Size, Efficiency, Reliability, and Cost Analysis of a Multiport Traction Inverter With Downsized DC–DC Converter for a Catenary/Battery Tram

The use of a neutral-point-clamped (NPC)-type multilevel converter as a multiport inverter (MPI) has recently been considered a promising solution for the compact integration of multisource systems in various applications. Despite increasing research interest in this topic, a comprehensive study of an MPI-based power conversion system for multisource rail applications is still lacking in the literature. This article presents a broad analysis of a quasi-single-stage (QSS) propulsion system that employs an NPC-type MPI and a downsized boost dc–dc converter for an urban tram vehicle with overhead line connection and onboard batteries. The control and dynamic performance are detailed and validated experimentally. Furthermore, the efficiency, weight, volume, reliability, and cost of the QSS system are evaluated and benchmarked against a conventional architecture for a case-study catenary/battery tram model. To this aim, analytical design equations, manufacturers’ data, electrothermal time-domain simulations, finite element method (FEM) simulations, and Monte Carlo-based lifetime analyses are employed. The analysis reveals that the QSS system can achieve significant savings in volume, weight, round-trip energy efficiency, and higher reliability due to intrinsic redundancy, but with increased part count, complexity, and cost.

Size, Efficiency, Reliability, and Cost Analysis of a Multiport Traction Inverter With Downsized DC-DC Converter for a Catenary/Battery Tram Emanuele Fedele , Diego Iannuzzi , and Ivan Spina Abstract-The use of a neutral-point-clamped (NPC)-type multilevel converter as a multiport inverter (MPI) has recently been considered a promising solution for the compact integration of multisource systems in various applications.Despite increasing research interest in this topic, a comprehensive study of an MPI-based power conversion system for multisource rail applications is still lacking in the literature.This article presents a broad analysis of a quasi-single-stage (QSS) propulsion system that employs an NPC-type MPI and a downsized boost dc-dc converter for an urban tram vehicle with overhead line connection and onboard batteries.The control and dynamic performance are detailed and validated experimentally.Furthermore, the efficiency, weight, volume, reliability, and cost of the QSS system are evaluated and benchmarked against a conventional architecture for a case-study catenary/battery tram model.To this aim, analytical design equations, manufacturers' data, electrothermal time-domain simulations, finite element method (FEM) simulations, and Monte Carlo-based lifetime analyses are employed.The analysis reveals that the QSS system can achieve significant savings in volume, weight, roundtrip energy efficiency, and higher reliability due to intrinsic redundancy, but with increased part count, complexity, and cost.

