# Modeling of Electrified Transportation Systems Featuring Multiple Vehicles and Complex Power Supply Layout

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Proposed Model Structure and Software Setup

_{veh}, supply section identifier k

_{sec}, vehicle collector current i

_{veh}, and position of the vehicle in section x

_{veh}. The selectors isolate vectors corresponding to particular power sections and store them in local matrices. It is worth noting that the number of vehicles within the section may vary in time, so the local matrix must be declared with respect to the maximum number of vehicles (because variable-size arrays are inefficient or not supported, depending on the programming environment used), and filled with dummy vehicle data in case of a lower vehicle number. The vehicles can run on different routes, and they will not necessarily enter the section always in the same order. Hence, an important role of the selector is to sort the vehicle vectors in the local matrix in order of their location. This is required by the main algorithm of the power section subsystem that merges power section and vehicles data and builds the electric circuit equivalent.

_{veh}and current collector voltages u

_{veh}. The voltage subsystems use deselectors to extract the collector voltage of particular vehicles. This completes the loop of model computations.

## 3. Vehicle Subsystem

#### 3.1. Reference Speed Profiles and Timetabling

#### 3.2. Vehicle Motion Dynamics

_{f}) and the route (additional resistance W

_{i}). The fundamental motion resistance of the vehicle is calculated as the sum of aerodynamic drag, transmission drag, and rolling resistance. The following second-order polynomial is used to approximate the value of the fundamental resistance force:

^{2}).

_{i}, related to route inclination, is calculated as:

#### 3.3. Control of Motive Force

_{em}generated solely by the electric motor. In most blended braking systems, the vehicle controller maximizes the use of electrodynamic brake to save friction brake pads and allow for generating the electric power that can be delivered to other vehicles. Therefore, it was assumed that friction brakes are engaged only if the total braking force exceeds the value defined by the electric drive relation between the motive force and velocity (Figure 5). Consequently, the motive force generated by the electric drive is computed as a total motive force with a lower saturation threshold set accordingly to the inverted (negative) maximal electric drive motive force at actual speed.

#### 3.4. Electric Drive Efficiency and Electric Current Computation

_{veh}collected by the vehicle is determined from mechanical power on electric drive output but also includes other important factors. The electric current is computed from the following formula:

_{em}·v) is the mechanical power on electric motor output (may be either positive or negative); P

_{br_res}is the power dissipated in the braking resistor (positive or zero); P

_{aux}is the power of auxiliary loads (positive); P

_{mech_loss}, P

_{em_loss}, P

_{inv_loss}, are the power losses in electric motor, power inverter, and the mechanical part of the drivetrain, respectively (positive or zero); and U

_{veh}is the voltage on vehicle pantograph.

_{em}generated by the electric motor.

_{br_res}dissipated into the heat in the vehicle braking resistor. This power is equal to zero during propelling and coasting. On the other hand, P

_{br_res}may be positive during braking if other vehicles on the same power supply section are unable to consume the electric power generated by regenerative braking in the considered vehicle. The power P

_{br_res}is controlled using the vehicle pantograph voltage U

_{veh}and voltage threshold levels. Typically, the braking resistor is engaged when the pantograph voltage exceeds 760 V. The power P

_{br_res}increases linearly with the further rise of U

_{veh}, reaching the full value of vehicle power balance at U

_{veh}= 790 V. Conversely, when the vehicle pantograph voltage falls below 580 V, the vehicle power is reduced linearly down to zero at U

_{veh}= 520 V, which is the minimum allowed voltage for traction drive of the analyzed vehicle.

_{aux}= 2.5 kW, derived from onboard recordings carried out in trolleybuses during their standstill. In the period when the recordings were carried out, heating and air conditioning were not used.

_{em_loss}in the electric motor and P

_{inv_loss}in the power electronic inverter is a complex problem. As the operating conditions of vehicle drives change in a wide range, assuming a constant efficiency would lead to considerable errors [38]. Trolleybuses in the considered transportation system use induction motor drive. The induction motor converts electric to mechanical power using the electromagnetic field. The efficiency of the induction motor is highly dependent on angular velocity and torque. While for most operating conditions the efficiency exceeds 90%, there are also low-efficiency regions corresponding to the low-speed and low-load operation. In order to accurately reflect motor power losses in the model, the efficiency map η = f(T,ω) is required. Since experimentally derived efficiency values were unavailable, the authors used parameters of the electric motor to set up a mathematical model, which was used to compute losses as a function of velocity and torque. The obtained dataset was loaded into the vehicle subsystem as a 2-dimensional lookup table, where the efficiency values for arguments between the defined points are computed using linear interpolation. A graphical representation of the derived efficiency map is shown in Figure 5.

