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Rail. Eng. Science (2022) 30(1):71–95 https://doi.org/10.1007/s40534-021-00261-y Traction power substation balance and losses estimation in AC railways using a power transfer device through Monte Carlo analysis 1 1 Vı´tor A. Morais Anto´nio P. Martins Received: 25 June 2021 / Revised: 8 October 2021 / Accepted: 10 October 2021 / Published online: 17 January 2022 The Author(s) 2022 Abstract The high dynamic power requirements present in 1 Introduction modern railway transportation systems raise research challenges for an optimal operation of railway electrifica- Electrified railways have constantly raised interest since tion. This paper presents a Monte Carlo analysis on the they are considered one of the most energy-efficient modes application of a power transfer device installed in the of transportation. It is known from the report of [1] that the neutral zone and exchanging active power between two railway sector is efficient when compared to other means of sections. The main analyzed parameters are the active transportation: the railway sector has a 9% market share in power balance in the two neighbor traction power substa- the transportation of passengers and goods in the European tions and the system power losses. A simulation framework Union and this is achieved with a final energy consumption is presented to comprise the desired analysis and a universe of 2%, in comparison with other sectors. The considerable of randomly distributed scenarios are tested to evaluate the power requirements of the railway transportation system effectiveness of the power transfer device system. The lead the railway operators to pursue actions to increase the results show that the density of trains and the relative energy efficiency, reduce the energy consumption bill and branch length of a traction power substation should be increase the infrastructure capacity, [2, 3]. considered in the evaluation phase of the best place to This work is framed within the IN2STEMPO project install a power transfer device, towards the reduction of the objectives—Innovative Solutions in Future Stations, operational power losses, while maintaining the two sub- Energy Metering and Power Supply—specifically in the stations balanced in terms of active power. smart power supply activities. Inserted in the Shift2Rail European program [4], the smart power supply activities Keywords Electric traction systems Monte Carlo seek to contribute to the development of a railway power analysis Power transfer device Power quality Railway grid in a fully interconnected and communicating system, power systems Smart railways [5]. In the smart power supply target of IN2STEMPO, one goal is to study Flexible AC Transmission Systems (FACTS) to exploit the full potential of the 25 kV, 50 Hz rail power supply system. Specifically, one of the FACTS under study is the Railway Interline Power Flow Converter (RIPFC) [6]. The RIPFC comprehends a power transfer device (PTD) in the neutral zone (NZ), providing double- side feeding to the catenary branch and respective trains, & Vıtor A. Morais and reactive power on both sides to stabilize the catenary vitor.fa.morais@gmail.com voltage. Antonio P. Martins The objective of this paper is to statistically evaluate the ajm@fe.up.pt effects of the inclusion of a PTD in the neutral zone of an Department of Electrical and Computer Engineering, Faculty of Engineering, University of Porto, Porto 4200-465, Portugal https://cordis.europa.eu/project/id/777515. 123 72 V. A. Morais, A. P. Martins electrified railway line. Mainly, the active power balancing [10, 23, 24]. Similarly, the co-phase system [25–28] , has in the two traction power substations (TPS) and the system similar characteristics in terms of an optimized 3-phase power losses are under consideration in this study. interface. Maintaining the objective of guaranteeing a high The first contribution of this paper is a simulation level of power quality at the 3-phase supply, additional framework to statistically evaluate the proposed PTD solutions are employed, e.g. the STATCOM [29–31]. compensation strategy (where the framework is capable to In recent years, a strong effort is being made to intro- be extended to additional statistical analysis). Then, the duce renewables and storage in railway systems. This second contribution is the evaluation of two scenarios, with tendency intends the satisfaction of several main objec- different PTD characteristics, when they are considered tives: i) alleviate the substations load and then avoid peak design constraints (namely, the catenary branch length and loads (peak shaving) and, at the same time, reduce the the sparsity/density of trains in the TPS). system losses [32–34]; ii) turn the railway system an even This paper is divided into seven sections. Sect. 2 addresses more environmental friendly [35]; and iii) provide the a scientific literature review on the topologies for power means for regenerative energy storage [36, 37]. transfer devices and on the control strategies. Section 3 pre- There are many factors such as weather conditions, sents the architecture for the simulation model necessary to driving style, schedule, and stop time in the stations which implement the required analysis. Then, Sect. 4 covers reduced alter the actual characteristics of train circulation con- scenario simulations to illustrate the advantages of this strat- cerning pre-defined ideal conditions. All of these factors egy, in terms of active power balancing and system power have some randomness degree [38]. losses. Section 5 covers the universe of parameters randomly The position in the sector, speed and acceleration of the analyzed with the Monte Carlo analysis methodology. Sec- train define both the consumed power and the voltage drop tion 6 presents the results and the discussion on the. Finally, in the line and respective losses and the power factor in the the conclusions are presented in Sect. 7. substation. Therefore, it is not possible to carry out a fully deterministic analysis of the various operating parameters of the railway subsystem [39, 40]. 2 Literature review Thus, several aspects of the power flow analysis regarding both the railway substations and the catenary are Electrified railways, DC or AC, must deal with several power better characterized from a probabilistic analysis [41–43]. quality issues, either in the railway subsystem itself and in the Analyses of feeder current profile, [44, 45], harmonic transmission/distribution system operator (TSO/DSO) supply propagation in DC [46] or AC railways [47], and the [7–10]. In the past, some passive solutions helped to alleviate voltage profile in the catenary [39, 48], have been per- these issues but their performance was dependent on different formed using probabilistic methods. The analysis of data operation parameters and has poor dynamics. Then, the use of from both real exploration and dedicated simulators allows power electronics based converters for power quality defining the probability density functions associated with increasing in railway systems has entered into the domain and factors that contain a probabilistic character such as the is continuously increasing [11–13]. Their purpose is quite number of trains in a section, the position, the consumed large and addresses different power quality issues in railway power, or the power in the substation [41, 49]. systems: transformer losses, catenary voltage stability, sub- The PTD is an additional element in the railway system station active power balancing, peak shaving, three-phase and the analyses of its effects, both on the balance of active current balancing, reactive power compensation [13–15]. It power in substations and on the redistribution of power should be mentioned that the static frequency converter (SFC) losses in the system, are the main objectives of this article. system is a kind of ‘‘one fits all’’ regarding all the referred As, the railway system becomes more complex, data power quality issues but this system is a stand-alone solution, clustering and probabilistic analysis are used, in particular, interesting for new lines, [12, 16–18]. Since the large majority the Monte Carlo method. The following section addresses of railway systems is based on some type of transformer the subsystem models, with particular focus on the devel- topology, the SFC system will not be further considered in this oped simulation framework. paper. Modern railway line voltage stabilization is made using a static VAR compensator (SVC), located near the neutral 3 Subsystem models zone [19, 20] , or using mobile reactive power compen- sation strategies [3, 21, 22]. The railway power conditioner Let us consider a generic 125 kV, 50 Hz double-track system (RPC) is employed in conjunction with V/V railway line as illustrated in Fig. 1 including a PTD in the transformers and offers very good performance regarding ND. In this configuration, and commonly, each traction 3-phase power balancing and power factor correction Rail. Eng. Science (2022) 30(1):71–95 Traction power substation balance and losses estimation in AC railways using a power transfer 73 Transmission system operator: three phase grid, 50 Hz TPS1 TPS2 Power transfer device Fig. 1 Simplified representation of the inclusion of a power transfer device on a neutral zone TPS1 TPS2 substation is electrically isolated from an adjacent one P Q Q 2 P ptd 1 ptd where this electric separation is made in the ND. This paper considers the inclusion of a power converter AC DC (a PTD) in the ND, having a back-to-back configuration, as DC AC illustrated in Fig. 2, being capable of independently control the reactive power injected in each side of the two sections Fig. 2 Simplified architecture of the electronic converter to perform (Q and Q ) and transfer active power between the two 1 2 the power transfer device function sides (P ). To limit the size of the problem, the work in ptd this paper is only focused on the management of active generate the branches and bus matrices of the power sys- power where the power factor of the PTD is unitary. tem based on the definition of the physical conditions. The specific converter structure can be based on dif- Then, this framework has two functional highlights: for ferent approaches but the most common is a multilevel one, each scenario, the physical characteristics can be estab- built with cascaded H-bridges, neutral-point clamped, or lished (either fixed or randomly defined), with the auto- modular multilevel converters. The transformers are matic power system modeling, and the scenario can be designed according to the power level to be transferred automatically evaluated (using a power flow solver). between sections, the reactive power injected in the ND, The implementation approach depends on the usage of and the voltage and current levels in the converters. Also, a an object-oriented language, where each simulation sce- parameter of high relevance in the system design either in nario follows a class of objects capable to implement the the transformer and in the converters is the efficiency level. functional highlights. This parameter ensures that the power losses value is kept The desired functionality was modeled in a MATLAB at a minimum and thus does not compromise the overall simulation framework where the power flow analysis is losses when using the PTD, particularly in the active power made using the MatPower tool. The simulation framework transfer mode. has the following functional requirements: 3.1 Architecture of the simulation framework 1. Must be capable of simulating all trains of two or four branches of each traction substation (respectively for The simulation model of a railway power system is a single and double track lines). particular power flow analysis, where the electric model is 2. Must be implemented in an object-oriented approach, dynamic. Specifically, the electric model depends on the enabling the analysis of an array of simulation number of trains and the position of each one (absolute/ scenarios targeting multi-core parallelization. Each relative position). Then, the power flow analysis of a rail- simulation scenario is one object, having intrinsic way power system is a snapshot simulation, where each properties and methods. simulated scenario has a specific matrix for the branches 3. Each simulation scenario (or object) must consider: and the buses of the power system. • All traction substations – TPS½1; 2; ...; T –in This work requires the development of a simulation 2 adjacent pairs; framework, available as open-source in the repository . • All branches of each TPS – br[1, 2] or The simulation framework purpose is to dynamically br[1, 2, 3, 4]; Repository: github.com/vitormorais/proj_railway_ptd. Rail. Eng. Science (2022) 30(1):71–95 74 V. A. Morais, A. P. Martins • All trains in each branch of each TPS – The output visible in Fig. 3 can be automatically gen- T½1; 2; ...; N; erated by the simulation framework. • All power transfer devices existing in the whole Since there are no trains in the left branch of the TPS1, line in the analysis – PTD½1; 2; ...; P. the branch impedance (br[2]: 2–3) corresponds to the impedance of a 20 km catenary line. The traction power 4. The essential methods of the class must be: transformer of TPS1 is represented by branch br[1]: 1–2. • Dynamic setup of all TPS branches; The automatic electric model generator ensures that the • Dynamic addition of N trains to a branch (placed in sum of the impedances of the right branch is equal to the specific positions, with specific apparent power total impedance of a 20 km catenary line (br[7] ? br[8] ? consumption); br[9] ? br[3] = br[2]). • Dynamic setup of power transfer devices; Regarding the PTD, the adopted model comprises two • Power flow analysis and automatic output series branches with a middle bus representing the constant generation; losses. The first branch (br[13]: 4–100) represents the • Automatic graphical generation of the electric series impedance of the PTD step-down transformer; the diagram. subsequent branch (br[14]: 100–101) is associated to the inverter conduction losses. The constant power losses in Let us consider a simple scenario having two traction bus 100 represent the transformer constant power losses substations, each one feeding a single-track 125 kV (no-load losses) together with the inverter constant power railway line, where both TPS are interconnected through a losses. power transfer device, and the respective two branches The simulation framework follows the UML diagram of (20 km and 15 km, respectively) have three trains each in Fig. 4. Each electric_model object has several properties different positions and with different apparent power. This (like the characteristics of the TPS, the information of train scenario can be simulated in the proposed simulation positions and respective power consumptions, the charac- framework. Then, the automatic graphical generation teristics of the PTD, and the relevant parameters for the output is illustrated in Fig. 3. br[6]: 6 8 No right trains asc TPS branch right 15 km PTD br[4]: 5 6 br[10]: 6 12 br[11]: 12 13 br[12]: 13 14 br[5]: 14 7 br[15]: 7 102 br[16]: 102 103 TPS2 ID:4 ID:5 ID:6 pos:1.6 pos:10.4 pos:13.2 ptd P:1.93 P:6.00 P:3.41 Q:0.86 Q:1.87 Q:2.56 Left trains asc TPS branch length 15 km PTD br[7]: 2 9 br[8]: 9 10 br[9]: 10 11 br[3]: 11 4 br[13]: 4 100 br[14]: 100 101 ID:1 ID:2 ID:3 pos:10.1 pos:14.7 pos:18.3 P ptd P:-0.08 P:-0.13 P:2.15 Q:-0.03 Q:-0.05 Q:0.27 Right trains asc br[1]: 1 2 br[2]: 2 3 TPS branch length 20 km TPS1 No left trains asc TPS branch length 20 km Fig. 3 Resultant implemented simulation model of the simple scenario (P stands for active power with units in MW, and Q reactive power with units in MVAr, while pos means position with units in km, and asc ascending direction.) Rail. Eng. Science (2022) 30(1):71–95 bus1 bus5 bus2 bus6 bus9 bus12 bus8 bus3 bus10 bus13 bus14 bus11 bus4 bus7 bus100 bus102 bus101 bus103 Traction power substation balance and losses estimation in AC railways using a power transfer 75 power flow solver). Also, each electric_model object has (number of trains, active power, and power factor of each several methods, which are the functions of the class, with one) for both TPS and the power flow is calculated. Finally, examples like: i) electric_model::generate_random_- the PTD is attached to the simulation framework with a trains() to start a new scenario with random train positions specific optimization strategy, the power flow is launched and respective power consumptions; ii) electric_- again and the final results are extracted. This procedure is model::run_powerflow() to perform the power flow analy- then evaluated as a scenario of two TPS without and with sis of the scenario; or iii) electric_model:: the PTD in the ND. attach_power_transfer_device() to include a PTD to the In the example of the application of the flowchart of scenario for optimization of the TPS power consumption. Fig. 5, the main objective is to balance the active power in Additional methods were also developed to load and save each TPS, with the compensation power in the power the simulation state, or to