Urban Transport XIX 201 Estmatng the benefts of energy-effcent tran drvng strateges: a model calbraton wth real data V. De Martns 1, M. Gallo 2 & L. D Acerno 1 1 Department of Cvl, Archtectural and Envronmental Engneerng, Federco II Unversty of Naples, Italy 2 Department of Engneerng, Unversty of Sanno (Benevento), Italy Abstract Ths paper descrbes the frst results of a research project where the man focus s to mplement a Decson Support System (DSS) to optmse energy consumpton of ral systems. In order to acheve ths objectve, we mplement an optmsaton module for the desgn of energy-effcent drvng strateges, n terms of speed profles, that requres a ralway smulaton model as a subroutne. Here we focus on the general framework of the optmsaton module and on the calbraton of the ralway smulaton model.all elaboratons are mplemented n a MatLab envronment, amng at defnng possble energy-effcent speed profles, n accordance wth energy-savng strateges, through optmsed speed profle parameters, n terms of acceleraton, target speed, deceleraton, coastng phase, and drvng behavour, represented by the jerk. The model s calbrated on real data recorded on a double track secton of a ralway lne n the cty of Naples (Italy). Intal results show that consumpton s very varable wth the speed profle and wth drver behavour, but the model s able to reproduce the average consumpton of each drvng strategy and should be able, wthn the DSS, to suggest the best drvng strateges for each ral secton. Keywords: energy-effcent drvng, ralway systems, optmsaton models. 1 Introducton Energy effcency n ralway systems s one of the emergng topcs n transportaton system research, snce ral travel s one of the best solutons for do:10.2495/ut130161
202 Urban Transport XIX satsfyng moblty needs, gven energy prces, urban growth and envronmental ssues. The optmsaton of the tran speed profle on a ral path s an mportant strategy for obtanng a good qualty of servce together wth meetng safety and energy effcency requrements (as shown by Dcembre and Rcc [1]). In ths specfc feld, ntal solutons can be obtaned by applyng Potryangn s prncple (see Hansen and Pachl [2]) to a smplfed and constraned explct formulaton of the problem where the decson varables are the swtchng ponts,.e. the tme nstants when the runnng regme changes. In recent years, n lght of the new technologes avalable, varous solutons have been proposed for dfferent problem scales, and, by analysng the network status, many optmsaton procedures have been descrbed, for example from Beugn and Maras [3], D Arano and Albrecht [4] and Lu and Golovtcher [5]. Moreover, Xuan [6] used perturbaton analyss to develop an alternatve set of necessary condtons for an optmal drvng strategy n some specfc track condtons, lke steep sectons, where tran drvng operaton usually dffers. Movng on to smulaton modellng of ralway networks, major mprovements were proposed by Mazzeo et al. [7] and Quagletta et al. [8] through the mplementaton of a smulaton framework for optmsng tran operatons n ralway systems, whle smulaton models were ntegrated wth travel demand estmaton by D Acerno et al. [9] n the case of ral falure management and by Gallo et al. [10] n the case of servce frequency optmsaton. Analyss of specfc ralway systems was performed by Lukaszewcz [11] on freght tran operatons and by Ke and Chen [12] on mass rapd transt plannng; the former analyses energy consumpton trends and ther relatonshp wth maxmum tracton rato, maxmum brakng rato, upper and lower restrctons of speed, and pre-brakng coastng dstance; the latter provdes a tool for block layout and runnng speed optmsaton n order to acheve the mnmum energy consumpton wth the maxmum tran capacty. Sgnfcant results can be found n Albrecht et al. [13] who analyse energy effcency n tran operatons and n Bocharnkov et al. [14], who study energy consumpton and ts relaton wth runnng tme. Gven the avalablty of contnuous nformaton systems, rather than the conventonal sgnallng systems that operate wth dscontnuous nformaton, tran operaton smulaton has been tackled wth dfferent technques: non-lnear programmng methods for energysavng control wth movng block sgnallng systems (see Gu et al. [15]); specfc optmal drvng models under fxed block and moble block condtons (Dng [16], Zhou et al. [17]); real tme control tools (Ba et al. [18]) that dynamcally nteract wth the nformaton systems n order to optmse tran operatons for dfferent track condtons and speed restrctons. 2 Problem descrpton and model formulaton The smulaton of complex systems, such as ralways, s one of the most wdely studed and appled methods to support the plannng and management of transportaton servces, accordng to a what f approach; the best soluton s found by smulatng dfferent scenaros and choosng the one whch best meets
