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Rail. Eng. Science (2021) 29(4):327–335 https://doi.org/10.1007/s40534-021-00245-y Optimal control and energy storage for DC electric train systems using evolutionary algorithms 1 2 2 • • Sam Nallaperuma David Fletcher Robert Harrison Received: 19 February 2021 / Revised: 23 June 2021 / Accepted: 24 June 2021 / Published online: 24 July 2021 The Author(s) 2021 Abstract Electrified railways are becoming a popular 1 Introduction transport medium and these consume a large amount of electrical energy. Environmental concerns demand reduc- Today with rising prices of energy and fossil fuels such as tion in energy use and peak power demand of railway gasoline, the demand for public transport has increased. systems. Furthermore, high transmission losses in DC With the adverse effects from global warming and railway systems make local storage of energy an increas- increasing prices of fossil fuels and decreasing amount of ingly attractive option. An optimisation framework based fuels, the use of green energy in transport have become on genetic algorithms is developed to optimise a DC crucial. Improving the transport sector has positive impact electric rail network in terms of a comprehensive set of on economic and social developments of many other sec- decision variables including storage size, charge/discharge tors depending on transport. To this end, numerous power limits, timetable and train driving style/trajectory to researches in the field of energy efficiency in rail transport maximise benefits of energy storage in reducing railway have been carried out [1–4]. However, none of the peak power and energy consumption. Experimental results approaches have investigated the effectiveness of opti- for the considered real-world networks show a reduction of mising the different aspects of train systems such as driver energy consumption in the range 15%–30% depending on profiles and battery storage simultaneously to obtain effi- the train driving style, and reduced power peaks. cient energy consumption. Another drawback of the current studies is that they mostly consider hypothetical simplified Keywords Autonomous control Intelligent transport networks that do not resemble the actual real-world railway systems Energy optimisation DC railway systems systems. To improve on this, we employ a comprehensive Energy regeneration train model that resembles the complex real-world system and validate against real-world data. We propose optimised network parameters for an existing real-world network. The objective of this study is to optimise train control and energy storage to reduce energy consumption. Since a railway transportation system is a large nonlinear complex system [5], achieving optimal driving profiles and battery storage for the entire network is a difficult task. From a computational perspective, the train trajectory optimisation problem of railway network under various constraints is a non-convex and highly nonlinear optimisation problem, which makes the challenge of finding an optimum train & Sam Nallaperuma trajectory alone is hard and it has been shown that the snn26@cam.ac.uk problem is NP-complete [6]. University of Cambridge, Cambridge, UK Given the complex and highly nonlinear nature of the problem, exact techniques have failed to optimise train University of Sheffield, Sheffield, UK 123 Braking Power Power Coasting 328 S. Nallaperuma et al. or a local storage at a substation if available). Traction trajectories. Meta-heuristic approaches such as genetic algorithms (GA) [7] and ant colony optimisation [8] have force is zero in coasting phase, where the train does not consume any power. In the braking phase, the train gen- shown great potential in the applicability on complex real- world problems in engineering domains given their ability erates power through doing work against the train move- ment. This energy can be used to feed back to the power to work on highly nonlinear problems with limited infor- mation. In the literature of train systems, genetic algo- source (grid or a local storage/battery). Figure 1 describes these phases of train motion and interactions with the rithms are applied to search the optimal train speed trajectory under the journey time and maximum operating power source. The work by Douglas et al. [2] considers single train speed constraints in some preliminary studies in railway simulation and multiple train simulation. The trains are run networks [9–13]. These studies have only considered simplified versions of real-world systems and single or few on predetermined routes, and each route is considered to have the four basic stages accelerating, cruising, coasting parameters to optimise, resulting their proposed models rather inapplicable to actual railway systems. In this study, and braking sequentially. This model does not incorporate storing the braking energy. The work by Sandidzadeh et al a GA-based approach is proposed for comprehensive real- world network optimisation based on actual data