Modeling and Simulation of DC Electric Rail Transit Systems With

2218 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 68, NO. 3, MARCH 2019 Modeling and Simulation of DC Electric Rail Transit Systems With Wayside Energy Storage Mahdiyeh Khodaparastan , Oindrilla Dutta, Mahmoud Saleh , Student Member, IEEE , and Ahmed A. Mohamed , Senior Member, IEEE

Abstract —Electric rail transit systems are large consumers of is no train/load on the system to absorb this energy, the voltage of electricity, which face challenges related to improving their overall the third rail will increase and protection devices will disconnect energy efficiency. Although various solutions have been proposed the train from the third rail and the rest of this energy will be to achieve this target, it is not feasible to implement and test all of them. Since finding the solution that is most appropriate to a given dumped into onboard resistors [1], [2]. One important solution system is typically a site-specific problem, an accurate, validated, is capturing this energy by installing wayside energy storage and reliable simulation tool is crucial. In this paper, a simulation systems (ESSs). model for studying wayside energy storage systems in dc electric Various types of energy storage systems are available, such rail transit system is presented. The proposed model provides a as batteries, supercapacitors and flywheels [3]–[5]. In order to reliable tool for analyzing the behavior of the transit system during intervals that span from a small fraction of time (milliseconds) select, design and size the ESS for a specific application, an up to 24 h. In order to validate the proposed simulation model, in-depth knowledge of system performance, such as the power its results were compared with real measurements of a standard profile of trains, substation power loading, available regenera- subway system. tive braking energy, etc., are required. Computer simulation is Index Terms —DC electric rail systems, energy storage systems, a fundamental tool for engineers to investigate a proposed new simulation tool, wayside connection. design, or a major modification to an existing system, before its implementation. Therefore, a reliable and accurate simula- I. I NTRODUCTION tion tool is required to model the DC electric rail systems for LECTRIC rail transit systems have been undergoing rapid investigating the implementation of ESSs. E development in order to meet the ever-increasing demand Simulation of electric rail systems has been studied since late for efficient and fast public transportation. Peak demand re- 1970s and several simulation and modeling tools have been pre- duction and increasing the system energy efficiency are impor- sented by both the industry and academia. There are software tant challenges for all the agencies, especially electric transit packages, such as: TrainOps developed by LTK [6], Sitras Sidy- system that is an enormous consumer of electricity. There- trac by Siemens [7], eTraX Rail Traction Power by ETAP [8], fore, new technologies and equipment are increasingly pro- Train Operation Model (TOM) developed by Carnegie Melon posed and designed to make transit systems more reliable and University [9], OpenTrack and Open Power Net developed efficient. by ETH University [10], [11]and Vehicle Simulation Program Currently, most of the trains are equipped with motors that (VSP) by Vrije University of Brussel [12]. have regenerative braking capability. In this type of vehicles, Generally, the simulation procedure of electrified transporta- during deceleration, the motors act as generators and produce tion systems is based on load flow calculations when trains are electricity. This energy, termed as regenerative braking energy, modeled with a current/voltage source [13], [14]. Most of the can be injected into the third rail and used by other neighboring work that has been done on load flow analysis of electrified accelerating trains or other possible loads of the system. If there transportation systems divide system modeling into two parts: (1) vehicle movement model; and (2) electric network model [15]–[17]. Railway dynamics, equations describing single train Manuscript received March 24, 2018; revised September 28, 2018 and motion and electric power supply load flow calculations are November 21, 2018; accepted January 4, 2019. Date of publication January 24, 2019; date of current version March 14, 2019. This work was supported in presented in [18]–[23]. part by the New York State Energy Research and Development Authority, Con- Beside the classical model of the train, new approaches like solidated Edison, and in part by New York City Transit. The review of this energetic macroscopic representation (EMR) method is also paper was coordinated by Prof. M. Preindl. (Corresponding author: Mahdiyeh Khodaparastan.) used to model electric rail transit system [24], [25]. EMR is M. Khodaparastan, O. Dutta, and M. Saleh are with the Smart Grid Labora- a graphical description tool that classifies the system into the tory, Department of Electrical Engineering, City University of New York, New basic inter-connected components, such as the source of energy, York, NY 10031 USA (e-mail: ,[email protected]; oindrilla270591 @gmail.com; [email protected]). accumulation of energy, conversion of energy, distribution of A. A. Mohamed is with the Smart Grid Laboratory, Department of Electrical energy and switching element [26]. Engineering, City University of New York, New York, NY 10031 USA, on leave Nowadays, most of the new trains are equipped with the re- from the Department of Electrical Engineering, Minia University, Minia, Egypt (e-mail: ,[email protected]). generative braking system. To recuperate this energy, solutions Digital Object Identifier 10.1109/TVT.2019.2895026 such as energy storage and reversible substation are proposed.

