chosen such that 300 , X1 , 800 and1300 , X2 , 1800.

Genetic Algorithm and Direct Search Toolbox 1.0.1(GATool) of the Matlab Version 7.0.0.19920 (R14) hasbeen used in this study. Only population number ischanged for the two cases considered in the paper. The restof the GATool parameters relating to cross-over fraction(¼0.8) and function (¼scattered), mutation function(¼Gaussian) and elite count (¼2) are left unchanged.


IETdoi:

www.ietdl.org

Figure 3 Input and output neural networks used for estimating time (T) and energy (E)

a 2-15-2 ANN for T and E estimationb 2-15-1 ANN for E estimation

Selecting TTarget ¼ 171 s, ETarget ¼ 5.0 kWh/vehicle/km,wT ¼ 10 and wE ¼ 90, a GA search was executed to findthe optimum coasting points for a travel time close to 171 s.The population size was set to 20, and the generationnumber was set to 500. This means that the GA calls thefitness function, which involves calculating the outputs ofthe ANN, 10 000 times. It should be noted that the largenumber of calls for the fitness function is not a problemsince ANNs are used. Otherwise, if ANNs were not used,the simulation software would have been linked directly tothe GA, and therefore 10 000 simulations would have beenrequired to be done. Considering the fact that making asimulation is computationally very expensive, it can beconcluded that using ANN in the optimisation stage hassubstantial computational advantages (see also next sectionfor a comparison).

For the given setup,X1 was found to be at 541 m, andX2 at1404 m from the first run of the GA. Since the GA starts withrandom values, it may find different solutions for a limitednumber of generations. Therefore each different setup (fordifferent target travel times) was optimised three times. Theresults for these optimisations are summarised in Table 2.

The coasting points found for different random startingvalues in Table 2 are very close to each other for a given


TTarget. This suggests that generation number of 500 ismore than sufficient to find near optimal solutions for thiscase. The GA with population size of 20 evolves through500 generations in ,3 min.

In the trials, many GA optimisation tests were carried outto understand the effect of population number andgeneration number on the accuracy of the optimisation. Itwas found that a GA with population size of 12 and 250generations or a GA with population size of 20 and150–200 generations produced almost identical results tothose using a population size of 20 and 500 generations(see Fig. 5). This means that if the GAs were calling thesimulation program directly, it would have been required toexecute around 3000–4000 simulations to obtain nearoptimum results. It must be remembered at this point thatonly 200 simulation test results were enough to train theANN. Nevertheless, both the number of generations andthe population sizes might need to be increased with agrowing number of variables.

Table 2 also demonstrates an important fact that the trainperformance at low voltage affects the coasting points;although the station distances are equal, the starting pointsfor coasting are found not to be equal in the first andsecond sections of the line.

Figure 4 Errors in output of ANN trained for

a E andb Its distribution histogram

177


178

&

www.ietdl.org

E and T in the first row of Table 3 are the energyconsumption per vehicle � kilometre and travel timesimulated by the trained ANN, respectively. DT is thetravel time increase compared with Tmin, and DE is theenergy saving attained compared with Emax. Both valuesare given in percentages. The train consumes 23.72% lessenergy if it is allowed to extend its run time by 3% of theflat-out travel time. The energy saving increases up to35.54% for a 6.6% rise in T.

The last row of Table 3 gives simulation results for energyconsumption (ESimuX) and travel time (TSimuX) for theobtained optimum coasting points. When these values arecompared with the ANN estimations, they can be said tobe almost identical. The maximum error of the ANNcompared with the simulator is ,1%. Velocity againstlocation plots for flat-out and other coasting regimes aregiven in Fig. 6.

It can be seen from Fig. 6a that the train cannot reach themaximum speed in the first section in the flat-out mode. Thisis because of reduced performance at lower voltages and lowacceleration rate. For the coasting cases; trains start coastingat the pre-set location found by GA. It should be notedthat the locations given in Fig. 6 are the middle points ofthe trains. Therefore the half-length of the train, 46 m, isdeducted from the given (optimum) locations. It needs tobe remarked that the same method described above wasapplied successfully for many other arrangements of threestations.

