Influence of Infrastructure and Operating Conditions on Energy Performance of DC Transit Systems

Abstract

Energy efficiency is more and more important for modern electrified transportation systems, requiring an understanding of the various indexes of performance (regenerability, receptivity, and energy losses, thus including braking recovered energy and energy loss in catenary) and of the influence of the main system parameters (headway, line voltage, substation separation, etc.). By means of electromechanical simulation, the most relevant parameters and system conditions are identified as influencing the efficiency performance and optimization capability. Besides the assessment of such efficiency performance indexes, identifying their typical ranges of variation, one further outcome is the identification of characteristic system parameter combinations that lead to extreme variations in the system energy efficiency itself. Such peculiar variations are caused by occasionally synchronized patterns of trains along the line and result in a significant local increase or decrease in efficiency. Efficiency drop scenarios in particular should be taken into consideration for worst-case analysis and to devise effective mitigations. To this aim, the effect of differently distributed passenger stations is considered.

1. Introduction

Modern electrified transit systems have explored different solutions to reduce the overall energy consumption of the transportation system [1,2,3,4,5]. On the one hand, traction energy consumption can be reduced to optimize the vehicle powertrain (e.g., improving on-board converters and mechanical parts for coupling and friction) or reducing vehicle resistance to motion through aerodynamic optimization and weight reduction [6]. Overall, it is demonstrated in [7] using improved experimental data and modern vehicles can provide statistically relevant energy savings. On the other hand, a better exploitation of regenerative braking energy can be achieved by means of energy storage systems [2,3] and reversible traction power substations (TPSs) [8], controlling train operations and driving profiles [9], practically exploiting the scheduled service time reserve [10], and even including cases of timetable disruption [11]. The latter, in particular, represents a high-level solution that does not require major changes to the infrastructure and can be implemented in the automatic train operation (ATO) subsystem for metros and the supervision center or the operation and control center (OCC) for railways [12,13,14,15,16]. Trains receive the parameters for driving to the stations ahead from information points (e.g., balises or radio tags) or from a continuous radio coverage system (e.g., CBTC or other train-to-wayside radio links). These parameters are based on a set of pre-calculated speed profiles for station-to-station routes, so that the system performance and energy consumption depend on optimized ATO speed profiles [12,16]. These can be selected to adapt to major changes in traffic scenarios, but in rare cases, they can follow traffic conditions in real time [17].

In general, the energy-efficient optimization of vehicle operation in transportation systems deals with energy conservation and in electrified transit systems in addition to the limitation of traction phases [13], which is mainly reflected in the utilization of regenerative braking energy [18]. Regenerative braking techniques have been largely adopted worldwide for several years now to convert vehicles’ kinetic energy into electric energy. Regenerated energy can be fed back to the traction supply network and used by other nearby running trains in the same supply section, reducing the overall energy consumption. Otherwise, energy may be fed back to reversible TPSs (feeding back the AC utility) and storage systems [19,20,21,22] (particularly useful if the country’s local regulations allow energy discounting [23]). As a last option, energy may be dissipated on large on-board resistors [24] to safely limit the pantograph voltage excursion (line voltage limits for European systems appear, e.g., in the EN 50163 [25]).

Recent research on energy conservation and on the optimization of regenerative braking energy [4,26,27,28] can be grouped in two categories: optimized braking control strategies and techniques to increase system receptivity. The former aim to increase the energy regenerated during braking, control the applied torque of traction motors [29,30], or optimize braking force distribution [31,32], thus modifying the vehicle braking speed profile. Detailed models of the onboard traction drive system have been proposed, which are applicable to a wide range of operating conditions [33], and have then been integrated with the entire traction grid, even for complex supply schemes [34]. Regenerative braking optimization is related to the more general speed–trajectory optimization problem, since the train speed profile is a direct consequence of the applied torque.

Even if the optimized braking speed–effort curves can increase the total regenerated braking energy, this does not necessarily reflect in the improvement in the global system energy efficiency. Techniques for increasing system receptivity aim to maximize the fraction of energy available for recovery that, after being subject to unavoidable constraints, is actually recovered and reused within the transportation system or fed back to the utility.

The receptivity factor is influenced by several parameters (as can be seen in [35] for a dc rail transit case). System receptivity, for example, depends on the mutual interaction between vehicles (energy flow between vehicles, generated by regenerative braking) and on the power supply system characteristics (e.g., longitudinal voltage drop, short circuit power, use of bidirectional substations, catenary voltage limits). To improve the overall energy efficiency of the system by increasing the receptivity, different methods were proposed and analyzed in the past [5,36,37,38]: selecting the electrification voltage level and fine tuning of the no-load voltage, reducing the traction conductor impedance and optimizing bonding and feeders, using of reversible substations and energy storage systems, etc.

In particular, the available power to and from the overhead contact wire can be increased by employing parallel feeding circuits and cross-connections, reducing the “electrical distance” between regenerating and absorbing vehicles [1]; this is, in fact, a not-so-invasive solution that can be gradually implemented in an existing system and which is often implemented when an increase in fleet and traffic is planned. Conversely, a reduction in the resistance of large cross-section conductors, such as the third rail and running rails, may be quite expensive in terms of the amount of required copper for paralleling cables. Running rails may instead be optimized at the design stage, observing that, for the same mechanical properties, there are types of rails with significantly lower electrical resistance [39].

Additionally, the integration of energy storage systems can lead to an increase in system receptivity, reducing the dependence of the effective regenerated braking energy on the instantaneous condition of traffic and power transmission network [40,41,42,43].

Improvement is also achievable by controlling train operations [11,44,45] in order to increase the probability of the presence of nearby powering vehicles when regenerative braking energy is available for regeneration. If the speed profile of each train is known, it is possible to increase the synchronization between absorbing and regenerating vehicles, adopting energy-efficient timetables by controlling train headway and dwell times at each station stop [9,46,47]. These techniques can be applied, in particular, when the control of the entire speed profile of running vehicles cannot be achieved. Otherwise, an overall traction control for the entire train route is absolutely preferable for generality and flexibility [13,16,48].