0018-9545 © 2019 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications standards/publications/rights/index.html for more information. KHODAPARASTAN et al. : MODELING AND SIMULATION OF DC ELECTRIC RAIL TRANSIT SYSTEMS WITH WAYSIDE ENERGY STORAGE 2219

In this regards, some research works have been done on modeling regenerative braking energy, energy storage systems and reversible substation modeling for application in rail transit systems [3], [27]–[36]. Among the research works which are being carried out in this field, only a few studies consider multi-train operation and/or the availability of regenerative braking energy and modeling wayside energy storage systems. In [37], multi-train simulation with onboard supercapacitors is presented. In [38], modeling of two trains running on the same line with both onboard and wayside supercapacitor ESS is presented. Simplified modeling of multi-train operation with both wayside and onboard supercapacitor is presented in [39]. In [40], a modified current injection power flow algorithm is used to model multi-train operation. The main contribution of this paper is to provide a simulation tool to study regenerative braking energy recuperation in DC rail transit system, and to investigate the performance of different types of wayside energy storage technologies on uti- lizing regenerative braking energy. In the proposed simulation technique, multi-train operation and several types of ESS technologies are considered and simulated. Another advantage of the proposed simulation tool over the previous works is the detailed system modeling. In the previous studies, the dynamic behavior of system components is neglected; trains and ESSs are modeled with current sources and substations are modeled Fig. 1. Substation schematic. as a voltage source behind a diode rectifier. In order to verify the reliability of the proposed simulation tool, the results are TABLE I validated versus real measurement from a subway system. SUBSTATION PARAMETERS The rest of the paper is organized as follows, the power supply network modeling is presented in Section II. Section III presents vehicle modeling and simulation. Modeling of different types of ESS is demonstrated in Section IV. Simulation and validation results are presented in Section V. A case study is presented in Section VI and finally, the paper is concluded in Section VII.

II. P OWER SUPPLY SUBSTATION MODELING In DC electric rail transit systems, the power required by trains is provided by a power supply network including rail network and substations. Generally, substations consist of voltage transformers that step down the voltage and a unidirectional rectifier that converts electricity from AC to DC. In order to increase the A detailed substation model that is used as a module in the reliability of the power supply, two sets, each consisting of a proposed simulation tool is presented in Fig. 1. The description transformer and a rectifier, are connected in parallel. One of the and values of the parameters related to each component are transformers is connected as Y- ∆ and the other one is connected presented in Table I. as ∆-∆ in order to avoid phase shift. A capacitor bank is added As mentioned above, vehicles get their required power from at the output of transformers for fixing its output voltage. There either overhead lines or third rails. Running rails provide a re- are circuit breakers, insulation and other protection devices at turn path for the current and make the power circuit complete. both AC and DC sides to increase the safety. The rail system network is divided into several sections to pro- Substations feed DC voltage to the overhead line or third rail vide easy operation, protection and maintenance. Sections are (a rail next to the running rail) to supply the train power. The connected to each other by means of traction circuit breakers. magnitude of DC voltage depends on the power demand and Depending on the status of circuit breakers, each section can be length of the third rail. Typical values are 600-750V. However, powered by one or two substations at both ends. there are also available systems with 1500V and 3000V [18]. When a train moves on the traction rails, the resistances be- More information about DC power supply networks can be tween the train and its departure and arrival points are changing found in [41], [42]. based on the distance between them at each time instant [43]. 2220 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 68, NO. 3, MARCH 2019

Fig. 2. Schematic of the train running between two passenger stations.