and sys- [4] takes a similar approach to model the power dynamics of a train network. In addition to the approach by Douglas tem parameters. With the significant improvements of 15%–30% in energy consumption on the tested UK Mer- et al. [2], this work considers the internal carriages of the train within the model. The work by Gavin et al. [3] studies seyrail network, our approach shows potential to be the UK Merseyrail system as a case study to build their deployed on other real-world railway networks. The rest of the paper is organised as follows. Section 2 models. They have experimented with the test train drives to validate their models. The validation results show that describes the foundations of the energy modelling and optimisation of trains, followed by a description of the their power consumption predictions closely resemble the actual train power consumption. However, these models do electrical and mechanical model employed in this work. Section 3 presents the optimisation framework followed by not consider the battery storage parameters and regenera- tive capabilities were not enabled during the experiments. experimental results in Sect. 4, and finally, Sect. 5 presents concluding remarks. The study by Ghaviha et al. [1] shows that by optimising driver profiles, energy consumption can be minimised. They use a dynamic programming algorithm for this. Similarly, the work by Amrani et al. [9] and by Wei 2 Preliminaries et al. [12] employed genetic algorithms to optimise driver profiles on simple networks. Their results show improve- Dynamics of train motion have been analysed in the con- ments in energy consumption provided from simulations text of energy efficiency. To analyse these models, the basic physical formulations regarding the motion and only. In contrast, the work by Zhao [13], the train trajec- tory optimisation algorithm has been developed and a field power have been used. Basically, the motion of a train depends on the traction, resistance and gradient forces. The test of the obtained trajectory has been carried out on a metro line. The field test results are very similar to the complexity of these models differs depending on the number of trains, substations, and the number of internal simulation results, proving that the developed train kine- matics model is effective and accurate. cars of a train. In general, a train journey between two locations consists of four action phases, namely accelera- In these works, however, they have considered battery storage parameters to be fixed and only driver profile tion, cruising, coasting, and braking. However, in real life, depending on the gradients of the route, speed limits and dynamic factors as time table changes, the actual stages of Power Substation the journey can be changed. The general physics formula to Battery determine the traction force is: Grid Ma ¼ T R Mg sin H; ð1Þ Cruising where M is the mass of the train, a acceleration, T traction force, R resistance force, g is the gravity and H is the gradient angle. The positive a represents the acceleration during the acceleration phase. a becomes zero during the cruising phase hence the traction force is equal to the Time summation of the resistance and gradient forces. In these two phases, train draws power from the power source (grid Fig. 1 Phases of train motion and interactions between power sources Rail. Eng. Science (2021) 29(4):327–335 Power Acceleration Speed Optimal control and energy storage for DC electric train systems using evolutionary algorithms 329 parameters were optimised. Moreover, in the current lit- regeneration, trains behave as voltage sources with internal erature, the feedback aspect of the energy has not been resistance. It is assumed that parallel tracks (with trains considered. When considering energy saving, using the running in opposite directions) are electrically bonded, so a regenerative energy from the braking is a very important section can be represented as in Fig. 2 where four trains are aspect. It is also observed that the validation of energy present. The electrical section network was pre-solved models against real-world data has not been carried out by using Kirchhoff’s laws. Specific cases are realised by set- majority of the exiting work. In order to overcome the ting the internal resistance of unneeded components to a limitations in the current literature, this study considers a high value and validated against the Qucs circuit simulator novel model incorporating regenerative energy, both driver [17]. Energy storage is located in sub-stations, on the grid- profile and battery storage parameters and that is validated side of the sub-station internal resistance. Energy stor- against real-world data from the UK railway network. age/battery parameters ignore specific technology and focus on capacity, charge/discharge rates, and efficiency. 