The problem of train operation control in an electrified transport system involves nonlinear large-scale and complex equations with stochastic and operational constraints [49]. Thus, the optimal speed trajectory may be found with non-deterministic optimization methods, such as genetic algorithms or other random search techniques [13,14,50,51]. Since algorithms are generally computationally intensive, the calculation of consumed traction energy and receptivity is often achieved by applying simplified power supply network models or a limited number of degrees of freedom in the train trajectory and traffic quantities. Nevertheless, when the energetic analysis aims to evaluate the overall system energy efficiency, the accuracy of some percentage already has a significant economic impact when applied to the yearly power consumption bill [52].

In these circumstances, the integration of an effective model for the calculation of traction energy and for the analysis of the power flow including train operation and control can lead to better energy exploitation and improvement in traffic control, both for system design and real-time control. The electromechanical simulation of the complete transit system [37,53,54,55,56,57,58,59] can help develop these models and accurately analyze the system energy efficiency, especially for the identification of critical configurations and their impact on system efficiency. Electromechanical simulation is a known method combining the mechanical equations of train movement and electric network equations, the latter setting the way electric power is delivered to trains at their respective current collection points.

In this paper, the energy efficiency of electrified transportation systems and the influence of some system parameters are analyzed: the main parameters for the evaluation of the regenerative capability and receptivity of the system are introduced and described, and the discussion is then extended to the system’s operational parameters affecting the amount of regenerative braking energy and receptivity. In particular, the effect on the system energy efficiency of the variation in service headway time is considered using a random dwell time added to station stops in order to obtain reliable estimates from the statistical point of view, also taking into account slight variations in patterns due to unavoidable and unforeseeable delays. The analysis is then extended to cover the power supply distribution scheme (varying feeding conductors’ cross-section and line no-load voltage) and network layout (varying passenger station locations). The objective is to understand the impact of each parameter by analyzing the observed effects resulting from a significant number of simulations so to have statistical significance.

The analysis is based on a realistic system simulation using a multi-train and multi-line traction and traffic simulator [55]. It was developed to simulate AC and DC traction systems for a wide range of phenomena in a user-friendly environment, as described in [56], (particularly stray current propagation [55] and induction phenomena). It has the capability to include regenerative braking and can evaluate the system energy efficiency [52].

The organization of this paper is as follows. In Section 2, the main energy efficiency parameters (specifically regenerability and receptivity) are thoroughly discussed, clarifying schemes either for the calculation of such indexes at the vehicle level, for a given time interval with one single operating condition taking place, or at a higher level in aggregated form. Section 3 presents the model of the transit system that is used for the analysis, having selected a geometry that is not too complex to facilitate the interpretation of the results and the observed behavior; it also shows the reference scenarios used for the analysis. Section 4 then reports and discusses the simulation results provided in separate subsections for each set of tests, for example, focusing on the influence of each individual system parameter introduced.

2. Energy Consumption and Efficiency Indexes

Due to the nonlinearity of regenerative braking, the assessment of energy consumption and related efficiency needs to include the absorbed energy, the energy available to return to the system, and the energy flow actually occurring between different vehicles for the various operating scenarios of the particular transit system. Two indexes are usually defined to evaluate the total energy consumption and the regenerative braking energy that is actually regenerated [60,61]: regenerability and receptivity.

2.1. Regenerability

Regenerability is the measure of the total recoverable kinetic energy that may be recovered as regenerative braking energy (in other words, the potential saving provided by the regenerative braking process) [8], which mainly depends on the vehicle speed profile and physical characteristics. A similar name appears in [62]: regenerative efficiency as the ratio of the regenerative energy (better called “used regenerative energy”) and the electrical braking energy, thus addressing the effective use of the available regenerative energy. Similarly, [58] provided the utilization factor that measures the percentage of used braking energy with respect to the total braking energy available.

A first estimation of regenerability can be achieved by only considering the kinetic energy involved in the braking phase. In order to compare the different transit systems and operating scenarios in a general perspective, the system regenerability index G_E is defined as the ratio between the total recoverable kinetic energy, considering all running vehicles, and the total system energy consumption over a period of time:

$$G_E={\displaystyle \sum _{k=1}^T\left({\displaystyle \sum _{i=1}^T{\overline{p}}_{a_i}\Delta t_k}/\left({\displaystyle \sum _{i=1}^{n_k}{\overline{p}}_{r_i}\Delta t_k}+{\displaystyle \sum _{j=1}^{n_{TP{S}_k}}{\overline{p}}_{TP{S}_j}\Delta t_k}\right)\right)}$$

(1)

where ${\overline{p}}_{a_i}$ and ${\overline{p}}_{r_i}$ are the average available and the actually generated regenerative braking power terms (not considering the energy burnt in the vehicle on-board rheostats, if any) of the i-th braking vehicle, respectively, ${\overline{p}}_{TP{S}_j}$ is the average generated power of the j-th traction substation, $n_k$ and $n_{TP{S}_k}$ the number of braking vehicles and the number of in-service Traction Power Substations (TPS) at the k-th instant, respectively, $\Delta t_k$ is the duration of the k-th time step, and T is the number of time steps required to span the entire time interval. If $\Delta t_k$ is small enough, then instantaneous powers may be considered instead of the average power values ${\overline{p}}_{a_i}$, ${\overline{p}}_{r_i}$, and ${\overline{p}}_{TP{S}_j}$.