Table 2 X1 and X2 values for different TTarge

GA run TTarget ¼171 s

TTarget ¼174 s

TTarget ¼177 s

X1 X2 X1 X2 X1 X2

1 541 1404 431 1370 352 1359

2 546 1402 433 1368 350 1361

3 540 1405 428 1373 352 1359

Figure 5 Change of value of fitness function of bestindividual (solution) gene with number of generations( TTarget ¼ 171 s, population size: PS ¼ 20)


5 Five passenger stations, twolines, multi-train caseA realistic line is used for this case. A 5 km section coveringthe first five stations of the Aksaray–Airport Metro line inIstanbul has been chosen as the test case. Fig. 7 gives theline layout for this purpose. The line is fed by threetransformer SSs.

Main features of the line are given below:

† Trains: four cars (all motored), 92 m.

† Nominal voltage: 750 V DC, Catenary system

† Catenary resistance per kilometre: 44.4 mV

† Track resistance per km: 20.6 mV

† SS ratings: 2 � 2400 kVA

The stations (Aks, Emn, Ulu, Bay and Sag) are located at50, 950, 2006, 3445 and 4875 m. The line is continuouslyrising with changing gradient values. It can be seen fromFig. 8 that the maximum gradient value is 3.7% andminimum is 22.4%.

Four-car (the same vehicles described in the threepassenger stations case) train sets are sent at every 150 sfrom both ends for 20 min. The station wait time is fixedto 20 s. Trains run downhill on Line SA and uphill onLine AS.

The energy consumption (E) per vehicle � kilometre forthe flat-out run is determined as 3.067 kWh. Averagetravel time (T1) for SA trains is 398 s, and 424 s (T2) forAS trains. The reason for the difference between traveltimes is clear: AS trains climb uphill, they lose some partof their tractive effort to overcome gradient forces andaccelerate slowly and cannot reach the maximum speed,whereas SA trains easily pick up speed because of thegravitational forces acting on them positively, and reach the

Table 3 ANN and simulator results for optimum X1 and X2

TTarget ¼ 171 s TTarget ¼ 174 s TTarget ¼ 177 s

X1 ¼ 541,X2 ¼ 1404

X1 ¼ 431,X2 ¼ 1370

X1 ¼ 352,X2 ¼ 1359

E ¼ 4.35 E ¼ 3.94 E ¼ 3.674

T ¼ 171.00 T ¼ 173.98 T ¼ 176.95

DT ¼ 3.01 DT ¼ 4.81 DT ¼ 6.60

DE ¼ 23.72 DE ¼ 30.86 DE ¼ 35.54

ESimuX ¼ 4.33 ESimuX ¼ 3.939 ESimuX ¼ 3.676

TSimuX ¼ 171 s TSimuX ¼ 174 s TSimuX ¼ 178 s


IETdoi

www.ietdl.org

Figure 6 Velocity against location for

a Flat-outb TTarget ¼ 171 sc TTarget ¼ 174 sd TTarget ¼ 177 s cases

:

maximum speed. The total trip cycle time (T ), excludingterminal station wait time, is 822 s on average.

The same procedure as before is followed and the ANN istrained for E and T. It took the simulation software tocomplete 4000 different five-station cases approximately in10 h using a 1.86 GHz Intel Core Duo computer with1 GB RAM. Three thousand of these data sets are used totrain, and 1000 of them are used to test ANN.