2.1 A real-world inspired train power model For a comprehensive description of the model formulation, we refer the interested reader to Fletcher et al. [14]. For the optimisation approach in this paper, we employ the real-world inspired railway network model presented in 2.2 Model validation with real-world data Fletcher et al. [14]. For completeness purposes, we present a brief description of the model formulation and validation Validation uses data for the Merseyrail Wirral line in the in the following. UK. Gradients and line speeds are taken from Network The rail network topology is defined by nodes (stations, Rail [18] and on-board and sub-station energy use from junctions, electrical substations, neutral sections) con- [3, 19]. Train location monitoring using GPS tracking was nected by lines with properties of length, end nodes, line- used for comparison with simulator predictions. Predicted speed limit and gradient, the latter two being functions of movement between a specified set of stations, simulated on position. Routes are defined by the sequence of lines over the basis of flat-out running, with the corresponding GPS which a train will run (direction, target traverse time for trajectory. The experimental results showed that there is a each line), nodes at which to stop, minimum dwell time and very close agreement with model predictions and actual departure time relative to the route start. A timetable de- train run. For a comprehensive description of the model fines which train runs on each route, and the time the train validation, we refer the interested reader to [14]. will depart. DC rail system voltages typically imply high current flows, needing short electrical sections to reduce losses. Substations are represented using open-circuit 3 Optimisation of energy consumption voltage and internal resistance [15, 16]. Trains drawing power are represented as resistances with their locations This section presents the optimisation of the energy con- determining supply transmission length. Conducting and sumption for a train network based on the electrical model return rails have a resistance per metre, giving an in-circuit described in the previous section. The objective of the resistance and energy loss that varies with train position. In optimisation process is to minimise the energy drawn from 2 R R R R 4 9 11 R =0.02 Ω 3 R =0.02 Ω 1 5 R R R 7 8 R 6 10 - - + + + Loop 1 Loop 2 Loop 3 Loop 4 Loop 5 - - I - I I I I 1 2 3 - 4 5 Track resistance 0.04061 Ω/km Fig. 2 Electrical model for a sample case of two substations and two trains drawing power from the grid and two trains regenerating. The local power storages are located at the substations Rail. Eng. Science (2021) 29(4):327–335 Substation 1 V =750 V Train 1 V =0 V Train 2 V =800 V Train 3 V =0 V Train 4 V =800 V Substation 2 V =750 V 2 330 S. Nallaperuma et al. outside sources. We employ genetic algorithms to imple- imposed by the government based on the location of the ment this optimisation process. train, and a maximum allowed current drawn from a sub- station at a time step of 1000 A (a constraint on power 3.1 Variables spikes). We consider solutions violating these constraints as infeasible. The variables for the optimisation are the driver profile parameters of the trains representing acceleration and 3.4 Evolutionary optimisation framework braking for the trains in the network and the energy storage parameters. The driver profile parameters represent the The class of popular heuristic optimisation algorithms control parameters for each time step for each train. Con- namely genetic algorithms (GA) are used in this study to trol parameters can vary between the maximum allowable optimise train control and substation energy storage. acceleration or brake and this is a feature of a train. We Owing to their general purpose appeal and ease of use, model this by a real-valued control parameter in the range evolutionary algorithms have gained a wide popularity in of 1to ?1 where negative values represent brake and the past decades [20, 7, 21]. In essence, evolutionary algo- positive values acceleration. The feasible values for the rithms mimic the natural evolution process to solve real- energy storage parameters are bounded by the standard world problems. The optimisation framework is built using limits in practice. The considered storage parameters are the genetic algorithm library ParadiseEO [22], which is the maximum storage of battery, the maximum regenera- available under an open source licence granting the rights tive power supplied to the grid, the battery storage upper to access the source code, to copy, modify and redistribute limit, the storage lower limit, the maximum grid charge the code. Algorithm 1 outlines the evolutionary optimisa- power, the maximum grid discharge power, the maximum tion process in general. The algorithm is initialised with a regenerative charge power, the maximum regenerative population, P, consisting of l instances which represent discharge power and the maximum grid supply power of different driver profiles and energy storage parameters the battery. (within a pre-determined range or selection). In each iter- Generally, an optimisation process must