On the one hand, ${\overline{p}}_{a_i}$ purely depends on the vehicle speed profile (i.e., the vehicle dynamics) that determines the recoverable kinetic energy. On the other hand, ${\overline{p}}_{r_i}$ and ${\overline{p}}_{TP{S}_j}$ depend on many other parameters, including the type, location, and state of vehicles and TPSs, as well as train-set characteristics (e.g., physical characteristics, powertrain efficiency and control, on-board auxiliaries), power system layout, and configuration. For a specific scenario or set of operating conditions, regenerability assesses the theoretical recoverable regenerative braking energy and indicates the potential saving of the considered system with respect to the total system energy consumption, which is calculated considering both the energy drawn from TPSs and the regenerated braking energy during vehicle operations.

2.2. Receptivity

The receptivity index can quantify the energy efficiency of a transit system, which is a measure of the fraction of power available for recovery that, after unavoidable constraints, is actually used. Various definitions have been applied for receptivity by various researchers [6,22,60,61]: receptivity may be defined first of all in terms of power or energy, and then calculated either at a single TPS or train, or for the whole transit system. In this work, receptivity is defined as the ratio of the braking energy that is actually regenerated to the recoverable kinetic energy, both calculated using pantograph quantities.

For the purpose of energy efficiency assessment, two receptivity definitions introduced by Forsythe [61] may be considered: one describes the instantaneous receptivity r_i in terms of the available regenerative braking power per vehicle; another (more useful to quantify energy saving) applies to a given set of system operating conditions, either instantaneously (in terms of power) or over a period of time (in terms of energy).

The instantaneous vehicle receptivity (IVR) r_i for the i-th braking vehicle is [61]:

$$r_i=p_{r_i}/p_{a_i}$$

(2)

where $p_{a_i}$ and $p_{r_i}$ are the instantaneously available and actually generated regenerative braking power terms of the i-th braking vehicle at any instant of time.

As for ${\overline{p}}_{a_i}$ and ${\overline{p}}_{r_i}$ in (1), the available regenerative braking power $p_{a_i}$ quantifies the maximum recoverable kinetic power, while the actually regenerated braking power $p_{r_i}$ does not consider the energy burnt in the i-th vehicle on-board rheostats. IVR is not particularly useful for global energy-efficiency analysis since it evaluates the fraction of regenerated energy for a single running vehicle. Equation (2) can be extended to a multi-train scenario, considering a set of system-wide operating conditions (i.e., the configurations of traction supply network and track, and the location and operating conditions of running vehicles).

Considering the j-th system operating conditions, the system instantaneous receptivity R_j is [61]:

$$R_j={\displaystyle \sum _{i=1}^{n_j}{p}_{r_i}}/{\displaystyle \sum _{i=1}^{n_j}{p}_{a_i}}$$

(3)

where n_j is the number of braking vehicles in the considered j-th system operating conditions.

The aggregate system receptivity (ASR), R_k, calculated considering different system-wide operating scenarios organized in different “cases”, is [61]:

$$R_k={\displaystyle \sum _{j=1}^{N_k}{\displaystyle \sum _{i=1}^{n_j}{p}_{r_i}}}/{\displaystyle \sum _{j=1}^{N_k}{\displaystyle \sum _{i=1}^{n_j}{p}_{a_i}}}$$

(4)

where N_k is the number of samples of the k-th case, and each case collects a set of scenarios with essentially constant operating conditions.

The computation of (2) per vehicle and (3) per system operating condition determines the range of variation of receptivity. ASR can then be estimated by repeating the calculation over a representative number of different operating conditions, accounting for their relative weight (i.e., frequency of occurrence, as already observed by Forsythe with different words).

Considering a correct and adequate time interval embracing several operating conditions, it is also possible to define receptivity in terms of energy rather than average power:

$$R_E={\displaystyle \sum _{k=1}^T{\displaystyle \sum _{i=1}^{n_k}{\overline{p}}_{r_i}\Delta t_k}}/{\displaystyle \sum _{k=1}^T{\displaystyle \sum _{i=1}^{n_k}{\overline{p}}_{a_i}\Delta t_k}}$$

(5)

where quantities are the same as in (1). If $\Delta t_k$ is small enough, (5) can be rewritten more compactly as:

$$R_E={\displaystyle \sum _{k=1}^T{\displaystyle \sum _{i=1}^{n_k}{r}_i\Delta t_k}}$$

(6)

This is the definition of receptivity that is used then in Section 4 to evaluate the various operating scenarios and the influence of system parameters, basing its estimation on the system-wide average quantities taken for the duration of the simulation.

Receptivity depends on many parameters related to the vehicle characteristics and operation, such as:

• Train operation frequency (headway time—HT);
• Type, location, state of the other trains;
• Power consumption of the train-set auxiliaries;
• Nominal braking deceleration;
• Curve of braking effort vs. velocity;
• Efficiency of on-board converters.

Additionally, power system configuration, TPS locations and distances, the line resistance/impedance seen at the pantograph, and as a consequence, the longitudinal voltage drops, selected nominal line voltage, short-circuit power level, and the allowed line voltage variation [25] also all have considerable effects on the receptivity index. Moreover, the relationships between system parameters and receptivity cannot be simply defined since the system quantities influence each other and the equations are nonlinear.

2.3. Aggregate Energy Efficiency Quantities

A third energy efficiency index may be defined at the system level: the product of regenerability and receptivity, RR = G_E × R_E, is calculated over a certain time interval. This quantifies the ratio between the actually generated regenerative braking energy and the total system energy consumption, thus assessing the total energy saving as a consequence of the system’s regenerative capability. This quantity makes the pair with the energy saving percentage calculated in [37] looking at the substation consumption for the two cases of systems without and with regenerative braking, as it implicitly takes into account the effectively used regenerative braking energy.

Considering (1) and (6), the time interval for calculation should be chosen to assure data consistency and to allow the comparison of results from different scenarios in terms of headway, the mean speed of running trains, and other operating parameters. With “data consistency”, it is not only intended that a sufficiently large set of data points are collected from simulations, but also that train operating conditions and distribution patterns along the line are repeated a sufficient number of times to avoid singular cases. In this work, for the results in Section 4, the time window is chosen to have an approximately constant number of simultaneously running trains: an early “warm-up” pre-simulation is performed before each test to fill the traction line with the correct number of running trains and reach the desired nominal configuration.