Fig. 4. Vehicle modeling process.

vehicle dynamic calculation stage, gearbox stages and motor’s drive stages. There are several forces applied to the wheels, including friction force (FR ), the force due to the wind (FW ) and gravity force (Fg ). These forces should be overcome by the tractive effort (FT ) created by the motors of the vehicle. In the ﬁrst stage, Fig. 3. Schematic of the variable resistance modeling. speed of the wheel ( v) and inclination angle of the path ( θ) are considered as inputs and using vehicle dynamic equations, (5) In order to simulate the movement of vehicles, rail sections are to (10), the tractive effort applied to the wheel is calculated and modeled by variable resistances. Variable resistances are mod- from there the required torque (Tw ) and angular speed (ωw ) of eled by a controlled voltage source, as presented in Fig. 2. A the wheels are determined and used as inputs for the next stage, section of the rail with a vehicle running from west to east is which is a gearbox. The role of a gearbox is to reduce the speed presented in Fig. 3. Equations related to each variable resistance of the motor drive connected to its shaft while increase output are presented in (1) to (4) [43]. torque of the motor drive. In the backward approach, using the equations that described the gearbox performance, (11) to (14), RP W = xp Rpow er rail (1) the required torque (TG ) and the speed of the motor drive (ωG ) are determined. RP E = ( L xp )Rpow er rail (2) − dv FT FR Fg FW = MM etro (5) RT W = xp Rtraction rail (3) − − − dt R = ( L x )R (4) F = f M g cos θ (6) T E − p traction rail R R M etro

Where RP W and RP E are the power rail resistances at west Fg = MM etro g sin θ (7) and east side of the train. Similarly, RT W and RT E are the trac- 1 F = C Aρv 2 (8) tion rail (running rail) resistances. Rpow er rail and Rtraction rail W 2 w are the resistances of power and traction rail per unit of length. FT r L is the distance between two passenger station and xp is the Tw = × (9) train position. 4ncars v ωw = (10) III. T RAIN MODELING r Where, M is the weight of the train, f is the friction There are two main approaches to model a train: m etro R factor, g is the acceleration gravity, C , A and ρ are drag coef- 1) Forward modeling, known as cause-effect modeling. w ﬁcient, front area of the train and air density, respectively. The 2) Backward modeling, known as effect-cause modeling. number of cars and the radius of the wheels are presented by n In forward modeling of the vehicle, the input (cause) and r, respectively. will be current/power absorbed by the vehicle. By following Gearbox equations in motoring condition are: the dynamics of every component of the vehicle, the speed of the wheels (effect) can be calculated. In backward model- Tw B TG = + (11) ing, the analysis is performed in the reverse direction, i.e., the γG γG speed of the wheels (effect) is considered as an input and, going ω = ω γ (12) backward through the various components, the current/power G w G required by the vehicle (cause) is calculated. Where, γG is the gearbox ratio and B represents the vehicle In this study, the backward methodology is used to model the losses and is calculated using (9). vehicles. The modeling process is presented in Fig. 4. B = T (1 η ) (13) As illustrated, there are three main stages to calculate the w − G required power of the train in the backward approach; including Where, ηG is the gearbox efﬁciency. KHODAPARASTAN et al. : MODELING AND SIMULATION OF DC ELECTRIC RAIL TRANSIT SYSTEMS WITH WAYSIDE ENERGY STORAGE 2221

Fig. 6. Block diagram of the braking chopper.