consider ation, k l offspring are produced by selecting a subset, C, objectives and constraints. In this project, the broader of the population, P, consisting k parents and applying objective is to understand what enables more energy effi- genetic operators to the selected individuals. Based on the cient driving and storage, whereby we can decrease the fitness a subset, D,of l individuals survives from the cost, and improve adherence to timetable and speed limits. population, P, for the next iteration and the process con- While these objectives are well defined, the constraints on tinues until a desired termination criteria is met. We can their achievement are complex. specify a certain number of generations as the termination condition or else until a certain fitness level is reached. 3.2 Objectives Minimising energy consumption is the objective. The Algorithm 1 (µ + λ)-EA : Evolutionary algorithm problem can be formulated as follows: Initialize the population P with µ GA individuals, i.e. a spread of potential driver profile and battery parameters. Find X ¼½x ; x ; ...; x ; ð2aÞ 1 2 n Select C ⊆ P where |C | = λ. For each I ,I ∈ C , produce offspring I I by crossover m 1 2 1 2 Minimise C ðXÞ¼ R E ; ð2bÞ e v j¼0 j and mutation. Add offspring’s to P . Fitness evaluation of all I ∈ P where X is a vector of variables containing the driver and Select D ⊆ P where |D | = µ . P := D battery parameters for whole network, n is the number of Repeat step 2 to 5 until termination criterion is reached. parameters, m is the number of trains in the network, C ðXÞ represents energy consumption within the network, fv ; v ; .. .; v g represents the set of trains within the net- 1 2 m 3.4.1 Initialisation of population work and E represents the net energy consumption for train v , respectively. A GA individual in the population represents a potential train control/driver profile and battery storage setting (to- 3.3 Constraints gether we call them railway parameters) instance. Such an individual is represented by a real-valued vector, where The constraints are imposed by the timetable, speed limits each GA gene [7] represents a real valued railway and the power spikes. We consider a maximum allowed parameter described in Sect. 3.1; i.e. this numerically delay of 0, speed limits as per the actual speed limit values Rail. Eng. Science (2021) 29(4):327–335 Optimal control and energy storage for DC electric train systems using evolutionary algorithms 331 captures the full description of a particular instance of the 3.4.3 Genetic operators railway parameter setting. Initialisation of the optimisation can start with a population of randomly selected combi- Genetic operators are applied to the selected parents to nations of railway parameters (chosen within realistic create new offspring from them. These operators are inspired by the biological evolutionary operators of bounds), or using heuristics. In our case we use a hybrid approach, initialising the search using (i) existing standard ‘‘crossover’’ and ‘‘mutation’’. Crossover is the process by which the next generation inherits genes from multiple values, and (ii) a proportion of randomly generated cases (i.e. combinations of higher capacity batteries or acceler- (typically two) parents to create new offspring. Once two parents are selected, we choose the value for a given ation and brake at the same time which are feasible but do not exist at present). This hybrid approach aims to give a control table parameter (a ‘‘gene’’) uniformly at random good starting point to the simulation without limiting the from either parent, a process of ‘‘uniform crossover’’. The diversity in the population. In this way, we can preserve mutation process makes a small random change to this diversity and still bias the process towards likely good newly created offspring. solutions. The mutation operator is designed to apply a small random perturbation to a chosen railway parameter. At each generation, a set of control parameters are chosen for 3.4.2 Selection mutation based on a probability distribution. The aim is to form new railway parameter settings Each step of the genetic simulation process requires the existing railway parameters to be taken in pairs as ‘‘par- which differ slightly from the current, thereby allowing a ents’’ from which the next generation of railway parame- wide range of combinations to be explored in a rigorous ters are created. We employ random selection to choose way, but without the computational overhead of attempting which railway parameters to combine as parents at each to simulate every combination of every parameter. Each step, these having previously through the survivor selection generation is tested (‘‘fitness test’’, see Sect. 3.4.4) to see stage of the previous generation ensuring only the best- whether its members are better or worse than the pro- ceeding, with the best going forward in a repeat of the performing are considered. This approach is simply a way to achieve mixing of the different railway parameters process. which may be combined, working towards finding espe- cially high-performing combinations. 