In addition, some other quantities, which effectively represent the normalized system performance for energy-efficiency analysis, are considered to evaluate and discuss the simulation results in Section 4: (i) the overall system energy consumption calculated at the TPS level; and (ii) the joule losses of the power supply network. To ensure data consistency and allow the comparison of results from different scenarios, instead of absolute values, energy consumption and system losses are normalized, and expressed with respect to the number of running vehicles and the total traveled distance. Thus, two related quantities are introduced and provided in the results in Section 4:

• The energy consumption per running vehicle and distance, EC_RVD, is the ratio between the overall system energy consumption calculated at the TPS level (including the traction energy and all power supply network losses) and the number of current running vehicles and total vehicle running distance in km;
• The system energy losses per running vehicle and distance, EL_RVD, is the ratio between the joule losses calculated for the power supply network (including losses in the catenary, return circuit, and TPSs) and the number of current running vehicles and the total travelled distance in km.

Finally, another energy efficiency index may be defined: with no powering trains nearby, regenerated braking energy contributes to the increase in line voltage up to the maximum allowed level. This energy, which we define as the system traction line energy (STLE) E_TL, can be calculated as:

$$E_{TL}=E_{TPS}+E_r-E_{lost}-E_{tr}$$

(7)

where E_TPS is the total energy supplied by TPSs, E_r is the total energy regenerated by running vehicles during braking, E_lost is the total energy lost in the distribution network, and E_tr is the total energy absorbed by trains. E_TL represents a fraction of the receptivity which is more related to the network (infrastructure) than to the running trains, and, as for EC_RVD and EL_RVD, can be expressed as a specific value vs. the number of running vehicles and the total traveled distance.

3. Modeling and Simulation

3.1. Electromechanical Simulator Architecture

The used electromechanical simulator integrates two main modules, namely the electric traction network (ETN) and the rolling stock (ROS), controlled by an overarching traffic module (shown in green in Figure 1) sharing an approach that is common to other electromechanical simulators. The overall simulation process is depicted in the flowchart of Figure 1.

The electromechanical simulator was named “traXsim” and has been used for some projects and publications [55].

The structure is quite general and similar to other electromechanical simulators. The structure is in reality more complex, containing functions for sensitivity analysis to parametric changes (such as temperature and ageing), which are not shown because they are irrelevant to the present problem.

3.1.1. Traffic Module

This module arranges and manages all elements related to train movement within the infrastructure and the interaction with the signaling system: the headway time, station stops, speed limits, minimum distance between trains, etc. In other words, it implements a simplified set of ATO, ATC, and ATP functions. For the purpose of this work, it is not detailed further and it is shown in Figure 1 as an external block controlling the movement of the trains along the network.

3.1.2. Electric Network Module

The ETN module represents the kernel of the electrical subsystem and is based on an electric network representation based on distributed parameters using multi-conductor transmission line (MTL) equations. The electrical simulator (ETN module) was validated against measurement results taken at various sites with various techniques [63] with advanced techniques to assess the curve similarity [64]. The use of MTL equations is evidently excessive if the scope is limited to DC power flow and DC quantities, but the simulator was originally designed for the solution of problems of induction [65] and harmonic propagation [66]. The followed approach could thus suitably include all electric network conductors and is applicable to an extended frequency range (considering the electrical parameters of conductors and the equivalent circuits of equipment and machines available up to several tens of kHz, including information from experimental data and the possibility of correcting the internal expressions based on specific data for a site). A simplified model with equivalent conductors may be adopted to accelerate simulations when the analysis is limited to power supply phenomena at DC (as in the present case) or a fundamental frequency (16.7, 50, or 60 Hz).

3.1.3. Rolling Stock Module

The ROS module in the traction mechanical subsystem is made of an electric and a mechanical sub-module: motion equations implement the train resistance to motion using train parameters and track information as detailed below, and then the interface with the electric sub-module determines the pantograph electrical quantities, e.g., in terms of absorbed power and current given the available line voltage information.

The ETN module actually feeds the train operating conditions back to the ROS electric sub-module and then to the mechanical sub-module, allowing to control conditions of insufficient or excessive voltage at the pantograph (e.g., activating traction power reduction and passing from regenerative braking to electric dissipative braking or mechanical braking). Train movement is applied with a conveniently fast simulation time (usually in the order of 0.1–1 s, but without limits to its reduction), interfacing with a simplified traffic management and signaling system module to regulate traffic and avoid collisions.

In general, the train movement along a route is ruled by the motion equations resulting from Newton’s second law of motion, implemented in its dynamic model. This is a common approach [45,62] at various levels of detail for the fed parameters. Train dynamics combine many force terms, first of all traction and braking effort, and then train resistance to motion and equivalent mass that include rotating mass. Propulsion during traction overcomes all resistance terms in order to accelerate the train; conversely, braking applied to the wheels decelerates the train by opposing the stored kinetic energy. When in motion, the overall train and rotating parts (wheels, shafts, axles, etc.) store kinetic energy, so that the equivalent mass of the train m accounts not only for the static (or “classical”) mass, but also for the rotating mass [67].

Whereas the acceleration/deceleration of train mass (on the right-hand side of (10)) and change in potential energy on a sloped track (represented by the term RF_i below in (8)) are well known from physics, resistance to motion is more complex and depends on both train and track characteristics: the term RF below is the train motion resistance, better detailed in (9), and RF_ρ quantifies the effect of track curvature.

$$R{F}_i=mgi$$

(8)

Track curvature effects are difficult to precisely quantify: curves with radii that are larger than approximately 250 m are commonly considered negligible; in general, a linear relationship with a practical coefficient k_tc is usually adopted, as provided by Profillidis [68]:

$$R{F}_{\rho }=0.01\left(\frac{k}{R_{tc}}\right)$$

(9)

where RF_ρ is in kN/t and assumes a gravity acceleration value of approximately 10 m/s², k_tc is dimensionless and varies in general from 500 to 1200, and R_tc in m is the horizontally measured curve radius.

$$TE\left(v\right)-RF\left(v\right)-R{F}_i\left(i\right)-R{F}_{\rho }\left(\rho \right)=m\frac{dv}{dt}$$

(10)

The traction or braking effort TE is in N (Newton); RF, RF_i, and RF_ρ are all expressed in N; m is in kg, the train speed v in m/s, the track grade i in % and the track curvature radius ρ in m.