controller in this technique which makes the controller fast and robust [45]. Most of the equations and description related to DTC controller is presented in the Appendix A. In summary, as illustrated in Fig. 5, the torque and flux are calculated from the voltage and current of the motor. Then the estimated torque and flux are compared with their references produced by the speed controller section. In the speed controller part, the speed of the motor, which is converted to m/s from rpm, is compared with Fig. 5. Vehicle modeling process. the reference speed and the error is applied to the PID controller, followed by a limiter block. The limits depend on the motor rat- ing. The output of this part is a reference torque. Flux reference For the braking process (negative torque), (11) can be modi- is also produced from motor speed and flux calculation block fied as follows: worked based on (15) [44]. T B T = w (14) 2 2 G γ γ Ls 2 Lr T G − G ψs = ψr + ( σL s ) (15) s LM LM ψr In the last stage, the calculated torque and speed from the 2 gearbox are given to the motor drive to calculate the current Where, σ = 1 (M /L s Lr ). required by the vehicle. The error of the− torque and the flux are given to the hysteresis In this paper, two models are proposed for drive modeling: 1) comparator, where the flux comparator has two limits based on Detailed model and 2) Approximate model. In detailed model- the following conditions: ing, every component of the vehicle’s drive is represented and modeled, which makes the model more accurate but more com- Hψ = 1 for eψ > +HBψ plex and it takes the longer time to simulate. The Approximate Hψ = 1 for eψ < HBψ model is less accurate but fast because it does not consider the − − dynamic behavior of every component. Where, eψ is the flux error and HB ψ are the upper and lower hysteresis band of the flux. Torque± hysteresis comparator A. Detailed Modeling has three limits based on the following conditions: Electric trains consist of several cars connected to each other. HT = 1 for eT > +HB T Each car has a set of motor drive and gearboxes connected to H = 1 for e < HB a shaft. Each shaft has two wheels connected to it. Typically, a T − T − T motor drive consists of the induction motors, an inverter and its HT = 0 for HB T < e T < +HB T controller, and a chopper circuit. To model the electric motor − drive, a direct torque control (DTC)DTC drive available for AC Where, eT is the flux error and HB T are the upper and lower machines in MATLAB/Simulink library has been modified and hysteresis band of the torque. The± flux hysteresis band has an adopted. A schematic of the motor drive is presented in Fig. 5. impact on stator current distortion and torque hysteresis band Control methods available for induction motor can be affect the switching frequency [46]. The hysteresis controllers classified into two main groups: 1) scalar-based controller outputs along with sector index (θe ) are used as inputs to the (control magnitude and frequency of variables in steady states); switching lookup table, presented in Table VI of Appendix A 2) vector-based control (control magnitude, frequency and [47]. the instantaneous position of space vector of the variable). The last component in the motor drive is the breaking chopper. Vector-based control also classified into filed oriented, feedback It consists of a resistor bank and an IGBT switch, which is linearization, direct torque control and passively based control controlled by a hysteresis controller. A schematic view of the [44]. braking chopper is presented in Fig. 6. The chopper circuit DTC control is used in this study to control the induction monitors the DC bus voltage, if the voltage goes above a pre- motor. This controller works based on control of stator voltage specified value (upper limit activation voltage), the IGBT switch (output voltage of inverter). In this control strategy, at each time turns on. Then, the excess power on the line will be dissipated step, a voltage vector is applied to the inverter in order to reduce in the resistor bank. The switch is turned off when the voltage the error of torque and flux. There is no intermediate current drops to the lower voltage limit (lower limit shut down voltage). 2222 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 68, NO. 3, MARCH 2019

B. Approximate Model Another approach that has been used for train modeling sim- pliﬁes the system by modeling each component with a gain factor representing its efﬁciency. The process of calculating torque and speed is similar to the detailed model. Using equations (5) to (10), the torque and speed applied to the motor drive are calculated. Then, the amount of power applied to the motor drive is calculated using equation (16).

P = T ω (16) d w × w Fig. 7. Battery model. Having the efﬁciency of the gearbox, motor and inverter, the amount of power and current requested from the main grid is calculated by (17) and (18):

P P = 4n d (17) t cars η η η gear m otor inv Pt It = (18) Vt In summary, given the speed proﬁle and using equations (5) to (10) and (16) to (18), the electric vehicle can be modeled as a current controlled source that is connected to the rail system.

IV. E NERGY STORAGE MODELING

Batteries, supercapacitors and ﬂywheels are three types of Fig. 8. Bidirectional DC/DC converter. technologies commonly used in DC electric rail transit systems. In the MATLAB/Simulink environment, there are avail- TABLE II DC/DC C ONVERTER PARAMETER able models for battery and supercapacitor. These two options are modiﬁed and adopted based on the desired design and parameters. To connect the battery and supercapacitor to the electric rail system, a bidirectional DC/DC converter is designed and modeled. The Flywheel energy storage system is modeled using a permanent magnet machine connected to a rotating mass. The detailed modeling description related to each type of ESS is presented in this section.