Urban Transport XIX 203 the proposed requrements. The energy-effcent speed profle optmsaton procedure for tran operatons proposed n ths paper s based on an optmsaton loop that ntegrates two dfferent modules: an optmsaton module and a ralway smulaton model. The optmsaton module conssts of a constraned gradent descent optmsaton algorthm that allows a local mnmum of the objectve functon to be found (n our case total energy consumpton), coupled wth a speed profle defnton model that verfes the congruence of tme and dstance covered. The gradent descent algorthm conssts n evaluatng, ntally at a startng soluton, the value of the optmsaton functon and ts gradent. It then chooses a second soluton n the drecton ndcated by the gradent, that s accepted as the startng pont for the next teraton f the value of ts objectve functon s lower than the prevous one, and so on. Snce the gradent descent algorthm gves only a local optmal soluton, f the objectve functon s not convex, a mult-start method that consders several startng ponts can be useful for explorng the soluton set, generatng more local optma. The constrants are some condtons on mnmum and maxmum acceleraton, speed and deceleraton, that take account of passenger comfort, speed lmts and safety; other constrants concern the total travel tme avalable, n lght of the reserve tme, whch s the tme that preserves tmetable ntegrty, avodng delays. Moreover, on analysng energy-savng strateges, other condtons on the coastng phase, n terms of startng and endng ponts, have to be consdered. The ralway smulaton model estmates delays, runnng tme reserve, energy consumpton from the mechancal tracton requred for moton, and the tractve effort actng on the wheel, ncludng also brakng acton. The energy-savng optmsaton model can be formulated as follows: subject to: * * * * * a,v,d,t,t arg mn Ea,V,d,T,T max S acc C T fc V * fc mn (1) a V, max,d,t C,T fc max allow max < V V (2) J 1 s < a (3) a max J 1 s < d (4) * C * fc d max T T (5) dec * V T fc Tmax T (6) S S S Dst (7) cruse where: a s the target acceleraton (a* s ts optmal value); V max s the target speed (V* max s ts optmal value); d s the target deceleraton (d* s ts optmal value); s the startng tme of coastng (T* C s ts optmal value); T C coast dec C fc
204 Urban Transport XIX T fc s the endng tme of coastng (T* fc s ts optmal value); E(.) s the total mechancal energy spent; V mn s the mnmum target speed that respects the scheduled arrval tme, wthout coastng; V allow s the maxmum speed on the secton allowed by speed lmts; J 1s s the acceleraton at 1 second, obtaned multplyng the jerkng value by 1 second; a max s the maxmum acceleraton compatble wth passenger comfort; d max s the maxmum deceleraton compatble wth passenger comfort; T dec s the tme needed to decelerate from a certan speed; T max s the maxmum travel tme compatble wth tmetable respect (t s the sum of the mnmum runnng tme and the reserve tme); S acc s the space covered durng the acceleraton regme; S cruse s the space covered durng the crusng regme; S coast s the space covered durng the coastng regme; S dec s the space covered durng the deceleraton regme; Dst s the total dstance to cover. Constrants (2), (3) and (4) lmt the values of speed, acceleraton and deceleraton respectvely; constrant (5) mposes that the startng tme of coastng must be lower than ts endng tme; constrant (6) ensures that the sum of the coastng endng tme and the tme necessary for the tran to brake s lower than, or at least equal to, the maxmum travel tme avalable; constrant (7) ensures that the space covered by the dfferent regmes s equal to the real dstance to be covered. The jerk value represents the varaton n acceleraton durng the acceleraton phase, and can be optmsed as well as the other movng parameters. However, due to some consderatons on the sgnfcance of ths parameter, n ths paper we dd not consder t for calbraton and thus assumed a fxed value. The man reason s that acceleraton, speed and deceleraton can be consdered target parameters for the drver, whle the jerk s closer to the drver s behavour. That sad, t can be taken nto consderaton as a target value to optmze n the case of drverless systems. The objectve functon can be formulated consderng the mechancal energy requred to move a vehcle along a gven track wth gven moton parameters, usually expressed as the ntegral of the related mechancal power over tme. The mechancal power s ntended to be the power measured at wheel-ral nterface and can be computed as the product of the tractve effort F and speed V: E = P ( t) dt V F ( V, t) dt (8) mech tt where the tractve effort F s defned n T, that s travel tme on the track (or part of t) under consderaton, and can be computed by solvng the dfferental equaton derved from Newton s theory, also known as Moton General tt