The train resistance force RF depends on speed with a universally accepted relationship involving up to second-order terms, known as the Davis equation, using the so-called Armstrong–Swift coefficients A, B and C, for constant, linear, and quadratic dependency on the train speed v:

$$RF=A+Bv+C{v}^2$$

(11)

The terms A and B include all static resistance terms and dominate at low speed (≤30 m/s, i.e., approximately 100 km/h), whereas the quadratic terms account for aerodynamic effects and become dominant at higher speed [53,69].

3.1.4. Train Movement and Simulation

The traction subsystem calculates the actual train speed trajectory and running time, while ensuring the fulfillment of speed limits and stop accuracy, as well as any traffic constraint in the case of multi-train simulation. The simulator fully implements train and track characteristics, such as adhesion limitation, and limits on acceleration, jerk, and maximum traction or braking effort.

The train model employs a mixed representation considering a single point to calculate the vehicle dynamics and a segment to determine the speed limit, accounting for train length and its track occupation, and ensuring that the entire train complies with speed limits. Train dynamics can be determined for the whole route by applying either a “time increment method” or a “distance increment method” to solve the dynamic model equation [14]; this is possible by assuming “RF” terms and dynamic train quantities that are constant within a simulation step (details are contained in [14]).

3.1.5. Simulator Validation and Accuracy

The simulator accuracy is not of paramount importance in the present context as the analysis is carried out in a comparative perspective, so that inaccuracy is reflected almost uniformly across cases, so that such errors (or deviations) would compensate at some extent in the final comparison. Nevertheless, the absolute reliability of the numeric results provided is dutiful, as in all scientific works.

A validation activity was carried out in 2014–2015 when a draft of the EN 50641 standard was available [70]. The reference cases were those indicated by the standard, and for the present work, we especially considered the 3 kV railway case. Without reporting all the details, the 3 kV test case provided by the EN 50641 saw a given track layout and trains of the high-speed, suburban and freight type, for which the necessary characteristics were provided, including tractive effort curve characteristics, auxiliaries power, efficiency, train mass values, and Davis coefficients. The 300 mm² equivalent cross-section of the catenary system used as reference in this work was implicitly derived by the indications of the standard. A synthesis of results is shown in

Table 1. Synthesis of validation results against the 3 kV test cases of the EN 50641 (draft) of 2014.

Train No.	Trav. Time (s)	Umean-useful (train) (s)	Average Voltage over Zone (V)
			0–10 km	10–20 km	20–30 km	30–40 km	40–50 km
101 (HS)	1021 [1008–1050]	3191.1 [3140–3335]	3150.8 [3059–3248]	2856.3 [2758–2928]	2432.2 [2421–2571]	3081.7 [3037–3225]	3474.2 [3436–3639]
102 (HS)	1020 [1009–1051]	3195.8 [3158–3354]	3344.6 [3277–3479]	2471.7 [2392–2539]	2821.5 [2722–2891]	3120.6 [3094–3286]	3176.8 [3025–3212]
103 (HS)	1021 [1012–1054]	3191.4 [3142–3336]	3150.4 [3040–3228]	2943.0 [2795–2967]	2511.8 [2405–2554]	3081.9 [3037–3225]	3472.1 [3432–3644]
104 (HS)	1020 [1010–1052]	3188.7 [3150–3344]	3313.3 [3169–3365]	2473.3 [2417–2567]	2723.1 [2599–2760]	3109.7 [3057–3247]	3171.7 [3025–3212]
201 (SUB)	1983 [1930–2008]	3331.6 [3292–3496]	3398.4 [3220–3420]	3237.1 [3047–3235]	2890.4 [2743–2913]	3415.3 [3350–3557]	3466.9 [3401–3611]

.

Accuracy is generally good with selected simulation output values falling within the prescribed tolerance intervals of the EN 50641 (2014), namely a ±3 % around an average value.

3.2. Reference Scenarios for Simulations

All simulation tests were performed considering a double-track 750 V DC urban light rail system shown in Figure 2. Each line, with two opposite running directions, has a total length of 11 km, but the analysis is focused on a central line section of 4.5 km, serving 12 passenger stations (six stations in each direction).

The system is fed by four TPSs (2.6 MVA each), ensuring a power density of approximately 0.9 MVA/km (and approximately 0.7 MVA/km, in case of one TPS failure); the power is delivered to the vehicles through a 300 mm² overhead catenary distribution system. The allowed voltage levels along the line are set as prescribed by the EN 50163 [25] (i.e., between 500 V and 900 V, for a 750 V DC line). The main characteristics of the simulated traction line are reported in

Table 2. Main characteristics of the reference transit line.

Model Parameter	Value
Total length	11 km
Number of passenger stations	12 (6 per track)
Mean distance between passenger stations	900 m
Number of TPSs	4
TPS rating	2.6 MVA
Nominal line voltage	750 V DC
Actual no-load line voltage	825 V DC
Power supply distribution system	300 mm2 overhead catenary (Cu)
Overhead catenary resistance	59.3 mΩ/km
Return circuit resistance (track)	18.6 mΩ/km

.