plot the resulting electric diagram transfer device being defined by the method electric_- of the scenario. model::tps_power_optimization(), where half of the power A new scenario is evaluated with the sequential launch is transferred in the NZ. In this flowchart, the first part (in of the methods of electric_model, as illustrated in Fig. 5. green) is to prepare the object for the power flow analysis: The initial step is to configure the electric parameters and first is defined the electric parameters (TPS traction trans- the two TPS under study. Then, the trains are generated former impedance, catenary impedance, among others), Train 1 Train ... id dir Train n id section dir abs_pos id section TPS1 apower dir Electric model abs_pos trains_right rpower section TPS2 number apower bus_no abs_pos Number_of_tps gen_index rpower id [] number branch_left tps_lenghts [] apower bus_index position [] bus_no gen_index branch_right tps_transformer_impedance rpower branch_index branch_left apower [] bus_index [] tps_transformer_susceptance bus_no trains branch_right pf [] branch_index [] tps_catenary_impedance branch_left trains_right rpower [] trains [] tps_catenary_susceptance branch_right trains_left abs_position [] trains_right tps [] ptd trains_left global_model_mpc ptd [] mpopt last_matpower_result trains_left PTD 1 powerflow_result global_model_mpc id [] plot_electric_ tps_number PTD n position [] sim_input_data [] dir version apower [] tps_number debug section base_MVA pf [] dir NZ_bus_pos gen[n x 21] section rpower [] reset_model() PTD_bus branch [n x 13] abs_position [] NZ_bus_pos test_case() PTD_branch bus [n x 13] PTD_bus test_statistics() transf_impedance PTD_branch generate_random_trains() transf_iron_loss transf_impedance add_random_trains() converter_impedance last_matpower_result transf_iron_loss test_random_trains() converter_constant_loss version converter_impedance losses_optimization() powerflow_result base_MVA converter_constant_loss tps_power_optimization() gen[n x 21] setup_tps() tps_power [n] branch [n x 17] setup_trains() min_voltage [n] bus [n x 13] add_trains() apower_losses [] CLASS: plot_electric order attach_power_transfer_device() rpower_losses [] et "plot_properties" run_powerflow() power_losses [] success tps_data [] process_output() transferred_power [] mpc_data [] iterations avg_position setup_electric_parameters() "electric_model_data" plot_electric_diagram() avg_weighed_position delta_power attach_electric_model() plot_electric_data() plot_tps() plot_branch() plot_train_info() plot_branch_info() plot_oval() Fig. 4 UML diagram of the resultant implemented simulation model Rail. Eng. Science (2022) 30(1):71–95 76 V. A. Morais, A. P. Martins START instantiate new “electric_model” object electric_model::run_powerflow() electric_model::setup_electric_parameters() electric_model::process_output() electric_model::setup_tps(2) electric_model::attach_power_transfer_device() electric_model::tps_power_optimization() electric_model::generate_random_trains( ) electric_model::run_powerflow() electric_model::process_output() END Fig. 5 Example of usage of an electric_model object to evaluate a new scenario and then is created a new physical simulation scenario 4 Reduced scenario simulation (where the number of trains can be random or fixed, as well as the respective apparent power and position in the Before entering a large-scale simulation analysis, it is branches, among other properties). The second part (in useful to analyze and validate some simple scenarios, in coral and blue) targets the specific simulation presented in which the quantitative and qualitative analysis should this paper: the evaluation of the installation of the PTD in validate a priori known conclusions. the NZ, in terms of power losses, where is obtained the This section evaluates two sets of simulation scenarios, knowledge of the system state before and after the starting with scenarios comprising two TPS and one train, installation. and then scenarios having two TPS and two trains (each To evaluate a universe of simulation scenarios, a second one supplied by a different TPS), using the simulation handler class was developed, which follows the UML of framework presented in the previous section. Fig. 6. Fig. 7 illustrates a simple simulation of one train and The purpose of this handler class is to hold the array of two TPS connected by a PTD. electric_model_objects and to extract the results on the Let us consider the following reduced scenario analysis, performed analysis. The main method of this class is the consisting of N scenario simulations, as in (1), where the eval_compensation(type,max_iter), where all the new power consumption and position of this train are randomly simulation scenarios are created, the random and fixed distributed following specific probability distribution parameters of each scenario are generated and the power functions (PDF). flow analysis is performed, following the flowchart of P ½1; 2; :::; N2½08 in MW train Fig. 5. : ð1Þ tps1 D ½1; 2; :::; N2½01 in % of d train cat;total This section was detailed with the implementation steps of the simulation framework capable to evaluate the For all N scenarios, the train power factor is fixed inclusion of the PTD for a universe of simulation scenarios. tps1 (pf ¼ 0:98ind:), the branch lengths are fixed (d ¼ 30 cat;total The Appendix section is also presented two details of the tps2 graphical user interface, in Figs. 26 and 27, where the km; d ¼ 30 km), the parameters of the TPS (Z ) and tps cat;total scenario random generation and the electric parameters the catenary are fixed (R ¼ 0:15 X=km, L ¼ cat cat menus are presented, respectively. 1:43 mH=km and C ¼ 12:4nF=km, where cat tps Z ¼ Z d ), and the parameters of the PTD are fixed cat cat cat;total Rail. Eng. Science (2022) 30(1):71–95 Traction power substation balance and losses estimation in AC railways using a power transfer 77 Electric model Number_of_tps Electric model MONTE CARLO tps_lenghts [] Number_of_tps Electric model tps_transformer_impedance numIterations tps_lenghts [] tps_transformer_susceptance electric_model_objects [] Number_of_tps tps_transformer_impedance ... tps_catenary_impedance monte_carlo_type tps_lenghts [] tps_transformer_susceptance tps_catenary_susceptance electric_diagram_fig_handler Number_of_tps Elect ric model tps_transformer_impedance tps_catenary_impedance tps [] results tps_lenghts [] tps_transformer_susceptance tps_catenary_susceptance global_model_mpc Number_of_tps handler tps_transformer_impedance tps_catenary_impedance tps [] mpopt tps_lenghts [] tps_transformer_susceptance tps_catenary_susceptance global_model_mpc last_matpower_result tps_transformer_impedance eval_compensation(type, max_iter) tps_catenary_impedance tps [] mpopt powerflow_result tps_transformer_susceptance attach_results_array(electric_model_objects_array) tps_catenary_susceptance global_model_mpc last_matpower_result plot_electric_ tps_catenary_impedance perform_statistical_analysis(type) tps [] mpopt powerflow_result sim_input_data [] tps_catenary_susceptance perform_ptd_analysis(type) global_model_mpc last_matpower_result plot_electric_ debug tps [] load_monte_carlo() mpopt powerflow_result sim_input_data [] global_model_mpc save_monte_carlo() last_matpower_result plot_electric_ debug reset_model() mpopt powerflow_result sim_input_data [] test_case() last_matpower_result plot_electric_ debug reset_model() test_statistics() powerflow_result sim_input_data [] test_case() generate_random_trains( plot_electric_ ) debug reset_model() test_statistics() add_random_trains() sim_input_data [] test_case() generate_random_trains() test_random_trains() debug reset_model() test_statistics() add_random_trains() losses_optimization() test_case() generate_random_trains() test_random_trains() tps_power_optimization() reset_model() test_statistics() add_random_trains() losses_optimization() setup_tps() test_case() generate_random_trains() test_random_trains() tps_power_optimization() setup_trains() test_statistics() add_random_trains() losses_optimization() setup_tps() add_trains() generate_random_trains() test_random_trains() tps_power_optimization() setup_trains() attach_power_transfer_add_r device( andom_tr ) ains() losses_optimization() setup_tps() add_trains() run_powerflow() test_random_trains() tps_power_optimization() setup_trains() attach_power_transfer_device() process_output() losses_optimization() setup_tps() add_trains() run_powerflow() setup_electric_parameters() tps_power_optimization() setup_trains() attach_power_transfer_device() process_output() plot_electric_diagram() setup_tps() add_trains() run_powerflow() setup_electric_parameters() setup_trains() attach_power_transfer_device() process_output() plot_electric_diagram() add_trains() run_powerflow() setup_electric_parameters() attach_power_transfer_device() process_output() plot_electric_diagram() run_powerflow() setup_electric_parameters() process_output() plot_electric_diagram() setup_electric_parameters() plot_electric_diagram() Fig. 6 UML diagram of the resultant implemented simulation model (R ¼ 0:47 X and X ¼ 0:94 X for the PTD trans- other half of current passes through the Z þ Z þ T;ptd T;ptd tps cat former, R ¼ 0:47 X and L ¼ 0 mH for the PTD 2Z þð1 aÞZ impedances. I;ptd I;ptd ptd cat inverter, and the no-load power losses are zero). Then, if the train is only supplied by the TPS1 with a Considering that the PTD operates to perfectly balance current I , the power losses can be estimated: s1 the traction power between the two TPS, then the formu- left : ð2Þ P ¼jI j R þ aR s1 tps cat loss lation of the system power losses can be illustrated in Fig. 8. On the other side, if the PTD forces the division of the Assuming jV j¼jV j, Z ¼ Z and near-equal I s1 s2 tps1 tps2 currents in the two TPS, where I ¼ I ¼ =2, and s1 s2 power factors, with a perfect power balance obtained with considering unitary power factors in TPS1 and TPS2, then: the PTD, the train current is divided in half, and with the jIj left same catenary length of the two branches, this results in the ; ð3Þ P ¼ R þ aR tps cat loss;ptd invariant power losses of Fig. 9 when it concerns to the a value. This constant power losses, P , are the sum of the z þz l r catenary, TPS and PTD losses, where half of the train current is associated to the Z þ aZ impedances, and the tps cat Rail. Eng. Science (2022) 30(1):71–95 78 V. A. Morais, A. P. Martins 30α km 30(1-α) km jIj right : ð4Þ P ¼ R þð1 aÞR þ R þ 2R tps cat cat ptd 30 km 30 km loss;ptd TPS1 Train NZ TPS2 right left left The intersection point, where P ¼ P þ P , can loss loss;ptd loss;ptd be obtained as following: ptd Z α Z (1-α) Z Z cat ptd tps cat R þ R þ R tps cat ptd a ¼ : ð5Þ ~ V s1 I ptd 2R Z Z cat ptd tps cat Then, for the considered assumptions, this results in s2 ~ a 0:6. This value means that the adoption of a PTD with Fig. 8 Formulation of the electric diagram for the one-train reduced the objective of power balancing leads to a minimization of scenario analysis the system power losses if the train is located between a and the NZ. The closer the train is to the NZ, the higher the Fig. 12 presents the results for a new testbed of sce- advantages in terms of the system losses, as expected. narios, where are considered two trains in each TPS branch Fig. 10 presents the evaluation of the difference of the in addition to the parameters of the previous reduced sce- system power losses for the N scenarios of (1). Each point nario simulation. Both trains of all N=10000 scenarios of the graph corresponds to a simulated scenario (without follow the expression in (1). and with the PTD), and the lines represent the equipotential The results after the inclusion of the PTD show final values where the power losses difference (‘‘after-before’’ power unbalance between the two TPS (±0.45 MW, cor- the PTD) is the same. Thus, negative values mean that the responding to 5.5 % of the maximum transferred power), PTD action reduced the power losses in the system. which are caused by the compensation strategy of the PTD. In the simulation results of Fig. 10, it is visible that the Essentially, the simulation framework performs an initial actual a value is close to the theoretic value of a 0:6, 0 0 power flow analysis for both TPS without the influence of from expression in (5). This result is obtained with the the PTD. Based on the difference of power in the two TPS, balancing in the two TPS visible in Fig. 11. this difference is used as a setpoint for the power transfer The previous reduced scenario analysis is useful to device and the simulation framework is subject to a final evaluate the advantages expected from the inclusion of the power flow analysis. Only with an iterative process is PTD. First, it should be highlighted that the major com- possible to reduce the final unbalance, which, in terms of pensation strategy is in the balancing of the two TPS. The implementation, means the need for a feedback loop if a example presented can reduce an unbalance from 8 MW to perfect balance is required. a maximum of 0.45 MW (with the majority of the unbal- A preliminary analysis of the system power losses ance values closer to 0 MW, thus a perfectly balanced before and after the inclusion of the PTD might not justify system in terms of power consumption). the adoption of the power converter. Only in a hypothetical scenario where the majority of trains are located near the NZ (where a [ a ) is justified the adoption of PTD. For (a) obvious reasons, the train position follows a uniform PDF TPS1 TPS2 Power transfer device System power losses as function of train position left MAX(P ) loss Power losses (with PTD) PTD (b) Inverter TPS PTD Catenary impedance ~ transformer Catenary transformer TPS1 Train TPS PTD PTD Inverter Z left tps MIN( P ) =P transformer Catenary impedance ~ transformer loss loss TPS 2 0 1 Fig. 9 Power losses evaluation with and without the inclusion of a Fig. 7 Illustration of the reduced scenario simulation: a physical PTD, for the one-train reduced scenario analysis, as function of the representation; b electric diagram normalized train position (a) Rail. Eng. Science (2022) 30(1):71–95 Power losses (without PTD) System power losses 0 -0.05 -0.15 -0.1 -0.05 Traction power substation balance and losses estimation in AC railways using a power transfer 79 across the entire railway line. Then, as illustrated by system power losses, the advantages of adopting a PTD lie Fig. 10, the majority of the scenarios increase in the system in balancing both TPS. power losses, when comparing the power losses before and after the inclusion of the PTD. When considering the PTD constant power losses, the 5 Monte Carlo analysis results of Fig. 10 are affected by an offset. For example, if these power losses are higher than 0.15 MW, all of the This section presents the details of the simulation scenar- simulation scenarios increase the system power losses. ios, specifically on the input parameters. Considering the This section leads to addressing the two metrics of diagram of Fig. 1, a simplified analysis of the adoption of a analysis when is considered the inclusion of the PTD: the PTD (to improve the railway infrastructure) can consider system power losses and the minimization of unbalance in two catenary branches of two subsequent TPS. the TPS power. For the following sections, any discussion The universe of simulation scenarios must cover several on results must consider an analysis on both metrics. As an parameters variation, such as: example, even if every scenario of analysis increases the • branch number of trains, 2 N; Power losses difference (“after-before” PTD) as function of train 1 position and power Losses (MW) 0.2 0.15 0.1 0.05 -0.05 -0.1 -0.15 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 TPS Train 1 position (percentage of branch length) NZ position position Fig. 10 System power losses difference before and after the inclusion of the PTD, as function of the train position and power consumption with 10 000 scenarios simulated Rail. Eng. Science (2022) 30(1):71–95 +0.05 +0.1 +0.15 +0.2 +0.05 +0.1 +0.05 Train 1 power (MW) 80 V. A. Morais, A. P. Martins (a) (b) 8 8 7 7 6 6 5 5 4 4 3 3 2 2 1 1 0 0 012 4 6 78 012 4 6 78 3 3 5 TPS1 power (MW) TPS1 power (MW) (c) (d) 90 600 60 400 30 200 0 0 012 3 45 7 8 -0.45 -0.4 -0.35 -0.3 -0.25 -0.2 -0.15 -0.1 -0.05 0 Delta TPS power (MW) Delta TPS power (MW) Fig. 11 Simulation results for the N=10 000 scenarios of Eq. (1): a active power in TPS1 and TPS2 before the inclusion of PTD; b Active power in TPS1 and TPS2 after the inclusion of PTD; c histogram analysis of the difference of power between TPS1 and TPS2; d histogram analysis after the inclusion of PTD • branch length, 2 R; With the generation of several random scenarios (where • TPS power profile, 2 R; the parameters follow PDF functions), and the collection of • train power consumption, 2 R; relevant statistics, thus it can be assessed the performance • train power factor, 2 R; of a decision policy or the value of an asset [50], or in this • train position, 2 R; work, the decision of the installation of a PTD. The usage of a specific railway line and a dataset of measurements The surface of this universe of simulation scenarios