A GA is then used to find the optimum coasting points fortwo different setups as given in the first row of Table 4. It

Figure 7 Five stations, two lines system


takes the GA to do such an optimisation (generationnumber 1000 and population size 30), around 5 min foreach setup. We observe that using GA directly with thesimulation tool would take approximately 150 h (insteadof 10.5 h including the time required for ANN) toproduce Table 4. Furthermore, in such a case, another75 h would be required (instead of 5 min) for eachdifferent target value and/or weight that is required to betried in the search for the most suitable solution. We also

Figure 8 Elevation of five-station system

179


180

& T

www.ietdl.org

Table 4 Five stations, two lines with multi-train optimisation case results

Setup for GA optimisation TTarget ¼ 835 s TTarget ¼ 860 s

wE ¼ 90; wT ¼ 10 wE ¼ 90; wT ¼ 10

Optimum coasting pointsfound by GA

606.4, 1740.4, 3017.7, 4200.9650.02, 1611.5, 3082.5, 4371.5

792.76, 1848.3, 3272.9, 4368.3650.02, 1507, 2984.1, 4350.1

ANN results for optimalcoasting points

E ¼ 2.67 E ¼ 2.50

T ¼ 835.00 T ¼ 860.20

DT ¼ 1.58 DT ¼ 4.65

DE ¼ 12.84 DE ¼ 18.25

SimuX results for optimalcoasting points

ESimuX ¼ 2.68 kWh/vehicle/km ESimuX ¼ 2.515 kWh/vehicle/km

TSimuX ¼ 834 s TSimuX ¼ 859 s

would like to remark that the simulation tool used in thisstudy is particularly fast. Using a slower simulation toolwould make the use of ANN in optimisation even moreadvantageous.

Results for two different TTarget setups are given inTable 4. The first row of Table 4 defines the setupparameters, and the second row gives the optimum coastingpoints for both lines. The first four values are for thedownhill Line SA, and the remaining four are for theuphill Line AS, shown in Fig. 7.

It can be seen from the third row of Table 4 that the ANNestimates that there will be 12.84% energy reduction for anincrease of 1.58% in trip cycle time. In the other column ofTable 4, E is by reduced 18.25% for a 4.65% increase in T,for which TTarget is 860 s.

Results from the ANN and simulations, which are given inthe last row of Table 4, are almost identical. ANN estimation


error for E is at most 0.008 kWh/vehicle/km and 1 s for Tfor both of setups.

It should be noted that the energy-saving potential seemsto be reduced drastically compared with the three-station caseconsidered in the previous section. For almost the same levelof time increase (4.81%), a 30.85% reduction in E is achievedfor the simple layout used in the three-station case, whereasonly a 18.25% reduction is possible for the more realisticfive-station case. It is possible to state that energy savingachieved in the five-station case is almost halved comparedwith the three-station case. One of the main reasons forthe lesser energy saving is the line alignment; the three-station case examined in the previous section is a flat line,whereas the five-station case has a hilly alignment. Thesecond reason is thought to be the regenerative brakingenergy; only a single train is used in the three-station case,whereas five-station case is a more realistic multi-train andmulti-line case. In this case, braking trains feed other trainson the line if the line is receptive. This feature reduces theenergy demand from utility, and thus there is less energy to

Figure 9 Velocity against location graphs for SA and AS trains with optimum coasting points for Ttarget ¼ 860 s


IETdoi

www.ietdl.org

be saved by coasting. In most of the cases, coasting results in areduction in braking time and a speed loss in the trains.Reducing the duration of the braking regime and the speedat which braking starts, in turn, results in a decrease in theregenerated energy. Therefore it is possible to claim thatcoasting scheme generally reduces regenerated brakingenergy. On the other hand, coasting schemes are usuallymeaningful in off-peak times, when the demand from theline is low. It is known that for such cases the receptivityrate is low, and hence, regenerated braking energy is not ofmuch use (unless energy saving equipment is used on boardor along the line). We remark once again that the proposedmethod in this paper handles such complicacies by using adetailed simulator and embedding the resulting data inANN. Nonetheless, the interaction of coasting andregenerative braking is a big issue in itself and deservesmore discussion in a separate paper.