I. INTRODUCTION
T HE use of battery energy storage systems (BESSs) in light rail vehicles (LRVs) has seen a significant increase in recent years [1].Onboard batteries can efficiently store the braking energy and release it when required, reducing the total round-trip energy drawn from the feeding line [2].Furthermore, the BESS gives driving autonomy on segments lacking electrification or during emergencies [3].Thus, battery hybrid trams benefit from higher round-trip energy efficiency, lower current absorption from the feeding line, and reduced need for electrified infrastructure [4].The authors are with the Department of Electrical Engineering and Information Technology, Università degli Studi di Napoli Federico II, 80125 Naples, Italy (e-mail: emanuele.fedele@unina.it;iandiego@unina.it;ivan.spina@unina.it).
Digital Object Identifier 10.1109/TTE.2023.3333379 In hybrid LRVs running under a 750 V dc catenary, the dc-link is at the catenary voltage and supplies the traction drive, which is predominantly based on the two-level voltage source inverters (VSIs) topology [5], [6].Researchers and manufacturers have proposed some variants employing multilevel neutral-point-clamped (NPC) traction inverters [7], [8], but for regional trains operating in 1.5-3 kV dc or 15-25 kV ac systems.The onboard storage devices are at a lower voltage and are connected to the dc-link through bidirectional dc-dc converters [9], [10].In this typical configuration, often called semiactive, the dc-dc converter processes all the power drawn from the BESS and must be sized according to its peak power rating.Since the storage system is involved mainly in the acceleration and braking phases [5], a converter with a high current rating is needed.High current ratings require bulky inductors and capacitors, increased power losses, and a larger cooling system.However, the volume and weight of the converters are frequently restricted by vehicle design constraints and must be considered with care [11].
The NPC-MPI is derived from the NPC multilevel circuit by replacing the dc-link capacitors with dc sources.It enables the transfer of power from two dc sources to the ac side through a single power conversion stage.Like other multiport converters, it is considered a promising interface for multisource integration [23], where it can be used alone, i.e., in singlestage layout, or in conjunction with downsized boost dc-dc stages, i.e., in quasi-single-stage (QSS) layout.The idea of employing an NPC-type converter as a multiport converter is not novel, and there are many studies in the literature that have investigated its application for renewable energy generation and multisource propulsion systems.An NPC-MPI in a singlestage configuration was analyzed and experimentally verified in [24] for a solar photovoltaic (PV)/battery hybrid system.However, despite extensive experimental evaluation, weight and volume savings in the MPI topology were not evaluated.In [25], an active NPC-MPI was evaluated for the integration of a BESS with a dc voltage source.The work presented a detailed discussion of control and modulation issues and provided a comparison with other standard configurations regarding the current stress on the IGBTs and diodes.However, the improvements in efficiency and power density of the single-stage NPC-MPI were not quantified.Similar findings were obtained in [26] for the single-stage integration of batteries and PVs with an NPC-MPI, where only dynamic aspects related to the modulation and control of the converter were considered.The QSS connection of a BESS to the grid through an NPC-MPI and a downsized boost converter was further analyzed in [27], [28], [29], and [34], in which experimental evidence of efficiency improvements in the QSS system was reported.However, the system under analysis was of a single-source type, with the BESS being the only source connected to both ports of the MPI.In addition, no quantification of the weight and volume improvements over a conventional semiactive architecture with cascaded dc-dc and dc-ac converters was conducted.The adoption of the NPC-MPI in a QSS configuration for battery electric vehicles and plug-in hybrid vehicles was first proposed and analyzed in [30] and [31], where several control modes were proposed and verified on a small-scale prototype, and the reduction in the peak power of the dc-dc converter was estimated for several driving cycles.However, no estimates of weight and volume savings in the filters and heatsinks of the downsized dc-dc converters were presented.In the field of rail propulsion systems, a single-stage NPC-MPI was proposed for a battery tram in [32].However, the work mainly focused on the feasibility of the concept and the proposal of an MPI modulation strategy, while the dynamic operation of the system under a real-case mission profile of the tram was not analyzed.Furthermore, no consideration of the size and efficiency of the MPI was given.The same architecture was further analyzed in [33], where the influence of the BESS voltage level on the MPI power processing capability was highlighted.However, no evaluation of volume and weight savings enabled by the MPI was performed.To the best of our knowledge, hardly any other research work has so far dealt with the NPC-MPI for a hybrid LRV and has evaluated the power losses, round-trip energy efficiency, volume, weight, and wear-out characteristics of an MPI-based QSS propulsion system.The authors have already presented the integration and control of the NPC-MPI in a QSS architecture for LRVs [35].However, a broader assessment of the QSS topology including size, reliability, and cost was beyond the scope of the work.
A summary of existing papers on the NPC-MPI is presented in Table I.All contributions address modulation and control issues of NPC-MPI converters in multisource systems for stationary and transportation applications.However, many research works do not adequately assess the potential advantages of this topology, and a comprehensive study of the efficiency, size, and reliability improvements achieved by the NPC-MPI in a real multisource rail vehicle has not yet been conducted.Furthermore, virtually all research works dealing with the NPC-MPI assume a magnetic-less configuration with filter capacitors at the MPI dc ports.However, second-order filters are the preferred option for medium-to high-power ratings and are always used in rail propulsion systems [6].The impact of an additional second-order filter at the MPI low-voltage (LV) port on the system weight and volume has never been considered and should be addressed.
To fill these gaps, this article presents a comprehensive analysis of a QSS propulsion system that employs an NPC-MPI and a downsized boost dc-dc converter in terms of efficiency, size, reliability, and cost.The analysis is based on Bombardier's Flexity 2 catenary/battery tram model and relies on a detailed estimation of the VA rating, power losses, weight, volume, and reliability characteristics of the power converters by means of analytical design equations, manufacturers' data, time-domain and finite element method (FEM) simulations, and Monte Carlo simulations.The results show that, for the tram model in question, the MPI-based QSS system can achieve a 13% reduction in volume and a 19% reduction in the weight of passive filters and cooling heatsinks.Furthermore, the overall conversion efficiency is improved, with round-trip energy losses reduced by 22%.The wear-out unreliability of the entire power conversion stage is also improved, thanks to the inherent redundancy provided by the QSS configuration.These benefits come with a 5% increase in the total cost and a higher system complexity.

TABLE II MAIN DATA OF THE CATENARY/BATTERY TRAM
The article is organized as follows.Section II introduces the QSS system architecture.In Section III, the modulation and control of the power converters and BESS in the QSS system are detailed.Section IV shows the experimental results collected from small-scale laboratory tests.Section V details the system design and comparison methodology, while Sections VI-VIII present the size, efficiency, reliability, and cost comparison results.The conclusion is drawn in Section IX.