_{inv_loss}are computed as the sum of switching losses of transistors P

_{t_sw}, reverse-recovery diode losses P

_{d_rec}, and conduction losses for both diodes P

_{d_cond}and transistors P

_{t_cond}[39,40]. All these losses need to be included because the typical voltage drop of 1.2–2.5 V on a semiconductor switch translates to kilowatts of losses.

_{veh_n}—the nominal voltage at vehicle collector (on inverter DC bus); Es

_{w_on}and E

_{sw_off}—energy losses for switching the transistor on and off, respectively; f—the switching frequency.

_{rec}—energy dissipated due to the reverse recovery charge current.

_{C}—collector current; U

_{CE}—collector-emitter saturation voltage; D—inverter duty cycle; cos$\phi $—power factor of the motor; and U

_{f}—diode forward voltage drop.

_{C}of the transistor and diode was assumed equal to the vehicle motor current I

_{veh}—averaged over the duty cycle. The motor power factor was implemented in the second term of Equations (8) and (9).

## 4. Power Supply Subsystem

#### 4.1. Traction Substation and Feeders

_{s}. Such a model reflects the voltage drop at substation output (at its DC switchgear) that is linear to the output current. The best method to derive the model parameters is to analyze the recordings collected during the operation of the considered substation. Approximating the relation between the substation output voltage U

_{sub}and output current I

_{sub}with a linear function allows for deriving both the idle voltage E (as the voltage for I

_{sub}= 0) and the series resistance (as the slope coefficient of the linear function).

_{fdr}whose values depend on the feeder length, cross-section, and the restiveness of the material used (typically aluminum). The trolleybus catenary is symmetrical, i.e., the feeders and the catenary contact wires are identical for positive and negative poles. For simplicity, each feeder is modeled as a single resistance R

_{fdr}, whose value is the sum of resistances of both negative and positive pole feeders. The feeders of the substation have different lengths and different load currents, so the output voltage for each feeder needs to be computed individually. The output voltage for the k-th feeder in the substation supplying n feeders is computed as follows:

_{s}is a function of the substation output current I

_{sub}. The resistance R

_{s}increases when the output current approaches zero and saturates at 1 GΩ for negative currents. Such a continuous change of resistance synergizes well with the voltage-dependent reduction of regenerative braking power implemented in the vehicle model and ensures stable operation of the numeric solver.

#### 4.2. Power Section

_{cat}. The catenary is assumed to have a unified value of unit resistance R

_{cat}′ expressed in Ω/m. Consequently, the resistances between the mentioned current and voltage sources are computed based on their distances. The layout of the catenary is fixed, which also refers to the positions where the feeders are connected to the catenary. The variable topology of the equivalent circuit is related to the number and positions of vehicles that run within the considered power section. This problem is resolved by assuming a maximal number of vehicles in the equivalent circuit. If the actual number of vehicles is lower, the current sources related to absent vehicles are set to zero (while their set positions may be arbitrary). Consequently, the absent vehicles do not influence the current distribution in the circuit. This approach leads to a fixed structure of the equivalent circuit, where the values of voltage sources, current sources, and resistances are not stationary. Such a circuit can be solved with relatively simple and fast methods.

_{fdr1}and U

_{fdr2}) are different. This case can be solved automatically, e.g., by nodal analysis, which leads to solving the following set of equations:

## 5. Experimental Verification

- substation total output current: sum of feeder currents in substation MR5;
- substation output voltage: voltage at substation MR5 output bars; and
- substation output energy: integral of the total output power of substation MR5.