Fig. 9 gives the velocity against location graphs of SA andAS trains for the TTarget ¼ 860 s case. When these graphs areexamined, it can be noticed that the GA finds very logicalresults, which could have been deduced by human experts.The trains are ordered to coast as soon as they are free ofthe 50 km/h speed limit restriction on Line SA wheregradient is mostly negative, whereas the trains on theopposite direction are ordered to coast as late as possible.Changing the 50 km/h speed restriction for coasting start(VC) would affect the results. Decision on the value of VCdepends on many parameters such as acceleration value ofthe vehicles and line characteristics. Reducing VC mayincrease the energy-saving potential especially in a line withsteep gradients.

6 ConclusionsCoasting schemes reduce energy consumption of mass railtransit systems. The coasting point values must be chosenoptimally taking into account of vehicle characteristics,operation conditions, power supply system configurationand line alignment features.

The paper gives a novel approach to the familiar subject ofcoast point optimisation for a DC metro line with respect togiven requirements of energy consumption and train run-times. The suggested optimisation also considers energy-saving potential over multiple lines, which also takesregenerative braking energy issue into account. GA is usedas the main technique to search for optimal starting pointof coasting, whereas ANNs are employed as an estimator ofthe energy consumption and travel time for a given set ofcoasting start points.

In this paper, optimisation studies were completed for athree-station with a single-train case and a two-line withfive stations and multi-train case using a simulator, ANNand GA. In these studies, it was shown that ANN can betrained with a small amount of data. ANN error levelscompared with simulator outputs are very satisfactory.

Electr. Power Appl., 2008, Vol. 2, No. 3, pp. 172–182: 10.1049/iet-epa:20070381

It was found for the given line configurations that theenergy-saving potential with coasting schemes for the sameamount of time increase is far less in the multi-train case,where trains regenerate and feed each other. In the three-station case, 4.81% increase in travel time with optimumcoasting points compared with the flat-out case creates30.85% energy saving, whereas in the five-station case4.65% increase in travel time with optimal coasting schemecreates only 18.25% energy saving.

Using ANN and GA in combination speeds upoptimisation, and bigger line segments with more stationscan also be optimised with this proposed method. A simpleway of application of the proposed method is using a driverinformation system (DIS). Aksaray–Airport LRT systemhas been recently equipped with such a system. It isplanned to find the optimum coasting points for differentheadways and enter these values into the DIS as time- andlocation-dependent values. The DIS will give a warning tothe driver for start of coast at these pre-defined locations.

It should be noted, however, that some operationalparameters are changing dynamically in real life. The trainweights and the station waiting times, for instance, affectthe energy consumption and the travel time. Authors areaware of staggering difficulties in finding optimum coastingpoints online for such operational variants. Nevertheless,the paper reveals the advantages of using ANN and itspossible application to optimisation of coasting points forthe case of multiple stations and multiple lines, and ithopefully paves the road for future research in this direction.

Future studies should include investigations towardsdiakoptics approach in the optimisation of coasting pointsfor very long lines. A transformer SS and/or a regenerativebraking train cannot feed a far away motoring train,because of possible existence of a closer SS and/or aregenerative braking train to the motoring train. Thismeans that an electrical sectioning can be done with minorerrors. This is an advantage for using diakoptics for verylong lines. However, different line geometries in differentsections of the line create a problem relating to thedistribution of the allowed travel time increase in total cycletime. Application possibility of diakoptics into the coastingpoint optimisation for very long lines is still in its earlyresearch stage. Further studies should be made into thedetermination of the minimum sufficient number oftraining data sets for ANN and the minimum generationnumber for GA.

7 AcknowledgmentsWe would like to thank Istanbul Ulasım A.S. for its help andsupport in supplying real-life data for the simulation process.We would also like to thank Istanbul MetropolitanMunicipality, which supports this research throughAcademic Research Assistance scheme. The authors are

181


182

&

www.ietdl.org

also indebted to all the reviewers of the paper for theirinvaluable comments and additions. The anonymousReviewer 2, in particular, is acknowledged for his/hermeticulous corrections.