A. Batteries 2) If VP C C < V set dis , discharging command up to a level The battery is modeled with a controlled voltage source in of SOC = 40% series with a resistance. This model is a generic dynamic model 3) If Vset dis < V P C C < V set ch , no charge or discharge and can represent the different types of rechargeable battery, takes place. such as Lead-Acid, Lithium-Ion, Nickel- Cadmium and Nickel- Where V PCC is the voltage of the line at the point of con- Metal-Hydride. Each technology can be modeled by adjusting nection of the ESS, V set ch and V set dis are voltage levels that its parameters and equations. Fig. 7 presents a schematic view of are set for triggering charging and discharging process, respec- the battery model. For the sake of brevity, the equations related tively. These voltage set values and charge/discharge current to battery model is presented in Appendix B. amplitudes depend on the application and goal of installing the The battery is connected to the system by means of the bi- ESS. directional DC/DC converter, presented in Fig. 8. Parameters related to the DC/DC converter is presented in During charging, only S1 is turned on and during discharging Table II. mode only S2 is turned on. More information about this type of bidirectional DC/DC converter can be found in [48]. The current B. Supercapacitors (I_command ) is produced by battery energy management unit that is working based on some general rules as follows: Similar to the battery, a supercapacitor is modeled with a 1) If VP C C > V set ch , charging command up to a level of controlled voltage source in series with a resistor, as presented SOC = 90% in Fig. 9. KHODAPARASTAN et al. : MODELING AND SIMULATION OF DC ELECTRIC RAIL TRANSIT SYSTEMS WITH WAYSIDE ENERGY STORAGE 2223

TABLE III FLYWHEEL PARAMETERS

Fig. 9. Supercapacitor model.

is coupled with the electric machine, its speed is equal to the speed of the machine. This speed is considered as an input to the rotating mass model. The speed of flywheel is limited between ωmin and ωmax , which are the minimum and maximum speed allowed for flywheel operation, respectively. If the input speed is Fig. 10. Discharging current and voltage of supercapacitor. beyond the speed limit of flywheel, this speed will change to the boundary value. Then the energy of the flywheel is calculated based on (20). 1 E = Jω 2 (20) 2 Where, E is the energy, J is the flywheel Inertia and ω is the flywheel speed. The flywheel power is presented by (21): dE P = (21) dt Having the power and speed of a flywheel, the mechanical torque input for the electric machine is calculated based on (22).

Fig. 11. Flywheel model. P T = (22) ω

As it is illustrated, if iS C = 0, self-discharge current is con- The electric machine used in this study is a permanent magnet sidered for the supercapacitor which affects the electric charge synchronous machine, which is controlled via a 3-level AC/DC (Q(t) ). Self-discharge current is defined based on (19) and converter. During the charging process, the converter acts as an Fig. 10 that shows the self-discharge phenomena of superca- inverter and the electric machine acts as a motor and speeds pacitor. up the flywheel. During the discharging process, the flywheel slows down and the motor acts as a generator, while the power C t α 1 if t toc t3 1+sR S C C T − ≤ electronic converter acts as a rectifier that injects the released C t α 2 iself dis = 1 if t3 < t toc t4 (19) energy of the flywheel to the third rail. The parameters and their −  +sR S C C T − ≤  C t α 3 values used for flywheel modeling are presented in Table III.  if t toc > t 4 1+sR S C C T −  V. V ALIDATION RESULTS Where, CT is the total capacitance, RS C is the internal resistance and α1, α2 and α3 are constants and are equal to the rate In order to validate our proposed simulation tool, a portion of of change of supercapacitor voltage at the corresponding time line 7 of NYCT consisting of 3 substation and 4 passenger sta- interval. tions is considered as a case study. The schematic of this system Supercapacitor output voltage is presented in Fig. 13. This system is simulated for several cases and the results are compared with real measurements. Firstly, C. Flywheels the results are compared for one cycle operation and then they are compared for 24 hours operation. A flywheel ESS consists of a rotating mass, an electric machine, which can act as a generator or motor, and power elec- A. One-Cycle Operation tronic interface. Schematic of flywheel modeling is presented in Fig. 11. In this section, several speed profiles from the real measure- The rotating mass is modeled based on the flywheel’s energy ment are given to the train model and the output results, i.e., and speed equations and limitations. Since the rotating mass Third rail voltage and current of the trains, are compared with 2224 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 68, NO. 3, MARCH 2019

Fig. 12. Validation results for one-cycle operation. from simulation closely follow the real measurements for current and voltage.