II. SYSTEM ARCHITECTURE
The catenary/battery tram model has a pantograph connection to the overhead 750 V line and onboard Li-ion batteries and can operate in catenary and catenary-free modes [4].Its main parameters are reported in Table II.The traction system in each of the two motored cars is shown in Fig. 1(a).It has a semiactive configuration, in which the catenary is directly attached to the dc-link supplying the traction drive, while the BESS is integrated through a bidirectional dc-dc converter.Since the dc-dc converter processes all of the BESS power, its current rating matches the maximum battery current, which has adverse effects on the converter power density.Moreover, the BESS power is processed in cascade by the dc-dc converter and VSI, which reduces the overall power conversion efficiency.LC filters across the dc-link mitigate high-frequency current harmonics and low-frequency voltage harmonics caused by the onboard switching converters and diode rectifiers in the feeding substations, respectively [6].
The replacement of the VSI with an NPC-MPI results in the QSS system shown in Fig. 1(b).The BESS is directly connected to the MPI LV port, whereas a downsized dc-dc converter can be employed for connection to the MPI highvoltage (HV) port.In fact, since part of the total BESS power is drawn from the MPI LV port, the dc-dc converter is partially bypassed and its power rating and cycling can be reduced.Notably, an additional LC filter is included at the MPI LV port to filter the switching harmonics from the BESS current.

III. QSS SYSTEM CONTROL
The control scheme of the catenary/battery QSS propulsion system consists of different layers: the control and modulation of the MPI and dc-dc converter, the coordination between the two converters, the high-level management of the BESS, and the control of the traction motors.The overall scheme is shown in Fig. 2. Motor control can be of any type and is not detailed because it does not alter the general control concept of the QSS system.Similarly, the dc-dc converter power control loop is of standard type and is not further discussed.The other control sections need further detail and are outlined below.

A. MPI Control and Power Regulation Characteristics
In the MPI, the catenary voltage and the BESS voltage appear at the MPI HV and LV dc ports, respectively, and there is no neutral point.Therefore, unlike a three-level NPC converter, there is no issue related to voltage balancing, and the main goal of the MPI modulation technique is to achieve the desired dc power distribution in conjunction with the ac current Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.control.Based on the NPC converter topology, proper selection of the switching states in each phase allows connecting either of the two dc sources to the ac side [23].When S 3k and S 4k are on, none of the dc sources supplies the kth ac output node.When S 2k and S 3k are on, the BESS is connected to the ac side.When S 1k and S 2k are on, the catenary is connected to the ac output node.Similar to the complementary switching of top and bottom devices in a two-level VSI, the switches S 1k -S 3k and S 2k -S 4k on the kth leg are complementary, i.e., they are driven by complementary gate signals, to avoid dclink short-circuits.
Among the different NPC-MPI modulation schemes presented in the literature, the multiobjective vector modulation proposed in [36] is considered due to its simple implementation and wide power regulation capability.The modulation utilizes a common carrier and two modulating signals per phase, which are derived based on the space-vector model of the NPC-MPI and appropriate zero-sequence component injection.The power regulation ratio (PRR), defined as is introduced, since the MPI linear modulation limits depend on this ratio rather than on p LV,mpi and p ac separately.In fact, the admissible area of PRR with respect to the peak lineto-line ac voltage vll resulting from the considered MPI modulation technique are shown in Fig. 3.The analytical expressions of the limit curves are also reported in the graph, where E b and E c are the instantaneous BESS and catenary voltages.Similar PRR-to-voltage regulation domains have been found for different modulation schemes [24], [27].Within the admissible range, the PRR can be varied to obtain flexible control of the magnitude and direction of dc and ac power flows.However, the PRR is significantly affected by the voltage level of the BESS, the catenary, and the traction motor.
As the ac voltage increases with motor speed, the ability to extract power from the BESS directly through the MPI LV port decreases.

B. MPI and DC-DC Converter Coordination
A coordinated control must allocate the total BESS power between the dc-dc converter input port and the MPI LV port to compensate for the limits of the MPI power regulation and draw the desired power from the BESS.The control should reduce the power processed by the dc-dc converter while ensuring that the BESS power is at its reference level.To achieve this, a rule based on the limit curves of the MPI PRR is implemented.By defining the reference BESS power ratio k * p as the BESS power reference divided by the ac active power it follows that when k * p is inside the PRR admissible range, all the BESS power flows through the MPI LV port while the boost dc-dc converter is inactive, i.e., When k * p is outside the PRR admissible range, the maximum power flows through the MPI LV port, and the remaining power is processed by the dc-dc converter Since the PRR limits vary with the motor voltage, BESS voltage, and catenary voltage, the calculation of p * mpi,LV and p * dcdc must be continuously updated even if the total BESS power reference p * b remains constant.