is, at enable the fitting of the PDF for each of the parameters, as least, S 2 NR . shown in the following statistical analysis. To reduce the universe of simulation scenarios, some assumptions must be made based on the Monte Carlo sta- 5.1 Statistical analysis tistical analysis. Being the Monte Carlo term associated with the process of modeling and simulating a system that In the following, it is considered the relevant characteris- is affected by randomness [50], this analysis requires that tics of a 250 km railway line with seven substations. The each of the parameters follows an appropriate probability first aspect analyzed in this work is on the catenary branch distribution functions (PDF). Rail. Eng. Science (2022) 30(1):71–95 Frequency TPS2 power (MW) Frequency TPS2 power (MW) Traction power substation balance and losses estimation in AC railways using a power transfer 81 (a) (b) 9 9 8 8 7 7 6 6 5 5 4 4 3 3 2 2 1 1 0 0 0123 789 0123 789 4 5 6 4 5 6 TPS1 power (MW) TPS1 power (MW) (c) (d) 140 450 0 0 -8 -6 -4 -2 0 2 4 6 8 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 Delta TPS power (MW) Delta TPS power (MW) Fig. 12 Simulation results for N scenarios of Eq. (1) for two trains: a active power in TPS1 and TPS2 before the inclusion of PTD; b Active power in TPS1 and TPS2 after the inclusion of PTD; c histogram analysis of the difference of power between TPS1 and TPS2; d histogram analysis after the inclusion of PTD length, where the distance of each branch is visible in • Long catenary branch lengths, following a normal PDF Fig. 13. with N ðl ¼ 21; r ¼ 2:5Þ. The branch distance of Fig. 13 does not follow a specific Statistical analysis for the respective clusters is presented PDF: it could be highlighted that the catenary branch dis- in the histogram graphs of Fig. 14. tance is uniformly distributed between 6 km and 30 km. Furthermore, this work considers two types of TPS, each Despite the uniform distribution of the length of the of them having a randomly defined number of trains, and a catenary branch, it would be interesting the analysis of randomly defined power consumption profile. clustered lengths. It could be argued that long lines can The first assumption is to define clusters of types of TPS. have much more branches and, then, a normal PDF func- The rationale behind this assumption is the following: the tion would be appropriate. Then, in this work, two clusters number of trains throughout the day will define the power of line lengths can be defined, where l is the average and r consumption requirements of this TPS. For example, a TPS is the standard deviation, following: covering a dense metropolitan area will be more likely to have more trains and higher power consumption than a • Short catenary branch lengths, following a normal PDF TPS covering a sparse rural area. with N ðl ¼ 15; r ¼ 2:5Þ; Rail. Eng. Science (2022) 30(1):71–95 Frequency TPS2 power (MW) Frequency TPS2 power (MW) 82 V. A. Morais, A. P. Martins • Sparse area, with Poisðk ¼ 0:3Þ; where the Poisson PDF is given by (6) and k is equal to the expected value of k. e k : ð6Þ Fðk; kÞ¼ Branch length (km) k! Then, this can be better illustrated in the fitting bar graph of Fig. 16. Regarding the TPS power consumption, a similar anal- ysis can also be made in Fig. 17. Considering the two clusters of TPS (dense and sparse areas), the power consumption is also directly related to this cluster, as visible in Fig. 17. Based on the available data, the clustered TPS power (b) consumption can be approximated to a log-normal PDF, as follows: • Dense area, with Lognormalðl ¼ lnð5e6Þ; r ¼ 0:75Þ; • Sparse area, with Lognormalðl ¼ lnð1e6Þ; r ¼ 1:00Þ; where the log-normal PDF is given by 1 ðln x lÞ Fðx; ½lrÞ ¼ pffiffiffiffiffiffi exp : ð7Þ 2r xr 2p 0 5 10 15 20 25 30 The histogram of the clustered TPS power consumption T branch length (km) and respective fitting is visible in Fig. 18. As stated, the data of power consumption presented in Fig. 13 a Line geographic relative coordinates (different x and Fig. 18 were fitted to the proposed log-normal PDF. y scales) and b branch lengths (in ascending order) of a 250 km railway line with 7 TPS However, this approximation should be taken with caution, since the performed statistical hypothesis tests from [51]do Short catenary lengths not prove that the data fits the distribution with a high Long catenary lengths degree of confidence. Regarding the train power consumption, from the available data is visible that this parameter does not follow any PDF. Even if the authors in [41] shows a possible fitting of multiple normal PDF, the histogram results of Fig. 19 lack the fitting for specific distribution functions. 8 101214161820222426 28 Then, this work assumes a uniform PDF for the train power Catenary length to comprise the diversity of types of trains present in the Fig. 14 Result histogram of 10000 branch lengths for the two defined dataset of more than 300 train journeys. clusters Regarding the train power factor, from the analysis of all available data, is visible a possible dependence of the train The seven TPS of the 250 km railway line under anal- power factor as a function of the train power, as illustrated ysis have the histogram in Fig. 15 regarding the number of in Fig. 20. trains, after the analysis of an extensive time-window For lower train power consumption values, the train concerning a specified time-table. From the results pre- power factor varies from 0.4 to 1. However, and as sented, two clusters of trains can be considered: expected, for higher train power consumption values, the • Dense area, covered by TPS1, TPS2, TPS6 and TPS7; train power factor is closer to unitary. • Sparse area, covered by TPS3, TPS4 and TPS5. Then, a bivariate PDF is fitted, where the power factor follows a normal distribution function and the l and r The two clusters are presented in the blue bars of Fig. 16. values depend on the train power consumption. Specifi- Based on the available data, the number of trains for both cally, as illustrated in Fig. 21, it was approximated these types of TPS follows a Poisson PDF, defined as: values to sigmoid functions. • Dense area, with Poisðk ¼ 1:4Þ; Rail. Eng. Science (2022) 30(1):71–95 Frequency B Traction power substation balance and losses estimation in AC railways using a power transfer 83 Fig. 15 Frequency of trains in a railway line covered by 7 TPS. The frequency corresponds to the number of seconds of a day where the TPS is feeding t trains (a) (b) 4 5 4 ×10 ×10 ×10 ×10 4.5 3.5 6 8 Data Data Fitted (λ=0.3) Fitted (λ=0.3) 4.0 3.0 3.5 2.5 3.0 2.0 2.5 3 4 2.0 1.5 1.5 1.0 1.0 0.5 0.5 0 0 03 1 2 4 56 03 1 2 4 56 Number of trains Number of trains Fig. 16 Frequency of trains for the two clusters and respective fitting: a dense TPS; b sparse TPS Rail. Eng. Science (2022) 30(1):71–95 Frequency Frequency 84 V. A. Morais, A. P. Martins TPS2 TPS3 TPS1 3500 3500 6000 3000 3000 2500 2500 2000 2000 1500 1500 1000 1000 500 500 0 0 0 05 10 15 0 5 10 15 0 5 10 15 Active power (MW) Active power (MW) Active power (MW) TPS4 TPS5 TPS6 TPS7 4500 4000 2500 2500 2000 2000 1500 1500 1000 1000 500 500 0 0 0 0 0 510 0 510 02 10 0 0 10 20 Active power (MW) Active power (MW) Active power (MW) Active power (MW) Fig. 17 Histogram graph of active power consumption for all 7 TPS of a 250 km railway line The resultant bivariate surface after applying the l and r The first step is to generate a random length cluster, curve values is presented in Fig. 22. following a Bernoulli PDF for each TPS branch, resulting in four equally distributed scenarios: 5.2 Scenario generation algorithm • TPS1 2fshort; longg; • TPS2 2fshort; longg. The previous analysis is essential to define an automatic Then, the length of the branch follows a normal PDF, as scenario generation that covers the universe of possible stated in the l and r values that led to Fig. 14. scenarios of a railway electrification line. Fig. 23 proposes an algorithm to generate a new scenario. Rail. Eng. Science (2022) 30(1):71–95 Frequency Frequency 18 Traction power substation balance and losses estimation in AC railways using a power transfer 85 TPS power histogram Fitted: μ= log(5); σ= 0.75 5 10 15 20 TPS power histogram Fitted: μ = log(l); σ = l 10 11 0 2 4 6 14 TPS power (MW) Fig. 18 Histogram graph of active power consumption for the two clusters of TPS and respective fitting: (a) dense TPS; (b) sparse TPS -1 -2 -3 -4 0123 5678 Train power (MVA) Fig. 19 Histogram graph of all train apparent power consumption. In this histogram, the frequency is in a logarithmic scale Furthermore, the third step is to generate a random type The fifth step is the generation of the TPS total power of TPS, or TPS cluster, following a Bernoulli PDF as well, consumption, which depends on the TPS cluster. Both resulting in four equally distributed scenarios: sparse and dense TPS power consumptions follow a log- normal PDF, where the l and r parameters are the ones • TPS1 2fsparse; denseg; that led to Fig. 18. • TPS2 2fsparse; denseg. Then, this TPS power consumption is associated with From the definition of the TPS cluster, the number of trains the number of trains on the branch, where the power of is generated in step four, based on the Poisson PDF that led each train is generated using a uniform PDF between a to the results presented in Fig. 16. minimum and a maximum, and a final gain is applied to all Rail. Eng. Science (2022) 30(1):71–95 Frequency Frequency Frequency (probability) 86 V. A. Morais, A. P. Martins 1.0 position follows uniform PDF. The type of conclusions to be made should be: ‘‘With the adoption of a PTD, during 0.9 more than 60% of the operation time-frame, the inclusion 0.8 of the PTD leads to an increase of system power losses’’, 0.7 and not ‘‘Only if all trains are closer to NZ during the 0.6 operation timewindow, is justified the adoption of the 0.5 PTD’’. 