B. 24 Hours Operation The single cycle operation of the rail transit model has been extended to a 24 hours operation for a more conclusive validation of the results. Besides, a 24 hours operation is imperative for the Fig. 13. Under study portion of electric rail transit system. study of peak demand reduction of substations. This prototype has been obtained on the basis of train scheduling by NYCT [49]. real measurements (5000 sample/second). Speed profiles which The schedule provides information such as, headway between are given to the train as an input and related current and volt- trains during different times of the day and the probability of age are presented in Fig. 12. As illustrated, in the first 15-20s, two trains exchanging regenerative energy during peak hours the speed increases with the maximum acceleration and conse- of the day. This data is used to obtain factors for every fifteen quently the current rises to its maximum. During the same time minutes interval of the day, which when multiplied with the interval, the voltage slightly decreases to a lower value. After power and energy profiles of a single train can provide the this, the speed increases with a smaller acceleration rate until it energy consumption during every 15 minutes of 24 hours (as reaches the maximum speed and the current gradually decreases real data sampled). Two examples of 24 hours power profile of to an almost constant value. substation 1 and 2 in the system under study are illustrated in During deceleration, motors act as generators and produce Fig. 14. electric current (the current is in reverse direction and here it As it is illustrated, the power demand reduces gradually at is shown with negative values). The current will have different night and then starts to increase in the early morning. There amplitude and shape, Based on the deceleration rate. In the last is a local maximum around 8:30 AM when the express and 20 seconds of deceleration, several fluctuations happen in the local trains run together and the time interval between trains is speed profiles which are reflected with larger fluctuations on the reduced to provide a fast and reliable service for a large number current. of passengers who are using transit system for commutation. The results from simulation versus real measurements show After this time, as it is expected the headway between running that, with each of the speed profiles, the current and the voltage trains increases and express train service stops. Therefore, power KHODAPARASTAN et al. : MODELING AND SIMULATION OF DC ELECTRIC RAIL TRANSIT SYSTEMS WITH WAYSIDE ENERGY STORAGE 2225

Fig. 15. Train, substation, and ESS current proﬁles.

Fig. 14. 24 hours power profile of the substation1 (a) and the substation 2 (b) in system under study. demand decreases and remains at an almost constant value until 3 PM in the afternoon, when the express service starts again. Also, the headway between running train decreases again and power demand increases until it reaches its maximum around 6:30 PM. In this time, the power demand of the substations goes Fig. 16. Application of ESS on reducing peak current demand. beyond 2 MW. Based on the approach explained earlier in this section, the 24 hours power profile of two substations are created and compared with real data. Those follow the same trend as real data and most of the time those are matched with each other. However, there are some points where they deviate from each other. This is due to the fact that the number of passengers on the trains may differ day by day, which affects the power drawn by the trains. Additionally, there may be a delay in the running time of some of the trains, so it affects the amount of power drawn from the substation in some 15 minutes interval. For example, if some delays happen and as a result of two trains, running in reverse direction, accelerate at the same time, twice the power of a Fig. 17. Third rail voltage with and without ESS. single train is requested from the substation, which increases the demand during that interval. sumed during acceleration is available for energy recuperation. This energy can be saved into the ESS and released during train acceleration and consequently reduced the power and energy VI. C ASE STUDY demanded from power supply substation [50]. In addition, it In this section, the proposed model is used as a tool to test the can improve the third rail voltage drop during train accelera- impact of installation of three different technologies, including tion. Fig. 16 shows the current profile of the train, substation 2 a battery, a supercapacitor and a flywheel, on peak demand re- current with and without ESS and charge/discharge current of duction. A portion of the system presented in Fig. 13, is selected ESS. The train current magnitude is higher than the substation as a case study. ESSs will be installed at substation 2. 2 current because the other substations also contribute to sup- Fig. 15 presents the speed, current and power and energy plying this current. When ESS installed in the substation as it profile of a train approaching substation 2. The change of to- is expected the current magnitude of the substation is reduced tal energy during acceleration (0 s-30 s) is about 14 kWh and and consequently the power demanded from it will be reduced. the change of total energy during deceleration (30 s-63 s) is During deceleration (30-63 s) ESS can be charged from regen- about 5kWh. In other words, almost 35% of the energy con- erative braking energy produced by the train. Fig. 17. present 2226 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 68, NO. 3, MARCH 2019