C. BESS Power Control
In a catenary/battery tram, the BESS is typically used to limit the current of the pantograph during acceleration and recover the maximum amount of energy during braking [6].This twofold control objective is achieved by the BESS power control block shown in Fig. 2, which consists of an excludable outer current control loop and an inner voltage control loop.During traction, the current controller (CC) is active and produces the HV dc-link reference voltage that limits the pantograph current to the maximum value i (max) c .When the vehicle brakes, the voltage of the HV dc-link is regulated to the reference value E * c,br .In either case, a voltage controller (VC) processes the HV-bus voltage error and produces the BESS power reference, which is then split between the dc-dc and MPI LV ports according to the coordination rule.
Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.

A. Setup Description
A small-scale laboratory test bench was built to experimentally validate the performance and control of the QSS catenary/battery traction drive.The rig is shown in Fig. 4 and consists of a diode bridge rectifier as a nonreceptive catenary, a BESS, MPI, and dc-dc converters, and an induction motor connected to a high-inertia flywheel set.The digital control runs on a dSPACE ds1103 platform.The main bench parameters are reported in Table III.The system voltage levels were selected by multiplying the voltage levels found onboard the catenary/battery Flexity 2 tram by a common factor, in order to preserve the MPI PRR characteristics with respect to the full-scale system.Specifically, based on the 250 V battery pack available in the laboratory, the rectifier voltage was set to 350 V to maintain the 750-530 V catenary-tobattery voltage ratio found on the full-scale tram (see Table II).All dc and ac currents and voltages are acquired by the dSPACE unit for control and monitoring.The control scheme matches the diagram shown in Fig. 2, with the catenary current limit set to 3 A and the braking voltage reference set to 355 V to reverse-bias the diode bridge during braking.

B. Dynamic Waveforms
The experimental waveforms of the QSS system over a typical traction cycle are shown in Fig. 5.The MPI correctly controls the motor dq currents during constant torque and fluxweakening operations.When the catenary current reaches 3 A during acceleration, the BESS starts to discharge.At this time, the ac voltage vll is lower than the BESS voltage E b , and the BESS power is managed entirely by the MPI while the dc-dc converter is not used.A few seconds after the crossing point between vll and E b , the MPI PRR limit is approached, and the MPI duty cycles reach the unity peak value.Consequently, the dc-dc converter begins to conduct.On the HV dc-bus, the flow of current in the dc-dc converter reflects a corresponding increase in the current of the MPI HV port.During cruising, the low power required from the BESS is compliant with the PRR limits, so that only the MPI is enabled while the dc-dc converter is bypassed once more.At the start of braking, the catenary power drops to zero and the battery recovers all the power generated by the motor.Since ac and dc power flows change rapidly, a zoomed-in view of this transient interval is also shown in the graphs.In the first instants, the braking power exceeds the MPI PRR limits, and a negative current flows through the dc-dc converter.However, the ac voltage vll soon falls below the BESS voltage E b , the dc-dc converter current drops to zero, and the MPI regains full capacity to recharge the BESS exclusively through the LV port.

C. Performance Indexes
To quantify the performance of the QSS system, two indices are introduced.The first index α i is the ratio between the absolute maximum currents of the dc-dc converter and BESS It quantifies the reduction in the dc-dc converter current, which impacts the size of the filters and the rating and stress of the switches.The test revealed a value of α i = 0.63, indicating a 37% decrease in the current rating of the dc-dc converter.The second index α E is the ratio between the roundtrip absolute energy delivered by the dc-dc converter and by the BESS It quantifies the reduction in round-trip energy processed by the converter in the QSS system, which affects the total heat generated due to power losses and hence the size and weight of the cooling heatsinks.The test resulted in a value of α E = 0.26, indicating a 74% decrease in the round-trip energy processed by the dc-dc converter.
V. METHODOLOGY

A. Design Procedure
The general procedure is shown in Fig. 6 is implemented to design the power converters in order to estimate and compare their size, efficiency, reliability, and cost.In each system configuration, the vehicle data and driving cycle profile are used to calculate the average currents in the traction circuit and obtain mission profiles for the dc-dc, MPI, and VSI converters.Specifically, a driving profile is considered that includes six stops for a total length of 2 km, with a two-stop nonelectrified section of 700 m on which the tram is powered exclusively by the BESS.A dwell time of 20 s is considered at each stop.The converter mission profiles are then used to size the semiconductor modules, filters, and heatsinks of each power converter, based on which the VA ratings, weight, volume, and cost are calculated.The detailed electrothermal model of the system (considered switching behavior, temperature evolution, and stray losses in filters) is ultimately simulated with Simulink1 and PLECS 1 blockset to calculate the power losses for the efficiency analysis and the thermal stress on the components for the reliability analysis.