3.4.4 Fitness function Based on the fitness value and constraint violations, feasible individuals are sorted and the best, k individuals The cost function in Eq. (2) introduced at the beginning of this section serves as the fitness function in the GA. The are selected for next generation as parents. basic architecture of the optimiser and train simulation model interaction is as shown in Fig. 3. Evolutionary optimisation algorithm Railway network Optimiser generated control simulator and battery parameter setting inputs Energy consumption outputs from railway network simulation Optimised railway network parameter values Fig. 3 Block diagram of the optimisation process Rail. Eng. Science (2021) 29(4):327–335 332 S. Nallaperuma et al. 4 Experimental results 4.1 Experimental set-up Experiments are conducted to find an optimal control strategy and storage settings for a rail network to achieve minimum energy consumption. The hyper-parameter set- ting for the GA includes a population size of 20 and crossover rate of 80%. The mutation rate is kept higher (of Expert 10%) at the beginning of the optimization process to help Optimised the exploration of the search space and it is gradually decreased (of 0.1%) to support exploitation when the pro- cess becomes closing to convergence. The experiments are based on two real-world scenarios on Merseyrail network in the UK with firstly, a simpler 0 1000 2000 3000 case of three trains running on a specified route and sec- ondly, all trains in the network running during a busy time Position (m) of the day. In both cases trains are set to run following the Fig. 5 Speed profile for a train taking the route from A to B based on actual time table and actual routes. expert and optimised parameters For benchmarking purposes, we run simulations based on an expert control strategy as well. The expert control processor, 15.5 GB memory and a GeForce GTX 1050 Ti/ strategies for each train are generated manually based on PCIe/SSE2. the physical laws of motion and train physics, and by adhering to the system constraints. The idea is to mimic 4.2 Fitness over generations human expert behaviour. The respective speed profiles generated by expert control strategy for the first experiment Figure 6 describes the fitness variation over generations. are shown in red in Figs. 4 and 5. The initial railway The fitness criteria represents energy consumption as parameter setting for the optimisation process is based on described in Sect. 3.4.4. The optimised speed profiles for this expert strategy. The respective parameters are as the trains are shown in blue in Figs. 5 and 6. It is observed explained in Sect. 3.1. that the optimal speed profiles have slightly lower speeds The experiments were run on a linux ubuntu 17.04 64 bit than the initial expert strategy (shown in red). It can be PC with Intel Core i7-7700HQ CPU @ 2.80GHz x 8 understood that with lower speed, the probability of having speed limit violations and power spikes are less. Never- theless, with the delay constraint, it is guaranteed that no delays (delays with respect to the train time table) are associated with the optimal speed profiles. The respective power profile for all the substations is shown in Fig. 7. A total energy consumption reduction of around 15% can be evident in this power profile. 4.3 Relative importance of driver profiles Expert versus energy storage variables Optimised We conduct further experimentation to study the relative importance of the variables representing railway parame- ters. The variables of this optimisation process are cate- gorised to two main categories: the variables determining the driver profile and the variables determining the battery 0 2000 4000 6000 storage. In this experiment we optimise each category while keeping the variables of the other category fixed. The Position (m) results for optimising driver profile and battery storage are Fig. 4 Minimisation of objective value (energy consumption) over shown in Fig. 8. The optimisation of the battery parameters the generations during the optimisation process Rail. Eng. Science (2021) 29(4):327–335 −1 Speed (ms ) -1 Speed (ms ) Optimal control and energy storage for DC electric train systems using evolutionary algorithms 333 Battery Driver profile 0 100 200 300 400 500 Generation 0 100 200 300 400 500 Generation Fig. 8 Minimisation of objective value (energy consumption) over the generations during the optimisation process for optimising the Fig. 6 Speed profile for a train taking the route from A to B based on driver profile parameters and the battery storage parameters only the expert and the optimised parameters the UK. We run the GA to optimise driver profiles and battery parameters for the Merseyrail network during a busy time. The constraints are considered as hard con- Expert straints, meaning speed limit violations, spikes and delays 1 Optimised do not occur during this optimal setting. Figure 9 describes the energy