0.4 The Monte Carlo analysis must consider the analysis of 0.3 0 2 10 12 4 6 8 the two parameters—the TPS length cluster and the TPS Train power consumption (MVA) density cluster—that are fixed for a specific railway line. This analysis allows the identification of the relevant Fig. 20 Evaluation of the train power factor as function of apparent characteristics of a railway line where the study of the power system power losses is essential to support this identifica- tion. The Monte Carlo analysis performed in this work will 1.0 be focused on listing the combination of characteristics of a 0.9 railway line (short or long TPS branches and dense or 0.8 sparse TPS clusters) that contribute to a higher number of 0.7 advantageous scenarios. 0.6 Regarding the number of scenarios necessary to be 0.5 evaluated, let us consider a repetitive simulation of 1000 01 2 34 5 67 8 randomly generated scenarios, throughout 1000 iterations (thus a total of one million scenarios), as illustrated in 0.20 Fig. 24. This figure presents the result metric for the mean 0.15 value of the power loss difference (losses after minus 0.10 losses before the installation of PTD). 0.05 The mean value converges to a power loss difference of 11.62 kW after the inclusion of a PTD. It is visible in the 01 2 34 5 67 8 results of Fig. 24 that if only 1000 scenarios are considered for analysis, the average can vary from 7.33 kW to Train power (MW) 16.97 kW, which might be unacceptable, (±41.5 % max- Fig. 21 Fitting of l and r values of the normal PDF for the power imum error, when compared to the 1 million average). If factor as function of train power there are considered 10 000 scenarios, from Fig. 24, the same value can vary from 10.3 to 12.51 kW (±9.4 % train power consumptions to ensure that the sum of all maximum error, when compared to the 1 million average). individual powers is equal to the TPS power consumption When 100 000 scenarios are considered, the maximum selected in step five. error is reduced to ±1.72 %, from a value variation from Using a normal PDF for each train, step seven generates 11.4 to 11.8 kW. a random power factor using the estimated train power Thus, only with a considerable amount of simulations is consumption and following the l and r parameters that led possible to increase the confidence level on the conclu- to the results in Figs. 21 and 22. sions. The minimum number of simulations required and Finally, for each TPS branch, based on the number of the computational needs to achieve the conclusions should trains and the TPS branch length, the position of each train be appropriately balanced. It could be argued that with this is estimated using a uniform PDF (a minimum distance analysis, the degree of confidence of the results generated between trains is ensured in this phase). through 100 000 scenarios is better than 2 %. Regarding the sigma value, similar convergence con- 5.3 Monte Carlo metrics clusions can be made. Both the average and variance val- ues are also useful to evaluate the percentage of scenarios In previous subsections, all the possible parameters that where the inclusion of the PTD is advantageous, as illus- affect the analysis of the inclusion of a PTD in a railway trated in Fig. 25. line were extensively analyzed. As stated in the previous Since the PTD for the 1 million simulated scenarios is reduced scenario section, the scenarios where the advan- modeled without constant power losses (the PTD only has tages (in terms of system losses) justify the adoption of a conduction power losses), there is a considerable PTD are when the train is near the NZ. However, the train Rail. Eng. Science (2022) 30(1):71–95 σ μ Train power factor Traction power substation balance and losses estimation in AC railways using a power transfer 87 1.0 As example, for the given histogram of Fig. 25, the per- centage value of the advantageous scenarios, Uðx 0Þ,is 0.9 39:7%. The final results presented in the following section are 0.8 obtained with the simulation of 100 000 scenarios (and a different PTD). 0.7 0.6 6 Results and discussion 0.5 012 3 4 5 67 8 This section addresses the evaluation of the PTD inclusion, Train power (MW) for 100 000 different scenarios. In particular, the compar- ison is on the different clusters of TPS and branch lengths. Fig. 22 Resultant randomly generated train power scenarios (active Two different analyses are made with different power power plus power factor) for proposed variable l and r values transfer devices: i) a PTD with typical permanent power losses, with a value of 50 kW corresponding to 20 % of the percentage of scenarios where the PTD is advantageous in total power losses; and ii) a PTD with reduced permanent terms of system power losses. power losses, 25 kW corresponding to 10 % of the total The percentage value of the advantageous scenarios can PTD power losses. The power losses at nominal power are be obtained from the definition of the cumulative distri- the same, 2 % corresponding to 250 kW of power losses bution function for the normal PDF, following: (when the PTD is in nominal operation, transferring 1 l 12.5 MW from one section to the other). Uðx 0Þ¼ 1 þ erf pffiffiffi ; ð8Þ r 2 The results for 100 000 scenarios in the following sub- sections are presented in Tables 1–4, where each row where erfðzÞ is the Gauss error function, given by comprises 10 000 simulated scenarios. Each cell of =2 Tables 1–4 refer to approximately 10000\16 scenarios. erfðzÞ¼ pffiffiffiffiffiffi e dt : ð9Þ 2p Scenario generation algorithm Start 1. Generate random value for length cluster 2. Generate random value for branch lengths 3. Generate random value for TPS cluster type 4. Generate random integer number of trains (based on TPS cluster type) 5. Generate random TPS power consumption (based on TPS cluster type) 6. Generate N random train power consumption (based on number of trains and TPS power consumption) 7. Generate N random train power factors (based on train power consumption) 8. Generate N random train absolute positions (based on number of trains and TPS branch length) End Fig. 23 Algorithm for the generation of a randomly distributed scenario Rail. Eng. Science (2022) 30(1):71–95 Power factor 88 V. A. Morais, A. P. Martins 0.02 0.08 (1000 scenarios) (1000 scenarios) (average: 10 1000 scenarios) (average: 10 1000 scenarios) 0.018 (average: 100 1000 scenarios) 0.07 (average: 100 1000 scenarios) 0.016 0.06 0.014 0.05 0.012 0.01 0.04 0.008 0.03 0.006 0.02 0.004 0.01 0.002 0 200 400 600 800 1000 0 200 400 600 800 1000 Iteration Iteration Fig. 24 Evaluation of l and r values for 1 million simulated scenarios 6.1 Power transfer device with typical power losses • If one TPS has a short branch and is a high density one, and the other TPS has a long branch and sparse density, then the average system power losses difference is near The results were obtained with a PTD with a nominal power of 12.5 MVA , where the total nominal losses are 10 kW higher than the global average (columns 6 and 2 % and 20 % of the total nominal losses are constant ones. 11); Table 1 presents the average of the system power losses • If one TPS has a long branch and high density, and the difference. The global average value is 55.8 kW. This other TPS has a short branch and sparse density, then the means that in the average of the simulated scenarios, the average system power losses difference