B. Mission Profiles and Sizing Specifications
The input and output current profiles of the inverter and dc-dc converter for each traction system are shown in Fig. 7, with absolute peak values reported in the text boxes.The VSI and MPI have an equal ac current profile with an absolute peak current of 950 A. The two mission profiles coincide because the motors operate identically in both configurations, as required by the common vehicle speed profile.On the dc side, the MPI and VSI current profiles differ significantly due to the additional dc port and the different dc power distribution occurring in the MPI.Specifically, the VSI input current reaches a maximum of 580 A, while peak currents of 410 and 480 A are recorded at the MPI HV and LV input ports, respectively.In the dc-dc converter, the maximum current is significantly lower in the QSS layout than in the semiactive layout, with a decrease from 710 to 400 A at the input and from 455 to 245 A at the output.
The mission profiles of the power converters result in the design requirements for power semiconductors, filters, and heatsinks reported in Table IV.

A. Weight and Volume
For weight and volume calculations, only inductors, capacitors, and heatsinks are considered, as they have the greatest impact on the volume and weight of the power converters [37], [38].Sizing and design procedures for the components are detailed in Appendix A. The weights and volumes of filters and heatsinks in each system architecture are shown in Fig. 8.
Input and output inductors, which are by far the bulkiest elements, are 33.4% smaller and 35.9% lighter thanks to the reduced current rating.Heatsinks also contribute to the improvement, with relative reductions of 41% and 37% in volume and weight, respectively, due to the reduced thermal load of the switches.In total, the dc-dc converter in the QSS system saves 26.21 dm 3 in volume (−34%) and 124.42 kg in weight (−36%).The volumes of filters and heatsinks in the inverters do not differ significantly, with the MPI requiring +2.8% more volume compared to the VSI due to the extra room required by the additional LC filter at the LV port.The weight is not significantly affected by the additional LV-port inductor, which has an iron-core design and shows a moderate reduction of 2.3%.When considering the entire power conversion stage, significant savings of 22.7 dm 3 (−13%) and 133.2 kg (−19%) for the volume and weight of passive and cooling components are achieved by the QSS layout.

B. Efficiency
The VSI and MPI round-trip energy losses and efficiency points obtained for one driving cycle are shown in Fig. 9.The energy losses are normalized with respect to the VSI.Conduction losses in the MPI increase from 41% to 48%, due to the doubled ON-state voltage drop when the inner switches are conducting.On the other hand, the switching losses in MPI are reduced from 46% to 30%.Most of the time, the MPI modulation works as a down-shifted PWM where only two legs are switched at the same time, while the standard VSI modulation switches all three legs simultaneously.Filter losses are located mainly in the air-core HV line filters.Since the MPI line inductor has a lower inductance and current rating, a reduction from 13% to 7% is obtained in filter losses.In total, round-trip energy losses are 15% lower in the MPI.The overall lower energy consumption is reflected in the efficiency graph, which shows higher values for the MPI.
The round-trip energy losses and efficiency of the dc-dc converter are shown in Fig. 10, where the losses are normalized relative to the semiactive layout.The reduced power rating of the converter in the QSS system has a significant impact on round-trip losses.Specifically, conduction losses are almost halved from 28% to 15%, switching losses are reduced from 41% to 31%, and Joule losses in inductors shrink from 31% to 8%.This results in a 46% reduction in the round-trip energy used by the converter.However, it should be noted that this results from the reduced amount of power processed and not from a higher efficiency of the dc-dc converter in the QSS configuration.As shown in the efficiency plot, the efficiency of the converter belonging to the semiactive system is higher because semiconductors with a higher current rating are used.Looking at the total power conversion stage, the QSS system achieves energy savings of 22% and therefore exhibits higher energy efficiency in the considered driving scenario.

VII. RELIABILITY
To compare the stress levels and lifetime characteristics of the semiactive and QSS systems, the wear-out of its components must be modeled and analyzed.To this aim, the mission-profile-based reliability assessment procedure employed in [39] and [40] is used.