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Radtke, A.; Muller, L.; Schumacher, A. DYNAMIS: A model for the calculation of running times for an efficient time-table construction. Trans. Built Environ.
**1998**, 34, 309–317. [Google Scholar] [CrossRef] - TranSys Research Ltd.; RailTEC at the University of Illinois at Urbana-Champaign; CPCS Transcom; Lawson Economics Research Inc.; National Cooperative Railroad Research Program; Transportation Research Board; National Academies of Sciences, Engineering, and Medicine. Comparison of Passenger Rail Energy Consumption with Competing Modes; Transportation Research Board: Washington, DC, USA, 2015; p. 22083. [Google Scholar] [CrossRef]
- Caramia, P.; Mottola, F.; Natale, P.; Pagano, M. Energy Saving Approach for Optimizing Speed Profiles in Metro Application. In Proceedings of the 2016 International Conference on Electrical Systems for Aircraft, Railway, Ship Propulsion and Road Vehicles & International Transportation Electrification Conference (ESARS-ITEC), Toulouse, France, 2–4 November 2016; pp. 1–5. [Google Scholar] [CrossRef]
- Alnuman, H.; Gladwin, D.; Foster, M. Electrical Modelling of a DC Railway System with Multiple Trains. Energies
**2018**, 11, 3211. [Google Scholar] [CrossRef] [Green Version] - Douglas, H.; Roberts, C.; Hillmansen, S.; Schmid, F. An Assessment of Available Measures to Reduce Traction Energy Use in Railway Networks. Energy Convers. Manag.
**2015**, 106, 1149–1165. [Google Scholar] [CrossRef] - Tian, Z.; Hillmansen, S.; Roberts, C.; Weston, P.; Zhao, N.; Chen, L.; Chen, M. Energy Evaluation of the Power Network of a DC Railway System with Regenerating Trains. IET Electr. Syst. Transp.
**2016**, 6, 41–49. [Google Scholar] [CrossRef] - Açikbaş, S.; Söylemez, M.T. Parameters Affecting Braking Energy Recuperation Rate in DC Rail Transit. In Proceedings of the ASME/IEEE 2007 Joint Rail Conference and Internal Combustion Engine Division Spring Technical Conference, Pueblo, CO, USA, 13–16 March 2007; pp. 263–268. [Google Scholar] [CrossRef]
- Tian, Z.; Zhang, G.; Zhao, N.; Hillmansen, S.; Tricoli, P.; Roberts, C. Energy Evaluation for DC Railway Systems with Inverting Substations. In Proceedings of the 2018 IEEE International Conference on Electrical Systems for Aircraft, Railway, Ship Propulsion and Road Vehicles & International Transportation Electrification Conference (ESARS-ITEC), Nottingham, UK, 7–9 November 2018. [Google Scholar] [CrossRef]
- Koseki, T. Technologies for Saving Energy in Railway Operation: General Discussion on Energy Issues Concerning Railway Technology. IEEJ Trans. Electr. Electron. Eng.
**2010**, 5, 285–290. [Google Scholar] [CrossRef] - Sanchis, I.V.; Zuriaga, P.S. An Energy-Efficient Metro Speed Profiles for Energy Savings: Application to the Valencia Metro. Transp. Res. Procedia
**2016**, 18, 226–233. [Google Scholar] [CrossRef] - Xiao, Z.; Wang, Q.; Sun, P.; You, B.; Feng, X. Modeling and Energy-Optimal Control for High-Speed Trains. IEEE Trans. Transp. Electrif.
**2020**, 6, 797–807. [Google Scholar] [CrossRef] - Bosyi, D.; Kosariev, Y. Modeling of the controlled traction power supply system in the space-time coordinates. Transp. Probl.
**2017**, 12, 5–19. [Google Scholar] [CrossRef] [Green Version] - Frilli, A.; Meli, E.; Nocciolini, D.; Pugi, L.; Rindi, A. Energetic Optimization of Regenerative Braking for High Speed Railway Systems. Energy Convers. Manag.
**2016**, 129, 200–215. [Google Scholar] [CrossRef] - Tian, Z.; Hillmansen, S.; Roberts, C.; Weston, P.; Chen, L.; Zhao, N.; Su, S.; Xin, T. Modeling and Simulation of DC Rail Traction Systems for Energy Saving. In Proceedings of the 17th International IEEE Conference on Intelligent Transportation Systems (ITSC), Qingdao, China, 8–11 October 2014; pp. 2354–2359. [Google Scholar] [CrossRef]
- Krzysztoszek, K. Mathematical Model of Traction Vehicle Movement. J. Autom. Electron. Electr. Eng.
**2019**, 1, 37–42. [Google Scholar] [CrossRef] [Green Version] - Krzysztoszek, K.; Luft, M.; Lukasik, Z. Digital Control Model for Electric Traction Vehicles. Procedia Comput. Sci.
**2019**, 149, 274–277. [Google Scholar] [CrossRef] - Train Energy and Dynamics Simulator (TEDS). U.S. Department of Transportation, Federal Railroad Administration. Available online: https://railroads.dot.gov/rolling-stock/current-projects/train-energy-and-dynamics-simulator-teds (accessed on 30 May 2021).
- OpenPowerNet Simulation Software for Traction Power Supply Systems. Institut fuer Bahntechnik GmbH. Available online: https://www.openpowernet.de (accessed on 15 May 2021).
- Dynamis. IVE mbH—Ingenieurgesellschaft für Verkehrs-und Eisenbahnwesen mbH. Available online: https://www.ivembh.de/softwareprodukte/simulation/dynamis.html (accessed on 25 June 2021).
- Matsuoka, K.; Kondo, M. Energy Saving Technologies for Railway Traction Motors. IEEJ Trans. Electr. Electron. Eng.