is around 6.3 kW inclusion of a PTD result in a power balance between two lower than the global average (columns 7 and 10). TPS with the disadvantage of increasing the losses in an In addition to the average value, Table 2 presents the average amount of 55.8 kW. Then, from the results of variance of the system power losses difference. Based on Table 1, further conclusions can be obtained: the application of the expression in (8) using the l and r Unfavourable scenarios Favourable scenarios -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 Power losses difference (MW) Fig. 25 Histogram of the power loss difference values for 1 million simulated scenarios Rail. Eng. Science (2022) 30(1):71–95 Frequency value (MW) value (MW) Traction power substation balance and losses estimation in AC railways using a power transfer 89 Table 1 Evaluation of system power losses difference (after minus before, average, in kW) with and without the inclusion of PTD for different clusters: TPS density and branch lengths TPS1 Dense Dense Sparse Sparse TPS2 density Dense Sparse Dense Sparse TPS1 length Short Long Short Long Short Long Short Long TPS2 length Short Long Short Long Short Long Short Long Short Long Short Long Short Long Short Long Scenario 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 57.8 60.0 59.4 58.1 58.4 68.2 49.8 59.2 56.0 48.6 64.9 57.8 50.6 51.1 51.0 50.7 65.9 61.0 59.4 57.6 57.1 56.9 67.3 47.2 56.4 59.1 47.4 67.0 58.8 50.8 49.9 50.8 50.5 64.1 57.5 57.3 59.3 62.5 58.5 64.8 50.3 56.7 58.2 48.7 64.4 58.6 50.6 50.7 50.6 51.1 62.3 60.4 56.3 55.3 57.6 58.1 67.1 46,9 57.0 54.1 49.3 65.6 59.9 49.9 50.3 50.8 50.3 56.6 58.6 56.6 58.4 57.8 58.3 56.1 65.8 48.8 60.7 56.3 47.3 66.4 58.1 50.9 50.6 50.3 50.2 56.8 57.5 61.5 53.1 59.3 58.6 65.2 48.4 55.7 58.5 51.8 65.6 56.6 50.8 51.0 50.8 50.3 55.0 57.3 55.6 57.1 56.6 57.1 66.0 49.7 56.6 59.4 49.9 68.0 56.2 50.3 50.8 50.1 50.4 53.2 60.0 56.2 57.0 55,4 57.1 64.9 54.9 55.8 57.9 47.8 63.5 55.5 50.5 50.5 50.3 50.2 51.4 56.4 59.1 55.9 60.2 60.3 63.7 49.0 60.0 58.1 52.4 66.2 56.1 50.5 50.8 50.6 50.5 49.5 58.0 58.8 54.6 58.5 59.7 65.8 50.6 52.6 55.6 52.1 65.3 55.1 50.7 51.0 50.7 50.8 Average 57.8 58.2 56.8 58.4 58.1 65.9 49.5 57.1 57.3 49.5 65.7 57.3 50.6 50.6 50.6 50.5 Table 2 Evaluation of system power losses difference (after minus before, variance, in kW) with and without the inclusion of PTD for different clusters: TPS density and branch lengths TPS1 Dense Dense Sparse Sparse TPS2 density Dense Sparse Dense Sparse TPS1 length Short Long Short Long Short Long Short Long TPS2 length Short Long Short Long Short Long Short Long Short Long Short Long Short Long Short Long Scenario 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 40.0 48.7 56.2 54.9 36.5 51.1 41.4 59,0 34.1 43.3 35.4 48.9 5.8 11.9 9.6 54.0 38.1 55.4 45.8 51.2 34.4 42.2 57.1 40,8 39.9 46.2 42.1 53.7 6.2 6.4 10.2 6.0 48.7 34.5 50.7 51.8 57.2 39.5 41.2 46.9 50,2 38.3 45.3 34.2 46.1 5.7 7.0 8.8 13.9 43.4 36.7 44.1 49.9 46.0 29.7 45.4 46.3 45,2 28.6 42.5 41.7 52.2 8.2 6.5 8,3 38.1 7.0 38.7 53.7 45.5 48.3 32.5 42.5 54.5 51,6 27.7 42.4 46.3 42.1 9.2 4.8 6.3 32.8 5.2 6.5 27.5 44.4 71.2 51.9 57.7 28.9 42.1 58.3 46,1 34.7 41.5 44.6 46.9 5.7 13,0 10.5 22.2 34.2 52.0 52.8 51.4 30.6 39.4 45.4 40,1 37.1 46.7 43.8 44.4 5.0 9.7 7.8 8.6 16.9 38.8 51.0 41.2 47.6 32.7 42.7 47.0 47,4 31.8 53.8 39.6 46.5 5.4 7.1 7.6 7.3 11.6 35.8 45.0 45.9 63.4 45.8 36.5 41.6 51,8 37.0 39.5 45.7 46.2 5.3 4.5 8.7 8.8 6.3 38.6 65.0 53.8 62.1 34.4 46.3 43.9 45,8 32.8 44.2 51.3 48.9 6.6 8.0 9.5 7.0 Average 38.0 53.7 49.5 54.0 34.5 43.0 48.2 47,8 34.2 44.5 42.5 47.6 6.3 7.9 8.7 7.7 values from Table 1 and Table 2, respectively, Table 3 – The probability of having favorable scenarios if one of presents the percentage of favorable scenarios where is the TPS is dense is 9.1 % higher than having both TPS advantageous the installation of a PTD in terms of system sparse (columns 5 to 12); – If both TPS are dense, the probability of having power losses. From the results of Table 3, it is identified the best favorable scenarios is 11.6 % higher than having both TPS sparse (columns 1 to 4). scenario (column 7) where the probability of having favorable scenarios is the highest (15.1 %). This scenario is Regarding the clustering associated with the TPS lengths, when TPS1 is dense and long and TPS2 is sparse and short. other conclusions are listed: Then, more limited conclusions regarding the spar- • The probability of having favorable scenarios if both sity/density can be made, as follows: TPS branches are short is 4 % (columns 1, 5, 9 and 13); – Due to the low r values in the scenarios having both • The probability of having favorable scenarios if both sparse TPS, Table 3 shows a near-zero probability of TPS branches are long is 9.2 % (columns 4, 8, 12 and having favorable scenarios (columns 13 to 16); 16); Rail. Eng. Science (2022) 30(1):71–95 6.5 Color scale Color scale 90 V. A. Morais, A. P. Martins Table 3 Percentage of favorable scenarios Uðx 0Þ, where the inclusion of PTD with typical power losses is beneficial for different clusters: TPS density and branch lengths TPS1 Dense Dense Sparse Sparse TPS2 density Dense Sparse Dense Sparse TPS1 length Short Long Short Long Short Long Short Long TPS2 length Short Long Short Long Short Long Short Long Short Long Short Long Short Long Short Long Scenario 1 2 3 4 5 6 7 8 9 101112 131415 16 7.5 10.9 14.5 14.5 5.5 9.1 11.5 15.8 5.0 13.1 3.3 11.9 0.0 0.0 0.0 0.0 15.1% 5.5 14.2 10.4 13.2 4.9 5.5 20.4 8.4 7.0 15.3 5.6 13.6 0.0 0.0 0.0 0.0 13.4% 12.9 12.6 13.7 7.0 5.8 14.2 12.9 6.4 14.1 3.0 10.2 0.0 0.0 0.0 0.0 11.7% 6.3 10.5 12.8 10.5 2.5 7.0 15.6 10.4 2.9 12.3 5.8 12.6 0.0 0.0 0.0 0.0 10.1% 8.4% 7.2 13.8 10.2 11.4 4.2 6.1 18.5 12.0 2.1 13.3 7.6 8.4 0.0 0.0 0.0 0.0 6.7% 9.8 19.4 15.3 15.2 2.1 6.1 20.4 11.3 4.6 10.6 7.1 11.4 0.0 0.0 0.0 0.0 5.0% 4.7 14.3 14.0 13.5 3.1 4.7 13.7 7.9 5.5 14.3 6.0 10.3 0.0 0.0 0.0 0.0 3.4% 6.1 13.6 8.3 12.2 4.0 6.4 12.1 12.0 3.4 18.7 5.4 11.6 0.0 0.0 0.0 0.0 1.7% 5.8 9.5 11.2 17.1 9.4 4.0 11.9 12.3 5.8 9.2 7.4 11.2 0.0 0.0 0.0 0.0 0.0% 17.3 6.6 18.3 15.5 4.1 7.8 12.5 12.5 4.5 11.9 10.1 13.0 0.0 0.0 0.0 0.0 6.4 13.7 12.5 13.9 4.7 6.3 15.1 11.5 4.7 13.3 6.1 11.4 0.0 0.0 0.0 0.0 Average Table 4 Percentage of favorable scenarios Uðx 0Þ, where the inclusion of high-efficiency PTD with reduced constant power losses is beneficial for different clusters: TPS density and branch lengths TPS1 Dense Dense Sparse Sparse TPS2 density Dense Sparse Dense Sparse TPS1 length Short Long Short Long Short Long Short Long Long TPS2 length Short Long Short Long Short Long Short Long Short Long Short Long Short Long Short Scenario 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 19.1 22.6 23.5 24.2 18.1 21.6 21.8 25.3 16.6 19.7 15.1 23.1 0.0 2.8 1.3 0.3 24.2% 17.4 22.3 21.7 22.2 15.6 17.4 26.6 19.9 19.1 23.5 17.7 23.6 0.0 0.0 0.6 0.0 21.5% 19.1 22.6 23.5 24.1 18.1 21.6 21.1 25.3 16.9 20.9 15.0 23.1 0.0 2.8 1.0 18.8% 0.3 17.5 22.2 21.2 22.3 15.8 17.4 27.0 19.9 19.0 22.0 17.8 23.7 0.0 0.0 0.8 0.0 16.2% 13.5% 16.5 22.5 21.6 22.9 18.2 17.0 22.4 22.3 19.1 22.8 14.6 20,.7 0.0 0.1 0.6 5.7 10.8% 18.2 19.6 23.0 20.8 15.5 18.5 24.2 22.2 15.1 22.8 18.3 22.1 0.1 0.0 0.3 0.0 8.1% 17.8 23.9 21.3 22.2 15.0 18.6 25.0 21.6 12.8 23.1 20.0 21.4 1.0 0.0 0.0 0.0 5.5% 0.0 19.4 26.5 24.4 24.5 13.4 18.3 28.0 21.5 17.9 21,.4 19.0 20.1 0.0 4.3 1.8 2.8% 15.8 22.8 24.7 23.3 16.0 15.8 23.5 17.9 18.0 22.9 17.1 20.8 0.0 1.4 0.1 0.3 0.1% 18.2 23.8 19.5 21.1 15.9 19.0 22.2 21.7 16.8 27.3 17.8 20.7 0.0 0.0 0. 