TABLE IV ESS C OMPARISON

Fig. 18. Stator and rotor flux rotation. the voltage of the third rail with and without ESS. During ac- Stator and rotor flux rotate with a linear speed in an approxi- celeration since the train consumes high current magnitude in mately a circular path. A vector diagram of stator and rotor flux a short period of time, the voltage of the third rail is dropped movement is presented in Fig. 18. In constant magnitude flux, suddenly to some lower voltage value (in extreme cases it can if the speed of stator flux increases, the angle δ is increased cause a damage to the train and other equipment connected to ψ and the torque value will reduce and if the speed of stator flux the third rail). Under voltage relay setting was set on 480 VDC decreases or goes to zero, the angle δ is decreased and the in our case study and nominal voltage is 650 VDC. During train ψ torque will increase. deceleration, regenerative braking energy is injected to the third On the other hand, the stator flux is a state variable that can rail and raise its voltage (here over voltage protection setting be controlled by the stator voltage based on (24). was set to 780 VDC). By installing ESS, this energy is used for charging ESS and voltage will be more stable. dψ s Vs = Vinv (n) = 2πf (24) To compare the performance of different technologies on peak dt demand reduction of substation 2; battery (Li-ion), supercapac- Inverter output voltage space vector Vinv (n) can be described itor and flywheel are sized for 10% peak demand reduction. The with (25) and (26). sizing information is presented in Table IV. The results show ( 2 )v ej(n 1)π / 3 n = 1, 2, 3, 4, 5, 6 V = 3 dc − (25) that to achieve a 10% peak demand reduction, battery needs to be inv (n) 0 0 , 7 oversized to be able to deliver required power during train acceleration (30 s). The cost comparison for each technology is also Vdc /√2 vdc = (26) presented in Table IV. Battery has the highest installation cost Vsrated and supercapacitor is the cheapest one. However, supercapacitor Where, V is the rms value of phase angle. For n = 1-6, need to be replaced every 5 years [28], therefore the total cost srated voltage vector called active and the rest are called zero. Active of the supercapacitor for 10 years is higher than the flywheel. vectors can move in forward and backward direction. VII. C ONCLUSION Applying the active voltage vector to the inverter switches, the speed of the flux increased based on (24) and consequently In this paper, a detailed simulation model for modeling DC δ increased so that torque reduced. By applying zero vectors, electric rail system is presented. DC electric rail system consists ψ flux movement will be zero and since the rotor flux continues its of substations, rail systems, trains and energy storage systems. movement, δ will reduce and therefore torque will increase. Backward modeling approach is used to model the vehicle. In ψ As illustrated in Fig. 6, the torque and stator flux are calculated other words, by having the speed profile of the vehicle, current, from dq components of voltage and current presented in (27) power and the energy of the vehicle can be calculated. Different to (31). Dq components of voltage and current are calculated types of ESS technologies including batteries, supercapacitors based on park transformation presented in (32) [47]. and flywheels are described and modeled. The simulation results are compared with real measurements for one cycle and 3P T = (ψs is ψs is ) (27) 24 hours operation. Comparison results showed the validity and e 4 ds qs − qs ds accuracy of the proposed simulation tool. The proposed simu- ˆ s 2 s 2 lation technique can be used as a reliable tool for investigating ψs = ψds + ψqs (28) the train performance in different case study, such as regenera- q ψs tive braking recuperation, potential application of ESS for peak θ = sin 1 qs (29) e − ˆ demand reduction and energy saving in DC electric rail systems. ψs

APPENDIX A ψs = (v R i )dt (30) ds ds − ss d The torque and the ﬂux of induction motor are related to each Z other based on (23): ψs = (v R i )dt (31) qs q − ss q 3 LM Z T = p ψr ψs sin δψ (23) 2 2π 2π Fa 2 Ls Lr LM Fd 2 Cos θ Cos ( θ ) Cos( θ+ ) − = − 3 3 F 3 2π 2π  b  Where, LM , Lr and Ls are the magnetizing, rotor and stator "Fq # " Sin θ Sin ( θ 3 ) Sin( θ+ 3 )# − − − − Fc inductances, respectively. ψr and ψs are rotor and stator ﬂux,    (32) and δψ is the torque angle. KHODAPARASTAN et al. : MODELING AND SIMULATION OF DC ELECTRIC RAIL TRANSIT SYSTEMS WITH WAYSIDE ENERGY STORAGE 2227

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