**2010**, 5, 278–284. [Google Scholar] [CrossRef] - Torreglosa, J.P.; Garcia, P.; Fernandez, L.M.; Jurado, F. Predictive Control for the Energy Management of a Fuel-Cell–Battery–Supercapacitor Tramway. IEEE Trans. Ind. Inform.
**2014**, 10, 276–285. [Google Scholar] [CrossRef] - Zarifian, A.; Kolpahchyan, P.; Pshihopov, V.; Medvedev, M.; Grebennikov, N.; Zak, V. Evaluation of electric traction’s energy efficiency by computer simulation. In Proceedings of the 2013 19th IMACS World Congress, San Lorenzo del Escorial, Spain, 26–30 August 2013. [Google Scholar]
- Du, F.; He, J.H.; Yu, L.; Li, M.X.; Bo, Z.Q.; Klimek, A. Modeling and Simulation of Metro DC Traction System with Different Motor Driven Trains. In Proceedings of the 2010 Asia-Pacific Power and Energy Engineering Conference, Chengdu, China, 28–31 March 2010; pp. 1–4. [Google Scholar] [CrossRef]
- Fathy Abouzeid, A.; Guerrero, J.M.; Endemaño, A.; Muniategui, I.; Ortega, D.; Larrazabal, I.; Briz, F. Control Strategies for Induction Motors in Railway Traction Applications. Energies
**2020**, 13, 700. [Google Scholar] [CrossRef] [Green Version] - Apostolidou, N.; Papanikolaou, N. Energy Saving Estimation of Athens Trolleybuses Considering Regenerative Braking and Improved Control Scheme. Resources
**2018**, 7, 43. [Google Scholar] [CrossRef] [Green Version] - Tian, Z.; Zhao, N.; Hillmansen, S.; Su, S.; Wen, C. Traction Power Substation Load Analysis with Various Train Operating Styles and Substation Fault Modes. Energies
**2020**, 13, 2788. [Google Scholar] [CrossRef] - Du, G.; Wang, C.; Liu, J.; Li, G.; Zhang, D. Effect of Over Zone Feeding on Rail Potential and Stray Current in DC Mass Transit System. Math. Probl. Eng.
**2016**, 2016, 1–15. [Google Scholar] [CrossRef] [Green Version] - Baumeister, D.; Salih, M.; Wazifehdust, M.; Steinbusch, P.; Zdrallek, M.; Mour, S.; Lenuweit, L.; Deskovic, P.; Ben Zid, H. Modelling and simulation of a public transport system with battery-trolleybuses for an efficient e-mobility integration. In Proceedings of the 2017 1st E-Mobility Power System Integration Symposium, Berlin, Germany, 23 October 2017. [Google Scholar]
- He, X.; Li, E.; Zhang, H. ASR Control of Distributed Drive Vehicles Based on CAN Bus and FlexRay Bus. In Proceedings of the 2021 IEEE 5th Advanced Information Technology, Electronic and Automation Control Conference (IAEAC), Chongqing, China, 12–14 March 2021; IEEE: Piscataway, NJ, USA; pp. 749–755. [Google Scholar] [CrossRef]
- Murvay, P.-S.; Groza, B. Efficient Physical Layer Key Agreement for FlexRay Networks. IEEE Trans. Veh. Technol.
**2020**, 69, 9767–9780. [Google Scholar] [CrossRef] - MathWorks Inc. Matlab Programming Fundamentals. Available online: https://www.mathworks.com/help/pdf_doc/matlab/matlab_prog.pdf (accessed on 11 April 2021).
- Shampine, L.F.; Reichelt, M.W. The MATLAB ODE Suite. SIAM J. Sci. Comput.
**1997**, 18, 1–22. [Google Scholar] [CrossRef] [Green Version] - Muginshtein, L.A.; Yabko, I.A. Power Optimal Traction Calculation for Operation of Trains of Increased Mass and Length. In Proceedings of the 2009 9th International Heavy Haul Conference, Shanghai, China, 22–25 June 2009. [Google Scholar]
- Szeląg, A. Electric Traction—Basics, 1st ed.; WUT Publishing House: Warsaw, Poland, 2019; pp. 28–29. [Google Scholar]
- Abrahamsson, L.; Skogberg, R.; Östlund, S.; Lagos, M.; Söder, L. Identifying electrically infeasible traffic scenarios on the iron ore line; applied on the present-day system, converter station outages, and optimal locomotive reactive power strategies. In Proceedings of the ASME/IEEE Joint Rail Conference, San Jose, CA, USA, 23–26 March 2015. [Google Scholar] [CrossRef]
- Spiroiu, M.-A. About the Influence of Wheel-Rail Adhesion on the Maximum Speed of Trains. MATEC Web Conf.
**2018**, 178, 06004. [Google Scholar] [CrossRef] - Bartlomiejczyk, M.; Mirchevski, S.; Jarzebowicz, L.; Karwowski, K. How to Choose Drive’s Rated Power in Electrified Urban Transport? In Proceedings of the 2017 19th European Conference on Power Electronics and Applications (EPE’17 ECCE Europe), Warsaw, Poland, 11–14 September 2017; pp. P.1–P.10. [Google Scholar] [CrossRef]
- Jakubowski, A.; Jarzebowicz, L. Constant vs. Variable Efficiency of Electric Drive in Train Run Simulations. In Proceedings of the 2019 26th International Workshop on Electric Drives: Improvement in Efficiency of Electric Drives (IWED), Moscow, Russia, 30 January–2 February 2019; pp. 1–6. [Google Scholar] [CrossRef]
- Patel, A.; Chandwani, H.; Patel, V.; Patel, K. Prediction of IGBT power losses and junction temperature in 160 kW VVVF inverter drive. J. Electr. Eng.
**2014**, 12, 1–7. [Google Scholar] - Wei, K.; Zhang, C.; Gong, X.; Kang, T. The IGBT Losses Analysis and Calculation of Inverter for Two-Seat Electric Aircraft Application. Energy Procedia
**2017**, 105, 2623–2628. [Google Scholar] [CrossRef] - Li, C.; Wang, H.; Bi, H. The Calculation Method of Energy Consumption of Air-Conditioning System in Subway Vehicle Based on Representative Operating Points. IOP Conf. Ser. Earth Environ. Sci.
**2020**, 455, 012177. [Google Scholar] [CrossRef]