0.1 17.9 22.9 22.4 22.8 16.1 18.5 24.2 21.8 17.1 22.6 17.2 21.9 0.1 1.1 0.7 Average 0.7 • If both TPS are dense and if one TPS branch is different 6.2 High-efficiency power transfer device from the other, the probability of having favorable scenarios is 13.1 % (columns 2 and 3); A second analysis was made with a more efficient PTD. • If one TPS is dense and short, and the other TPS is The total nominal losses are still 2 % of the nominal power sparse and long (columns 6 and 11), the probability of of 12.5 MW. The constant power losses are 10 % of the having favorable scenarios is 6.2 %; nominal power losses. • If one TPS is dense and long, and the other TPS is Table 4 presents the percentage of favorable scenarios sparse and short (columns 7 and 10), the probability of where is advantageous the installation of a PTD. having favorable scenarios is 14.2 %. Similar to the analysis made for the PTD with typical power losses, the percentage results in Table 4 show the best scenario being the same (column 7), where the Rail. Eng. Science (2022) 30(1):71–95 4.8 Color scale Color scale Traction power substation balance and losses estimation in AC railways using a power transfer 91 probability of having favorable scenarios is the highest scenarios are the ones where one TPS is dense and long, (24.2 %). and the other TPS is sparse and short (columns 7 and 10) to The conclusions for the sparsity/density are the achieve the highest probability of having favorable sce- following: narios (14.2 % for PTD with typical constant losses, or 23.4 % for highly efficient PTD). • The scenarios having both sparse TPS show an average In an opposite situation, if both TPS are sparse, from the of 0.65 % in the probability of having favorable results achieved, it is expected that the probability of scenarios (columns 13 to 16); having favorable scenarios is residual (near-zero for the • The probability of having favorable scenarios if one of typical PTD, and near 1 % for PTD with reduced losses), TPS is dense is 19.3 % higher than having both TPS leading to the conclusion that, if there is a choice, it is not sparse (columns 5 to 12); justified the installation of a PTD in this cluster of TPS. As • If both TPS are dense, the probability of having visible in Fig. 16, for this scenario, the probability of not favorable scenarios is 20.8 % higher than having both having any train in both TPS can be estimated using the TPS sparse (columns 1 to 4). Poisson PDF for the sparse area. This value is around The conclusions for the clustering associated with the TPS 54 %, wherein in all operation scenarios, the PTD only lengths are the following: accounts for the unfavorable constant losses. Also, in this scenario, the probability of having one train either in one of • The probability of having favorable scenarios if both the TPS branches is around 33 %, and considering Fig. 10 TPS branches are short is 12.8 % (columns 1, 5, 9 and of the atomic scenario, from all of these scenarios, only 13); 40 % of these are advantageous. • The probability of having favorable scenarios if both It should be highlighted that the inclusion of the PTD TPS branches are long is 16.8 % (columns 4, 8, 12 and installation in the railway electrification system leads 16); always to a more balanced railway power supply. Despite • If both TPS are dense and if one TPS branch is different the major focus of the results presented in this paper are on from the other, the probability of having favorable the system power losses, it is clear that once this system is scenarios is 22.7 % (columns 2 and 3); installed, the power demand of the trains in a catenary • If one TPS is dense and short, and the other TPS is branch is distributed among the adjacent TPS. sparse and long (columns 6 and 11), the probability of The compensation strategy illustrated in this work having favorable scenarios is 17.9 %; depends on the measurement of the power consumption in • If one TPS is dense and long, and the other TPS is both TPS. Then, in a practical implementation of this sparse and short (columns 7 and 10), the probability of strategy, it might be required a real-time communication having favorable scenarios is 23.4 %. system to transfer the measurements remotely between When compared to a PTD with typical constant power both TPS and the PTD control system. losses, Table 4 shows a considerable increase in all the Finally, this work does not address the control of the probabilities for having favorable scenarios, as expected. PTD reactive power. As stated in [3], a reactive power This increase is on average 10.5 percentage points compensation device can improve the power quality in the (scenarios 1 to 12, with 1.2 percentage points in standard railway electrification, specifically with the stabilization of deviation). the catenary voltage (allowing to an increase in the Since the constant power losses of this PTD analysis are infrastructure capacity). In the limit scenario presented in 25 kW (half of the typical PTD), if both TPS are sparse [3], the catenary power losses can be reduced by more than (columns 13 to 16), there is a slight increase in the prob- 50 % if the reactive power in the railway electrification is ability of having favorable scenarios (in the neighborhood handled. The practical implementation of the strategy of 1 %). proposed in this work must also consider the management of the reactive power, for improved operation of the PTD 6.3 Discussion system. The analysis previously made is useful if the study of the implementation of a PTD in the NZ is strictly subject to the 7 Conclusion system power losses. If is needed an analysis on the best location to install one PTD from a universe of possible This paper addresses the effects of the inclusion of a Power alternatives, then the first analysis is to evaluate the branch Transfer Device between two sections of a railway line lengths and the TPS density. In particular, when compared based on a Monte Carlo statistical analysis. The main to all possible scenarios, it is concluded that the best analyzed parameters are the active power balancing in the Rail. Eng. Science (2022) 30(1):71–95 92 V. A. Morais, A. P. Martins two substations and the system power losses difference functions. Specifically, the number of trains follows a with/without the installation of the PTD. Poisson PDF, the TPS power consumption follows a Log- The proposed methodology considers a generic electri- Normal PDF and the train power factor is statistically fication where several scenarios can be simulated and dependent on the train active power. where each scenario has several different parameters. The final results of the Monte Carlo analysis show that, From a reduced analysis scenario, the adopted strategy depending on the density of trains and on the branch is capable to balance the power in both TPS with a small lengths, the scenarios where these factors are different for maximum error (5.5 % in the presented analysis). How- the two TPS can result in considerable higher losses if not ever, this TPS power balance is achieved with non-negli- carefully considered. However, the PTD system can always gible system power losses. Specifically, if it is considered balance the two substations, thus implementing double-side an ideal TPS and an ideal PTD (R ¼ 0 and R ¼ 0, feeding and can also reduce the system total losses in some tps ptd resulting in a ¼ 0:5), if the train is in the half of the specific scenarios. branch closer to the TPS, then the adoption of a PTD results in higher losses than if no PTD is installed. Appendix To contemplate a generic scenario coverage, then an extensive statistical analysis was made in this paper, using The graphical user interfaces for the developed framework data and measurements obtained from a 250 km railway line with 7 TPS. It was concluded that some of the are shown in Figs. 26 and 27. parameters follow specific probability distribution Fig. 26 Graphical user interface of the developed framework: random scenario generation menu Rail. Eng. Science (2022) 30(1):71–95 Traction power substation balance and losses estimation in AC railways using a power transfer 93 Fig. 27 Graphical user interface of the developed framework: definition of electric parameters for the catenary electrification and the PTD Acknowledgements This research was funded by FCT (Fun- dac¸a¯o References Cieˆncia e Tecnologia) under grant PD/BD/128051/2016. The research is also associated with the Shift2Rail In2Stempo project (grant 1. International Energy Agency (IEA) and International Union of 777515). This work was partially supported by FCT R&D Unit Railways (2017) Energy consumption and CO2 emissions focus SYSTEC—POCI-01-0145-FEDER-006933/SYSTEC funded by on passenger rail services. FEDER funds through COMPETE2020 and by national funds through 2. Pilo E, Mazumder S, Franco I (2014) Railway electrical smart the FCT/MEC, and co-funded by FEDER, in the scope of the PT2020 grids: an introduction to next-generation railway power systems Partnership Agreement. and their operation. IEEE Electr Mag 2(3):49–55 3. Morais VA, Afonso JL, Carvalho AS, Martins AP (2020) New Open Access This article is licensed under a Creative Commons reactive power compensation strategies for railway infrastructure Attribution 4.0 International License, which permits use, sharing, capacity increasing. Energies 13(17):4379 adaptation, distribution and reproduction in any medium or format, as 4. 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Railway Engineering Science – Springer Journals
Published: Mar 1, 2022
Keywords: Electric traction systems; Monte Carlo analysis; Power transfer device; Power quality; Railway power systems; Smart railways
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