Urban Transport XIX 205 Equaton, by a dscrete approach. Gven a generc temporal step of 1 second, the followng may be wrtten: F( V ) M f p v ( t t 1 ) R V,TRACK (9) where R(V, TRACK) can be computed by analysng the vehcle and lne resstances. More specfcally, t can be assumed that resstances can be computed wth the Sauthoff formula regardng specfc vehcle resstance: R 2 V K M K M V K V (10) 1 2 3 and wth the formula of Roeckl (10), as regards the lne resstances due to curves, and wth the weght force component (11), wth regard to resstances due to the slopes: Rr Rr 6.3 = M V 55 4.91 = M V 30 R r 300 m r < 300 m (11) M g (12) 1000 Fnally, R(V, TRACK) can be defned as the sum of (10), (11) and (12): R V,TRACK R(V ) Rr R (13) The acceleraton can be computed wth the followng formula: where: V a a ( t t ) 1 1 J ( t t 1 ) (14) a1 J ( t t 1) (a) a (15) a1 J ( t t 1) (b) consderng both the approach to the target value of acceleraton (a) and the approach to the target value of speed (b). The same consderatons can be supposed for the deceleraton values. The model of speed profle defnton allows energy-effcent results, as n the case of mplementaton of energy-savng strateges, through the defnton of the startng and endng ponts of the coastng phase, T C and T fc. For a gven coastng strategy, the speed profle model verfes the consstency of the profle n terms of travel tme avalable on a gven track and the dstance
206 Urban Transport XIX covered,.e. constrants (5), (6) and (7), usng the moton parameters generated by the optmsaton algorthm. In practce, the startng and endng ponts of the coastng regme are defned a pror by a coastng strategy; the drver has a planned coastng regme at a gven track pont. In ths paper we use the ASAP strategy (As Soon As Possble), whch means that the drver starts coastng as soon as he/she can; ths strategy assumes the exstence of a drvng assstance system. The model for speed profle defnton may already be suffcent for the computaton of the energy consumed. However, t does not contemplate the randomness of events on the ralway network, such as nteracton between vehcles. Therefore, from ths pont of vew, ts use could be evaluated wth the presence of drver assstance systems, drverless trans or smple networks such as urban and suburban lnes. Energy Optmzaton Module Ralway Smulaton nput: a,v max, T C, T F, d output: Energy, Delay, Runnng Reserve Tme Optmzaton Algorthm nput: Energy output: a,v max,d Speed profle defnton model: nput: a,v max,d output: Speed profle,t C, T F Yes Congruence on tme and space? No Fgure 1: The optmzaton loop. In fg. 1 the proposed optmzaton model s reported. Gven a set of target parameters of moton (a, V max, d), the model for defnng the speed profles calculates, at each one-second tme step, the relatve speed profle. The startng tme of the coastng phase, T C, s sought at each step wth a parallel algorthm that runs eqn (9), where tractve effort F(V ) s not appled and the varaton of speed and the related resstances at each step has to be computed. In other terms: RV,TRACK V (16) M f t t ) p ( 1
Urban Transport XIX 207 and the speed profle wth the coastng phase s accepted f the followng two condtons gven from constrants (6) and (7) are respected: 1. T + T dec (V(t)) = T max 2. Space covered at tme T max = space to be covered These condtons mean that the whole runnng tme reserve has to be used. The frst condton requres complance wth the maxmum tme avalable, T max, makng due allowance for the fact that at tme t we must add the tme T brake (V(t)) requred for brakng from speed V at tme t wth a deceleraton d. The second condton requres that the whole dstance n queston be covered. 3 Calbraton procedure Although the model descrbed n the prevous secton s a useful tool for evaluatng energy-effcent strateges, t cannot guarantee correct numercal results for each specfc case wthout calbraton. Calbratng a smulaton model conssts n fndng the values of some parameters such that the model wll reproduce wth accuracy the measurement observed from the real system. The calbraton procedure s generally performed by formulatng an optmsaton problem n whch the objectve functon to mnmse represents the devaton of the smulated measures from the observed ones. In ths paper, we need to calbrate the resstance parameters n order to better evaluate effectve power requrements and energy consumpton. The model representng the calbraton procedure can be formulated as follows: Kˆ obs sm arg mn f ( E, E( K) ) (17) KI where: Kˆ s the vector of the model parameters we wsh to calbrate,.e. resstance parameters; I s the doman of feasblty of the model parameters, that can eventually be constraned; f s the functon that measures the dstance between observed and smulated measures of performance; n ths paper we use the RMSE%; E obs and E(K) sm are, respectvely, the observed and smulated measures of system performance, where the smulated ones depend on the model parameters to calbrate. In ths paper we use energy consumpton as a measure of performance. 4 Numercal results The proposed model was mplemented on a MatLab platform usng the Optmzaton Toolbox, and some results were obtaned consderng prelmnary tests and data from the Italan natonal research project SFERE. Data refer to