**Figure 6.**Typical structures of power sections and their equivalent circuits: (

**a**) power section supplied by one set of feeders connected at the boundary; (

**b**) power section supplied by two sets of feeders at boundaries; (

**c**) power section supplied by one set of feeders with a branch in the middle part.

**Figure 8.**Trolleybus lines and stops in the supply area of substation MR5 (on-request stops are marked in grey).

Parameter/Vehicle | 26Tr (Single) | 27Tr (Articulated) |
---|---|---|

Vehicle length | 12 m | 18 m |

Number of axles (powered) | 2 (1) | 3 (1) |

Nominal motor power | 200 kW | 250 kW |

Maximum motive force | 36 kN | 36 kN |

Mass (empty) | 11,400 kg | 18,290 kg |

Passenger capacity | 91 | 131 |

Nominal voltage | 660 V DC |

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**MDPI and ACS Style**

Jakubowski, A.; Jarzebowicz, L.; Bartłomiejczyk, M.; Skibicki, J.; Judek, S.; Wilk, A.; Płonka, M.
Modeling of Electrified Transportation Systems Featuring Multiple Vehicles and Complex Power Supply Layout. *Energies* **2021**, *14*, 8196.
https://doi.org/10.3390/en14248196

**AMA Style**

Jakubowski A, Jarzebowicz L, Bartłomiejczyk M, Skibicki J, Judek S, Wilk A, Płonka M.
Modeling of Electrified Transportation Systems Featuring Multiple Vehicles and Complex Power Supply Layout. *Energies*. 2021; 14(24):8196.
https://doi.org/10.3390/en14248196

**Chicago/Turabian Style**

Jakubowski, Aleksander, Leszek Jarzebowicz, Mikołaj Bartłomiejczyk, Jacek Skibicki, Slawomir Judek, Andrzej Wilk, and Mateusz Płonka.
2021. "Modeling of Electrified Transportation Systems Featuring Multiple Vehicles and Complex Power Supply Layout" *Energies* 14, no. 24: 8196.
https://doi.org/10.3390/en14248196