consumption reduction over the algorithm run and it is observed that optimised driver profiles and battery storage have reduced the energy consumption by 25%. Figure 10 demonstrates the respective total power con- sumption for the expert (in red) and optimised (blue) parameter settings. The respective expert and optimised − 1 − 2 1,543,902,900 1,543,903,200 1,543,903,500 1,543,903,800 1,543,902,600 Time (s) Fig. 7 Power profile for the network describing the total power drawn from the grid for the expert and the optimised parameter settings achieved slightly better fitness (lower energy consumption) within 500 generations than the optimisation of the driver profile parameters. When we are provided with a limited budget and costs associated with re-configuring parame- ters, higher important parameters can be prioritised accordingly. 4.4 Real-world scenario on Merseyrail peak hours 0 250 500 750 1000 Generation We further extend our experiments for a more complex Fig. 9 Minimisation of energy consumption over the generations real-world case. This is the complete Merseyrail network in during the optimisation process for Merseyrail network Rail. Eng. Science (2021) 29(4):327–335 Power (MW) Energy consumption (MJ) Energy consumption (MJ) Energy consumption (MJ) 334 S. Nallaperuma et al. Expert Expert Optimised Optimised -1 1,543,644,200 1,543,643,400 1,543,643,800 1,543,643,600 1,543,644,000 0 2000 4000 6000 8000 Time (s) Position (m) Fig. 10 Power profile for the Merseyrail network describing the total Fig. 11 Speed profile for a train taking the route from Birkhead North power drawn from the grid for the expert and the optimised parameter to Hoylake based on the expert and the optimised parameters settings Expert Table 1 Initial and optimised values for battery parameters for a Optimised electrical substation Parameter Initial Optimised (MW) (MW) Max storage of battery 180 267.63 Max regenative power to grid 0.75 0.78 Storage upper limit 162 150.37 Storage lower limit 90 78.89 Max grid charge power 144 133.20 Max grid discharge power 144 159.21 Max regenative charge power 153 142.02 Max regenative discharge power 117 91.17 Max grid supply power 0.75 0.79 0 5000 10,000 Position (m) battery storage parameter values are presented in Table 1. Fig. 12 Speed profile for a train taking the route from Hoylake to Figures 11 and 12 present the respective speed profiles for James Street based on the expert and the optimised parameters two routes namely Birkhead north to Hoylake and Hoylake to James Street. In both cases, it is observed that the 5 Conclusion and future work optimised speed profiles yield to lower speeds and less energy consumption. Nevertheless, these profiles adhere to Energy optimisation for a highly complex nonlinear real- the timetables as considered within the optimisation world DC electric railway system is presented in this work. process. A comprehensive set of parameters are optimised simul- taneously covering the driver profile and the battery storage settings using evolutionary algorithms. Optimised results show a 15%–30% reduction in total power consumption for two different scenarios in the UK Merseyrail network. Relative importance of different railway parameters are Rail. Eng. Science (2021) 29(4):327–335 Power (MW) −1 −1 Speed (ms ) Speed (ms ) Optimal control and energy storage for DC electric train systems using evolutionary algorithms 335 9. Amrani A, Hamida AB, Liu T, Langlois O (2018) Train speed studied where battery parameter optimisation results in profiles optimization using a genetic algorithm based on a ran- slightly higher reduction in energy consumption than driver dom-forest model to estimate energy consumption. In: Transport profile parameter optimisation. Future work will concen- Research Arena (TRA) 2018, Vienne, Austria. https://hal. trate on extending the experiments to different subsets of archives-ouvertes.fr/hal-01767006/document 10. 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Wei L, Qunzhan L, Bing T (May 2009) Energy saving train long as you give appropriate credit to the original author(s) and the control for urban railway train with multi-population genetic source, provide a link to the Creative Commons licence, and indicate algorithm. In: 2009 International Forum on Information Tech- if changes were made. The images or other third party material in this nology and Applications, Chengdu, Vol. 2, pp. 58–62 article are included in the article’s Creative Commons licence, unless 13. Zhao N (2017) Field test of train trajectory optimisation on a indicated otherwise in a credit line to the material. If material is not metro line. IET Intell Transp Syst 11(5):273–281 included in the article’s Creative Commons licence and your intended 14. 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Railway Engineering Science – Springer Journals
Published: Dec 1, 2021
Keywords: Autonomous control; Intelligent transport systems; Energy optimisation; DC railway systems; Energy regeneration
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