8 References

[1] ACIKBAS VE S., SOYLEMEZ M.T.: ‘Catenary system parallelingand its effect on power consumption and regeneratedenergy recuperation’. 4th Int. Conf. Electrical andElectronics Engineering (ELECO 2005), Bursa, Turkey, 7–11December 2005

[2] ACIKBAS S., SOYLEMEZ M.T.: ‘Parameters affecting brakingenergy recuperation rate in DC rail transit’. ASME/IEEEJRC 2007, Colorado, USA, March 2007

[3] ACIKBAS S., SOYLEMEZ M.T.: ‘Energy loss comparisonbetween 750 VDC and 1500 VDC power supplysystems using rail power simulation’, Computers inRailways IX, (WIT Press, 2004), pp. 951–960,ISBN:1-85312-715-9

[4] Istanbul Ulasim Internal Report: ‘Aksaray – HavalimanıHafif Metro Hattı istasyon giris ve cıkıslarındaki hız sınırınınve arac maksimum ivme degerinin arttırılmasının etkileri(Effects of increasing vehicle acceleration rates andstation entrance speed limits in Aksaray–HavalimanıMetro line)’, 2006 (in Turkish)

[5] CHANG C.S., SIM S.S.: ‘Optimizing train movementsthrough coast control using genetic algorithms’, IEE Proc.Electr. Power Appl., 1997, 144, (1), pp. 65–73

[6] WONG K.K., HO T.K.: ‘Coast control of train movement withgenetic algorithm’. Evolutionary Computation Congress,2003, ISBN: 0-7803-7804-0, vol. 2, pp. 1280–1287

[7] WONG K.K., HO T.K.: ‘Coast control for mass rapid transitrailways with searching methods’, IEE Proc. Electr. PowerAppl., 2004, 151, (3), pp. 365–376


[8] WONG K.K., HO T.K.: ‘Dynamic coast control of trainmovement with genetic algorithm’, Int. J. Syst. Sci., 2004,35, (13–14), pp. 835–846

[9] BOCHARNIKOV Y.V., TOBIAS A.M., ROBERTS C., HILLMANSEN S.,GOODMAN C.J.: ‘Optimal driving strategy for traction energysaving on DC suburban railways’, IET Electr. Power Appl.,2007, 1, (5), pp. 675–682

[10] SOYLEMEZ M.T., ACIKBAS S.: ‘Multi-train simulation of DC railtraction power systems with regenerative braking’,Computers in Railways IX, (WIT Press, 2004),pp. 958–968, ISBN:1-85312-715-9

[11] Available at: www.simulatorx.com, accessed August2007

[12] GOODMAN C.J., SIU L.K., HO T.K.: ‘A review of simulationmodels for railway systems’. IEE Int. Conf. Developmentsin Mass Transit Systems, 1998, pp. 80–84

[13] SOYLEMEZ M.T.: ‘Effects of power line voltage drops onsimulation of DC fed railway systems’, Int. Railway Symp.,, (2006, 12) Ankara-Istanbul

[14] GOLDBERG D.E.: ‘Genetic algorithms insearch, optimization and machine learning’ (Addison-Wesley, 1989)

[15] CHEN J.F., LIN R.L., LIU Y.C.: ‘Optimization of an MRT trainschedule: reducing maximum traction power by usinggenetic algorithms’, IEEE Trans. Power Syst., 2005, 20, (3),pp. 1366–1372

[16] CHUANG H.J., CHEN C.S., LIN C.H., CHU S.H.: ‘Optimization ofinverter placement for mass rapid transit systemsusing genetic algorithm’. IEEE/PES Transmission andDistribution Conference and Exhibition: Asia and Pacific,Dalian, China, 2005

[17] GORDON S.P., LEHRER D.G.: ‘Coordinated train controland energy management control strategies’, IEEE 0-7803-4852-4, 1998


coasting point optimisation for mass rail transit lines using artificial neural networks and genetic...

Documents