A. Time-to-Failure of Components
Wear-out failure analysis of power electronic converters typically focuses on semiconductor switches and capacitors, as they are the most vulnerable and prone to aging [41].The number of cycles to failure N f in a semiconductor device due to solder joint and bond wire fatigue, which are the dominant failure mechanisms [42], is calculated using the modified Coffin-Manson Arrhenius empirical model [43] with where T j and T j are the junction temperature mean value and swing over the power cycle, respectively, T 0 is the initial temperature value for low-temperature swing conditions, t ON is the rise time of the temperature cycle, A 0 , A 1 , C, λ , and k th are technology-related constants available from manufacturer data, α is the Coffin-Manson exponent, and E a and k B are the activation energy and Boltzmann's constant.The empirical lifetime model of dc-link film capacitors is expressed by [44] where L n represents the rated lifetime under rated voltage V n and hotspot temperature T n , L o is the capacitor expected lifetime under rated operating temperature T o and voltage V o , and n 1 and n 2 are aging constants available from the literature.Simulation results from the detailed system model are used to obtain the evolution of junction temperatures T j in the semiconductors and the hot spot temperatures T o and terminal voltages V o of the capacitors.The temperature profile of each semiconductor is decomposed into N h stressor classes, where each class h is defined as the set {T j,h , j,h , t }.The number of cycles in each class n h is calculated the rainflow algorithm.applying the well-known Miner's rule, the annual accumulated damage (AD) of each semiconductor is then obtained as Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.where from ( 9), N f,h is the number of cycles to failure that corresponds to the hth stressor class, and N y is the number of times the mission profile is repeated over one year of operation of the tram.Similarly, the annual AD of each dc capacitor is obtained as where T k is the duration of capacitor operation under kth operating temperature and voltage and L o,k is the corresponding expected lifetime given by (10).
The annual AD values for each component are deterministic, as they are obtained from the lifetime models described by ( 9) and (10).However, the wear-out end-of-life (EOL) is inherently random due to the uncertainty in lifetime models, component parameters, and stressor evolution.Therefore, uncertainty is introduced, and the stressors and lifetime model parameters are modeled as normally distributed with 10% variation around their rated value at a 90% confidence level.Monte Carlo simulation is used to obtain the corresponding distribution of annual AD in each component.The inverse of the AD distribution represents the EOL distribution, which typically fits with a Weibull distribution f (t) [39].Its integral gives the cumulative time-to-failure distribution or unreliability F(t) from which the reliability R(t) = 1 − F(t) is obtained, indicating the life expectancy of the component with a prescribed confidence level [42].Fig. 11 shows the AD distribution, the EOL density distribution, and the unreliability obtained for the MPI switch S 41 .

B. Reliability of the Power Conversion Stages
The reliabilities of the single components must be combined using reliability block diagrams (RBDs) to obtain the overall reliability of the power conversion stage.Since the catenary/battery tram is a multisource system, there are multiple operating modes that comply with the vehicle mission profile and are characterized by different reliability functions.Here, two different modes are considered: hybrid-traction operation, in which the tram is powered at full rating by both sources, and battery-traction operation, in which the tram draws power exclusively from the onboard BESS, even if at a reduced rating.A third possibility of catenary-only operation is not considered because it is not compatible with the driving scenario, which comprises catenary-free sections.This means that, in case of battery power unavailability due to power electronics failure, tram service would be stopped immediately.For both semiactive and QSS systems, the unavailability of full-rating hybrid power results from a failure in any capacitor or semiconductor in the dc-dc converter or traction inverter.The corresponding RBD is the series connection of all power semiconductors and capacitors, as shown in Fig. 12(a) and (b).Consequently, the reliability of the two propulsion systems in hybrid-traction mode is given by the product of individual component reliabilities where R S,i and R C,i are the reliabilities of the ith switch and capacitor, respectively.For battery-traction mode, the semiactive system has no redundant conduction paths, and power can flow from the BESS to the motors only when the dc-dc converter and traction VSI are available.Therefore, the RBD and reliability of the semiactive system in this mode are equal to those in the hybrid power mode.In the QSS system, battery power can flow through either the LV port of the MPI (LV path) or through the dc-dc converter and the HV port of the MPI (HV path).The corresponding RBD is shown in Fig. 12(c) and features the parallel connection of components in the LV and HV paths.The QSS system reliability in battery-traction mode is therefore given by where The reliabilities of the individual converters and of the entire power conversion stage for both operating modes are compared in Fig. 13.It is worth remarking that the analysis is not aimed at obtaining exact lifetime estimations (which would include precise knowledge of the annual variation of ambient conditions and time-based maintenance actions), but rather at deriving a fair comparison under reasonable assumptions and approximations.The B 1% lifetime of the MPI (i.e., the life span corresponding to 1% reduction in reliability) almost coincides with that of the VSI and is not affected by the higher part count, due to the reduced losses and lower thermal stress in the semiconductors.On the other hand, the partialpower operation of the dc-dc converter in the QSS system determines a relevant reduction in the thermal cycling of its components, with a significant increase in B 1% lifetime.The extended reliability of the dc-dc converter reflects in an overall lifetime improvement of the QSS layout over the semiactive layout, with the B 1% lifetime of the QSS system being significantly longer compared to the semiactive system for the battery-traction mode.Overall, a five-year operation results in the hybrid-mode reliability of 94.7% and 97.6% for the semiactive and QSS systems, respectively.In batterytraction mode, it increases to 99.6% for the QSS layout due to the redundancy provided by the MPI.

VIII. COST
Due to the complexity of a power electronic converter, a detailed cost evaluation comprising all its components would be a complex task.In this section, the cost comparison will focus on power semiconductors, capacitors, inductors, heatsinks, and electronics for gate drive and sensing, as they are the main drivers of overall system cost [45].