Each running vehicle consists of a bidirectional four-car fixed train-set, with a nominal power of 4 × 100 kW and an overall length of approximately 50 m. The traction effort curve and the resistance to motion of the considered vehicles on a flat track are shown in Figure 3, while Figure 4 shows the service planning diagram of the reference scenario for a service headway time of 90 s (the headway time is indicated in the following by the quantity HT). Each train run is characterized by the so-called “flat out” operation, i.e., the train runs at maximum speed without violating the system constraints (as said, adhesion limitation, limits on vehicle acceleration, jerk, maximum traction, and braking effort).

The track layout was intentionally chosen to be as simple as possible: the double-track line is straight and flat with constant speed restrictions and evenly spaced passenger stations. The simple layout allows one to analyze the influence of different operational and electric network parameters on energy efficiency indicators and on the overall energy consumption, assuring a regular pattern of the station-to-station speed profile of running trains. Then, small variations in the running speed profiles are introduced and compared to the reference scenario.

A random dwell time, DT between 0 and 5 s is added to the constant stop time (ST) of 25 s at each station using a uniform distribution. Random quantities were used to verify the robustness and stability of the solutions and how critical the synchronization between vehicles is for the overall system behavior and its energy efficiency. Each configuration is thus analyzed by repeated simulations and some indexes are evaluated by means of their statistical estimates using a Monte Carlo approach. For statistical consistency, dispersion and robust estimates (based on trimmed mean) are reported.

4. Simulation Results on Test Cases

Besides analyzing the headway time influence, a few parametric changes are applied, such as the catenary cross-section, nominal no-load line voltage, and station distribution, to verify the effect on system efficiency. The tests whose results are reported and discussed in the following are summarized in

Table 3. List of the test cases and expected results.

Test Identification	Analyzed Parameters	Expected Results	Section/Figures
(A) Headway time	60–510 s	- Overall system efficiency robustness to slight HT variations - Low HT provides higher receptivity.	Section 4.1
(B) Catenary cross-section	250–600 mm2	- General improvement in receptivity for larger cross-section	Section 4.2
(C) No-load line voltage	750–825 V	- Increase in receptivity at lower voltages due to larger margin regarding maximum line voltage - Energy losses correspondingly increase due to larger current	Section 4.3
(D) Passenger stations distribution along the line	100–300 m shift regarding even distribution	- Reduction in “resonance effect” of system energy efficiency indexes - Reduction in dispersion of such indexes calculated for randomly distributed dwell time	Section 4.4

.

4.1. Variation of the Service Headway Time

In metro and urban railway systems, trains are dispatched with an assigned time interval between them, namely the service headway time (HT), which is constant in various parts of the day following a pre-assigned timetable. In general, HT varies from approximately 70–90 s for very tight headway scenarios to several minutes and is often considered a quality-of-service indicator. On the other hand, small variations in the stop time at stations caused by passenger operations can affect the service headway regularity (called dwell time, DT, and added to the station stop time, ST). The adjustment of the overall stop time at stations is a common practice to maintain HT regularity independently of other system constraints (e.g., related to the traction performance and signaling commands) [71].

A first energetic analysis is performed to assess the effect of the headway time on the energy efficiency parameters introduced in Section 2 and on the overall system energy consumption. Simulation tests are carried out for 55 different HT values, ranging from 60 s to 510 s. HT = 60 s corresponds to the maximum train frequency compatible with the signaling constraints and safety distance between trains. At the other end of the HT interval operation with HT = 510 s, only two running trains are involved, one per track, from the first to the last station, within the simulation time window. Using a random DT at each station stop, for each HT value, simulations are repeated 20 times.

In general, a low HT implies a high train frequency and increases the probability of concomitant vehicles with different operating modes (i.e., traction and braking mode) in the same line section. Thus, a lower HT is expected to provide higher values of receptivity and lower values of the energy consumption per running vehicle and distance EC_RVD.

Figure 5a shows the value of the receptivity index calculated for different HT values. From the first simulations, significant variability of the results was noticed for small variations in HT and DT; for this reason, robust statistics are adopted, including the calculation of mean values trimming out a given percentage of outliers (the so-called “trimmed mean”). Figure 5b shows the trimmed mean of receptivity values, excluding 20% of outliers data for each HT value. The actually recovered braking energy varies from 100% down to approximately 75% of the totally recoverable kinetic energy for the varying service HT. Figure 5 reveals significant fluctuations in the receptivity and large dispersion of data for most HT values. The large dispersion of receptivity values is caused by the random DT at station stops. This behavior suggests that even small dwell time perturbations can significantly affect the system receptivity. In addition, the combination of some HT values of the distance between stations and of the train speed profile may result in the concomitant presence of vehicles with complementary operating modes or with the same operating mode, boosting up or dropping down the resulting receptivity and causing the observed fluctuations. These significant fluctuations that are dependent on infrastructure and operating conditions may be named “system resonances” (in Figure 5a,b, the receptivity drops approximately every 100 s of HT). However, most of the high receptivity values correspond to relatively low HT values, and for large HT values, the fluctuations are less noticeable (as clearly shown in Figure 5b, receptivity tends to decrease with increasing HT). This is confirmed by the analysis of EC_VRD for different HTs.

The specific energy supplied by TPSs clearly increases for an increasing HT, suggesting that a high operation frequency corresponds to the more efficient exploitation of the available energy (see Figure 6a). Nevertheless, the energy consumption also shows significant fluctuations, especially for low HT values. As with receptivity, some HT values correspond to unfavorable operational conditions (as in this case, peaks of energy consumption occur approximately every 100 s of HT).

As shown in Figure 6, the available kinetic energy (identified by regenerability) varies from approximately 25% up to 70% with respect to the overall system energy consumption, when plotted vs. HT. The regenerability tends to decrease for increasing headway, suggesting that, at least for the considered scenario, energy losses in the traction line become significant (with respect to the available kinetic energy) if the operating frequency is reduced and the trains are thus on average farther away.

Additionally, as for receptivity and EC_VRD, regenerability shows significant fluctuations and some HT values lead to much lower values. These HT values identify unfavorable operational conditions (in terms of the vehicle distribution, location, and operating mode) from the viewpoint of recoverable energy exploitation. This is confirmed by the calculated energy losses (see Figure 7) observing the peaks in energy loss caused by a particularly large distance between the vehicles exchanging the regenerated power.