208 Urban Transport XIX drect measurements on a ral track n the cty of Naples (Italy) on whch a vehcle was equpped wth a tran operaton montorng system; the data collected regard consumpton on the tracton unts and speed profle parameters. The ral track consdered s a double track of 1,700 m between two statons at the begnnng and end of the track wth no sgnallng systems. The track s at ground level, and there are no slopes and curves. Gven the characterstcs of the track, ths prelmnary test can be ntended as smlar to a generc staton-tostaton urban lne. Energy [KwH] 14 12 10 8 6 4 2 0 Energy consumpton 1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91 96 101 Tme [sec] RMSE% = 0.064345 K1 = 0.03728 K2 = 0.00149 K3 = 0.00069 Energy OBSERVED Energy SIMULATED Fgure 2: Energy consumpton observed and smulated for acceleraton and crusng regmes. Model calbraton was approached by fxng n our model the speed profle parameters observed, so that the model can reproduce the observed speed profles, and comparng the energy consumpton. For our purposes, only drvng regmes that requre energy consumpton,.e. acceleraton and crusng, were consdered. Fg. 2 reports the energy consumpton trend of the calbrated model compared wth the energy consumpton measured on board. In the fgure the value of RMSE% between the observed and smulated values s also reported, as are the calbrated values of eqn (10) that computes vehcle resstances. In our case, lne resstances were consdered rrelevant. The frst smulaton results are reported n fg. 3. The tme optmal speed profle s reached by assumng the maxmum allowable speed lmts on the track, n accordance wth the maxmum allowable acceleraton and maxmum allowable deceleraton n comfort condtons, assumng a jerk parameter of 0.3 m/s 3. In ths case the track was covered n 99 seconds. All parameters are summarzed n table 1. For the evaluaton of energy-effcent drvng strateges a runnng tme reserve of 17 s was consdered. The energy-savng speed profle was computed consderng a T max of 116 seconds, wth a coastng phase of 47 seconds The coastng phase begns 44
Urban Transport XIX 209 Fgure 3: Speed profle n tme optmal and energy-effcent drvng strateges wth the correspondng energy consumpton. Table 1: Optmsaton results. acc v dec T c T fc E (Kwh) T (s) Res. tme (s) Tme Optmal 1.2 24 1.2 12.42 99 Energy Savng 0.96 21.58 0.99 44 91 7.96 116 17 seconds after the tran starts runnng and t ends at second 91. The energy saved wth ths profle s around 4.45 KwH, that s about 36% less than the tme optmal speed profle energy consumpton. In ths case, as expected, optmsed speed profle parameters are qute dstant from the tme optmal ones and t s worth notng that, for a practcal applcaton
210 Urban Transport XIX of the optmsaton results, advanced drvng assstance systems or drverless systems are requred; n other cases drver s error should also be computed. 5 Concluson and future work Ths paper focused on an optmsaton model and ts calbraton, for mnmsng energy consumpton by defnng optmal speed profles. Intal results on a smple double track lne showed the model s ablty to defne the optmal energysavng speed profle for a gven runnng tme reserve and that the energy balance by adoptng energy-savng strateges can be consderable. Buldng on these frst results, future tests wll focus on three man aspects: ) more complex ralway networks for tests, ) mprovement n the optmsaton module for energy recovery applcatons, wth supercapactors both on board and at electrc substatons, and ) senstvty analyss on the optmzaton results consderng both energy savng and energy recovery strateges. Acknowledgement Partally supported under research project PON SFERE grant no. PON01_00595. References [1] Dcembre, A. and Rcc, S., Ralway traffc on hgh densty urban corrdors: capacty, sgnallng and tmetable. Journal of Ral Transport Plannng and Management, 1(2), pp. 59 68, 2011. [2] Hansen, I.A. and Pachl, J., Ralway tmetable and traffc: analyss, modellng, smulaton, Euralpress: Hamburg, Germany, 2008. [3] Beugn, J. and Maras, J., Smulaton-based evaluaton of dependablty and safety propertes of satellte technologes for ralway localzaton. Transportaton Research Part C, 22, pp. 42 57, 2012. [4] D Arano, A. and Albrecht, T., Runnng tme re-optmzaton durng realtme tmetable perturbatons. WIT Transactons on the Bult Envronment, 88, pp. 531 540, 2006. [5] Lu, R. and Golovtcher, I.M., Energy-effcent operaton of ral vehcles. Transportaton Research Part A, 37(10), pp. 917 932, 2003. [6] Xuan, V., Analyss of necessary condtons for the optmal control of a tran. Ph.D. thess, Unversty of South Australa, Adelade, Australa, 2006. [7] Mazzeo, A., Mazzocca, N., Nardone, R., D Acerno, L., Montella, B., Punzo, V., Quagletta, E., Lambert, I. and Marmo, P., An ntegrated approach for avalablty and QoS evaluaton n ralway systems. Lecture Notes n Computer Scence, 6894, pp. 171 184, 2011.
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