A. Power Switches and Electronics
cost of semiconductors and control electronics is estimated based on the data of producers and distributors found on the market with respect to the VA rating requirements reported in Table IV.A unit cost of 660 $ per switch is considered for the 1.7 kV/1200 A employed in the VSI and for the MPI outer switches.The 1.2 kV/1200 A IGBTs in the MPI inner switch positions are estimated at a cost of 625 $ per unit.In the dc-dc converters, the 1.7 kV/400 A and 1.7 kV/225 A IGBTs for the semiactive and QSS systems are priced at a per-unit cost of 190 $ and 300 $, respectively.
Current and voltage sensors are required for proper control of the semiactive and QSS systems.Based on the maximum ac traction current, 1500 A current sensors at a unit price of 220 $ are considered for the VSI and NPC-MPI, whereas 300 and 400 A sensors at a unit price of 80 $ are selected for the dc-dc converters.Furthermore, dc voltage sensors rated for 1500 V are selected for the VSI, for the MPI HV-port, and for the dc-dc converter output, and voltage sensors rated for 750 V are considered for the MPI LV-port and dc-dc converter input.From the analysis of distributor data, a unit price of 250 $ is considered for voltage sensors regardless of their voltage class.
Gate driver boards with voltage insulation, interlocking, fault monitoring, and protection functionalities are considered at a unit price of 200 $.Based on the circuit diagrams in Fig. 1 and considering that each board can drive a complementary pair of IGBTs, three boards are needed for the VSI and dc-dc converters, while six boards are required by the NPC-MPI.

B. Filters and Heatsinks
The cost models presented in [45] and [46] are used for inductors and capacitors.The following unit cost model is considered for dc film capacitors: where V 0 and C 0 are the capacitor-rated voltage and capacitance, and proper values for parameters a C , b C , and c C can be extracted based on distributor data.For inductors, a cost model comprising material and labor costs is employed L = σ core W core + (σ wdg + σ lab )W wdg + fc mat + fc lab (17) where W core and W wdg are the core and winding weight, respectively, σ core , σ wdg , and σ lab are specific material and labor costs per weight, respectively, and fc mat and fc lab are fixed material and labor costs, respectively.
For cooling components, costs are estimated based on distributor data.The resulting unit cost model considered for a 300-mm heatsink and fan unit is CS = fan + σ hs V hs (18) where V hs is the extruded heatsink volume and fan and σ hs are the fixed fan cost and specific heatsink cost per volume.Numerical values for the cost parameters are given in Appendix B.

C. Total Cost
The overall costs for the semiactive and QSS power systems are compared in Fig. 14.As predictable, the inverter cost increases by 16% in the QSS architecture.Power semiconductors and control electronics show the greatest impact on cost difference since the NPC-MPI has twice the number of switches, driver boards, and voltage sensors with respect to the VSI.The additional LC filter at the MPI-LV port does not have a significant cost impact as a result of the compact design of the extra iron core inductor.The cost of the dc-dc converter in the QSS system is 35% lower due Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.to the reduced current rating of power semiconductors and inductors and the smaller cooling components.On the other hand, the cost of the control electronics is unchanged because of the equal number of switches.Putting together the two costs and looking at the overall power conversion stages, a moderate 5% cost increase (+1.6 k$) is estimated for the QSS system.

IX. CONCLUSION
This article presented a broad analysis of a QSS power conversion system for a multisource tram with an overhead line connection and onboard batteries.The QSS system uses an NPC-MPI and a downsized dc-dc converter to integrate power sources with traction motors.The QSS system topology and complete control have been detailed and its dynamic performance over a typical traction cycle has been experimentally evaluated on a reduced-scale laboratory test bench.The experimental results have demonstrated the feasibility of the proposed QSS system control scheme and its potential to achieve substantial reductions in the peak current and round-trip energy of the dc-dc converter.
To evaluate the actual benefits of the QSS conversion stage compared to a standard semiactive layout for a casestudy commercial catenary/battery tram model, the power losses, size, reliability, and cost of the two systems have been analyzed with the aid of analytical design equations, manufacturers' data, electrothermal time-domain simulations, magnetic and thermal FEM simulations, and Monte Carlobased reliability simulations.Table V presents a summarized comparison of the results obtained.The analysis has revealed that, for the tram model in question, the QSS layout can achieve significant savings in the volume and weight of the power conversion stage and lower round-trip energy consumption, thanks to the optimized routing of battery power and consequent downsizing of the dc-dc converter.The reliability of the QSS conversion system under different operating modes is also improved due to the redundant conduction paths provided by the MPI converter.These advantages come at the cost of increased part count, system control complexity, and cost.