During vehicle braking, the simulator ROS module controls the braking effort at the wheels, switching from regenerative braking to dynamic or mechanical braking, if the voltage at the pantograph exceeds the maximum allowed traction line voltage. The different vehicle operating modes (speed profile and vehicle dynamics) during the train run result in a significant fluctuation of pantograph voltage values, as shown in Figure 8 for different HT values imposed on the transit system: the voltage increases at braking, and voltage visibly deeply drops when the acceleration occurs. The fluctuation of the pantograph voltage clearly decreases with increasing HT, since the probability of concomitant vehicles in powering mode loading the same line becomes smaller.

With no powering trains nearby, the regenerated braking energy contributes to the increase in the system traction line energy (STLE) and the line voltage up to the maximum allowed level, as described in Section 2. The specific STLE, expressed per vehicle per km, and shown in Figure 9, clearly increases with the increasing HT: for a high train frequency, most of the regenerated energy is absorbed by nearby trains, while, for larger HT values, the fraction of regenerated energy recovered for traction decreases due to the lack of nearby powering trains, thus increasing the traction line energy, E_TL. The STLE calculation thus supports the correct quantification of the terms contributing to the system’s receptivity.

The total energy savings due to the regenerative capability of the considered system can be finally assessed considering the product of regenerability and receptivity RR, as shown in Figure 10. The actually generated regenerative braking energy varies from 70% to 20% of the total system energy consumption for varying HT and random DT. As with the regenerability index, the behavior of RR is characterized by significant fluctuations, suggesting that, even a small HT perturbation can cause significant variation in the actually regenerated braking energy. Nevertheless, RR clearly tends to decrease with the increasing HT and the fluctuations are less noticeable.

4.2. Variation of the Traction Line Equivalent Cross-Section and Resistance

The analysis of the energy-efficiency parameters for variable HT and random dwell time DT at the stations is repeated for different power supply distribution schemes. In particular, three different overhead catenary systems other than the aforementioned 300 mm² catenary system, are tested and compared. Overhead catenary distribution systems with the Cu equivalent cross-sections of 250 mm², 300 mm², 450 mm², and 600 mm² (with the contact and messenger wires in electric parallel) are considered. Figure 11 and Figure 12 show the fitting curves for receptivity and specific energy consumption, EC_RVD (per vehicle per km), respectively. Fitted curves are obtained by applying the “smoothing spline” method of the Matlab^® Curve Fitting Toolbox.

System receptivity tends to increase with the equivalent overhead catenary section, and consequently, the system energy consumption decreases. For large catenary cross-sections, the traction supply line resistance decreases, reducing voltage drops across the catenary as well as the average current drawn through the catenary conductors. This behavior is confirmed by the analysis of the energy losses on the power distribution network. Figure 13 shows the energy losses per vehicle per kilometer for different HT values, varying the overhead catenary equivalent section.

Each curve in Figure 13 has the same behavior: peaks in the system energy consumption are aligned at the same HT, even for different catenary cross-sections. In the same way, the relative minima of the four curves share approximately the same HT values. This confirms that relative minima and maxima in energy consumption curves correspond to a particularly favorable and unfavorable combination of operational conditions and the layout of the transit network; such “system resonances” can be identified and defined at the design stage and they are quite independent in the power distribution network (the same is observed in the next section for line voltage variations).

The energy loss clearly decreases with the increasing cross-section. Consequently, the ratio between the actually generated regenerative braking energy and the total system energy consumption tend to decrease with the reduction in the catenary equivalent cross-section.

4.3. Variation of the No-Load Line Voltage

Considering the TPS no-load output voltage value V_TPS,noload, a common practice is to set the actual value approximately 10% higher than the nominal value, “pumping up” the little available power, or in other words, preventing unavoidable voltage drops. Energy efficiency indexes are then analyzed for variable HT and random DT with different TPS no-load output voltage values of 750 V, 775 V, 800 V, and 825 V.

Figure 14, Figure 15 and Figure 16 show the fitted receptivity index, energy consumption, and energy losses curves, respectively. A lower V_TPS,noload increases receptivity since the difference between the mean line voltage and the maximum allowed line voltage level (that is fixed) increases and there is more room for regenerative braking to increase the traction line energy (as can be seen in Figure 14). On the other hand, a lower average line voltage level increases the current absorbed by vehicles (drawn traction power being equal), impacting on line losses, as confirmed by Figure 16. The system energy consumption per vehicle per km vs. the no-load TPS voltage is approximately constant, as shown in Figure 15. This behavior suggests that the increase in system receptivity is nearly completely balanced by increased energy losses on the traction line due to the higher absorbed current intensity.

4.4. Variation of the Track Layout (Passenger Stations Locations)

Local minima and maxima of the energy quantities show a repetitive pattern that we have called “system resonances”: they are now further analyzed, disturbing the regular pattern of passenger stations (thus acting on the infrastructure) which, for the reference scenario, are evenly distributed every 900 m. Some passenger stations are shifted, also changing the station-to-station speed profiles of the running trains as a consequence. The total length of the track and the total number of passenger stations per line is the same for all scenarios, thus keeping constant the mean distance between stations. Two different track layouts (called S01 and S02) derived from the reference scenario are considered. The location of passenger stations—relative to the position of the first station of each line, namely STN01 and STN07—are reported in

Table 4. Location of stations in the examined scenarios of line layout variation.

Passenger Stations	Ref. Scenario S00	Scenario S01	Scenario S02
STN01	0 m	0 m	0 m
STN02	900 m	1000 m	1000 m
STN03	1800 m	2100 m	2100 m
STN04	2700 m	2700 m	2700 m
STN05	3600 m	3600 m	3600 m
STN06	4500 m	4500 m	4500 m
STN07	0 m	0 m	0 m
STN08	900 m	900 m	600 m
STN09	1800 m	1800 m	1800 m
STN10	2700 m	2700 m	2800 m
STN11	3600 m	3900 m	3900 m
STN12	4500 m	4500 m	4500 m

. Passenger stations from 01 to 06 are on the first track, and the remaining stations (from 07 to 12) are on the second track (with opposite traffic direction). The S01 and S02 scenarios do not aim to represent a more realistic use case with respect to the reference scenario: their objective is to disturb the initial regular pattern of passenger stations in order to further analyze the effect of stop locations on the identified system resonance.

The fitted curves of receptivity and EC_RVD are shown in Figure 17 and Figure 18, respectively. Figure 17 shows significant differences in receptivity for the considered scenarios due to variations in speed profiles caused by the changes in station locations and consequently in the inter-station journey. Figure 18 reveals some variations in the system resonance positions on the HT axis, confirming that local minima and maxima mainly depend on the combination of operational conditions and transit network layout.

Trimmed mean (excluding 20% of outliers) and standard deviation were calculated for all scenarios: when “disturbing” the regular pattern of passenger stations, receptivity dispersion seems to decrease and the curves flatten, suggesting that, with the irregular track layout, “system resonances” are less critical. This is confirmed by comparing the insets of Figure 19, showing receptivity and its standard deviation (by error bars) vs. HT for the three scenarios S00, S01, and S02 of Table 4. Error bars in Figure 19b,c are smaller on average than in Figure 19a.

An irregular station pattern seems to lead to smoother system resonances; however, it does not mean that system resonances are less critical in a real case. Other track properties (e.g., track profiles and different speed restrictions) affecting vehicle resistance to motion also influence the regenerated and absorbed power, as well as the mutual interaction between vehicles. Nevertheless, for the considered scenarios, the variation in station locations tends to reduce the time intervals with concomitant vehicles with the same operating mode (i.e., powering or braking) and the overall excursion of receptivity: we see a reduction in the spread in the 100–300 s HT interval from the 0.16–0.17 of Figure 19a to 0.13–0.14 of Figure 19b and to less than 0.10 in Figure 19c. Then, not only is the spread reduced, but the receptivity minima are increased, with a positive impact on the worst recoverable energy performance (improving from 0.78 to 0.81 and 0.83). At the same time, we must acknowledge that the maximum attained values are also somewhat reduced, but only by approximately 0.02.

5. Conclusions

Electromechanical simulation is a necessary step in any study of the energy efficiency in electrified transit systems, when different operating conditions and infrastructure elements must be considered, including their mutual influence. The regenerative capability and receptivity of the system are introduced and evaluated with respect to a selected set of operating and infrastructure conditions: the headway time between trains, no-load line voltage, catenary cross-section, and passenger station distribution. These are, in the authors’ opinion, the most relevant system-wide parameters at the design stage, which are thus also a useful suggestion for designers. Other system efficiency indexes are also considered, such as the product of regenerability and receptivity, system energy consumption, and line losses per vehicle per km.

The study was carried out by means of an integrated electromechanical simulator that includes the mechanical and electrical modules of running vehicles, supplied and interconnected by the traction supply network. The running vehicles interface with the traction supply line, absorbing and exchanging power during acceleration, coasting, braking, as well as catenary and substation losses. The statistical consistency of each analyzed condition is tested by applying a random dwell time added to each station stop. Such dwell times not only simulate variability due to contingency (e.g., due to passengers’ behavior), but are also effective means of testing the robustness of a solution.

In the several considered cases, it was observed that synchronization between vehicles in complementary operating conditions (acceleration and braking) is quite relevant for a significant exchange of regenerated energy, which is also influenced by voltage drops and losses in the traction supply circuit; the farthest trains are effectively involved in the energy exchange if catenary resistance and losses are conveniently low. Parametric curves of the energy efficiency indexes are reported for the considered system conditions.

The analysis revealed that there are combinations of system parameters (infrastructure, operating and service conditions, power supply) that have an impact on the overall energy efficiency and lead to a decrease in system energy efficiency (e.g., receptivity and regenerability values), increasing the specific energy consumption (EC_RVD). Such conditions occur repeatedly for short and long headway times (HT), influenced by a counterproductive synchronization of running trains that was called “system resonance”. Due to the mutual interaction between different system parameters, finding a relationship between a specific operating parameter (such as headway time) and the presence of a system resonance is not a straightforward task. However, the efficiency drop may be significant, especially at low headway times when receptivity values are at maximum. Its identification and evaluation by electromechanical simulation should be carried out as early as possible to support the high-level system design, allowing to verify and optimize both service times as well as average and maximum power consumption for supply circuit design and energy efficiency for the optimization of system operation.

The analysis suggests that system efficiency should be evaluated, exploring a wide range of operating conditions, introducing disturbing variables (such as random dwell time at station stops) for uncertainty and variability evaluation and ensure that the normal operating conditions are sufficiently far from the identified system resonances. In other words, a random dwell time is not only useful to replicate usual contingency during stops at stations, but also to demonstrate the robustness of a reached optimization point.

More specifically, as expected, the improvement in the traction supply distribution by reducing the catenary system resistance generally has a beneficial effect on the improvement un receptivity and reduction in losses. Conversely, the reduction in the no-load substation voltage improves the receptivity (giving a greater margin for braking with respect to the maximum allowed line voltage), but at the same time increases line losses, because keeping the absorbed power unchanged (keeping the same performance between cases), the lower voltage correspond to larger line currents.

Future research directions are the addition of new system parameters that may be relevant to the assessment of the variability of energy efficiency indexes. A significant work is being carried out on this subject with regard to energy storage systems that could be, however, considered as add-ons rather than elements of a traditional DC transit. Additionally, the analysis of more complex transit networks is an important step to test such considerations in more realistic scenarios, for example, including junctions and mixed traffic (e.g., commuter and regional or long-distance trains).