A. Inductors Design
The inductance of each leg inductor at the dc-dc converter input is obtained as [14] where N l is the number of legs, f sw is the switching frequency, d ′ is the duty cycle of the dc-dc converter bottom switches, i * dcdc is the peak-to-peak target ripple in the total input current, and ⌊•⌋ is the floor operator.Considering the average input current îdcdc in the inductor over the converter mission profile, the inductor peak current rating is obtained as Iron-core inductors are selected at the dc-dc converter input.
The LC filters of the dc-dc converters, VSI, and MPI HV-port are designed to filter the high-frequency harmonic currents injected by the converters and filter the low-frequency voltage ripple engaged in the catenary by the diode rectifier substations.Their cutoff frequency f cut is selected at 35 Hz, approximately a decade below the catenary voltage ripple [6].Air-core inductors are considered, which is a typical choice for line filters [6].The MPI LV-port LC filter is connected to the BESS and is designed to filter current harmonics due to switching.Therefore, its cutoff frequency is selected at 75 Hz based on the MPI switching frequency [47].An iron-core design is considered for the inductor at the MPI LV port.After the selection of the cut-off frequency, the inductance is calculated as where C is the filter capacitance, whose sizing equation is given later.By assuming that all the ripple current flows into the filter capacitor, the absolute peak current for which the inductor must be designed coincides with the maximum average current that must flow through the filter.Each inductor is designed through a FEM-assisted analytic procedure.For iron-core inductors, the Metglas 1 2605SA1 C-shaped amorphous cores with foil windings [48] are considered due to their suitability for high-current applications [14].Two C-shaped cores are paired to obtain an EE equivalent core as shown in Fig. 15(a).Multiple EE cores are then stacked according to the design needs.The design is based on the areaproduct approach as follows [49], [50].
1) Define the target inductance, maximum peak current î L , winding current density, maximum core flux density Bc ≤ B sat = 1.56 T, window utilization factor k u , and current waveform factor k i .2) Calculate the required area product A * p as 3) Select and arrange the minimum even number of cores N c with an effective core area A c , window area of A w , and mean magnetic length l m that yield an area product A p equal or greater than A * p .4) Calculate the required number of turns as 5) Calculate the required airgap length as where µ r is the relative permeability of the core considering the dc-flux bias.This analytical design is then adjusted and validated through magnetic simulations using FEMM4.2 1 software.The specific winding losses are evaluated as p w = ρ J 2 0 , and the specific core losses are calculated using the modified Steinmetz equation [49].The total specific losses are then entered into a steady-state FEM thermal simulation in FEMM4.2 with an ambient temperature of 45 • C, forced air cooling with a heat transfer coefficient of 50 W/m 2 K, and class-H resin insulation [6].If the temperature limits of 180 • C and 150 • C are not reached in the insulation and core, the procedure ends; otherwise it is repeated considering a lower current density in the winding.Magnetic and thermal FEM simulations of one dc-dc converter input inductor are shown in Fig. 15(b).The mass and volume of the inductor are calculated as where δ cu and δ fe are the densities of copper and core material.
For air-core inductors, the multilayer winding geometry of width c and height h shown in Fig. 16(a) is considered.The inductor has n l layers, N t turns per layer, and is realized with square cross section conductors.To obtain the desired inductance with the minimum length of wire, Brooks coil geometry is chosen.The inductance value of a Brook coil is given by L = k L cN 2 t , where k L = 2.029µ 0 .The design procedure goes through the following steps.
1) Define the target inductance L, maximum peak current î L , winding current density J 0 , conductor height h c , and cross section utilization factor k u .2) Calculate the height c as 3) Estimate the number of turns as 4) If N t is an exact root, pick n l = n t = √ N t .Otherwise, pick n t = ⌊ √ N t ⌋ and n l = n t + 1. Recalculate the width c and height h based on n l , n l , and h c .5) Refine the number of turns based on the inductance equation for air-core axis-symmetric inductors [11].The preliminary design is then validated by magnetic and thermal simulations in FEMM4.2 as shown in Fig. 16(b) for the MPI HV reactor.The volume and mass of the inductor are then obtained as m L = 3π hc 2 δ cu (29)

B. Capacitors Selection
The dc-dc converter output capacitor is sized as Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
where îdcdc,out is the peak value of the averaged current flowing in the filter, d is the duty cycle corresponding to the maximum boost ratio, and V * is the desired voltage ripple across the capacitor, which is selected at 1% of the rated catenary voltage.The peak rms current of the capacitor is . ( For the VSI input capacitor, the following sizing equation is used [51], [52]: where îac is the peak ac current, m = 2 d/ √ 3 with d the maximum peak value of the VSI duty cycles, and V * is selected at 1% of the rated catenary voltage.The peak rms current in the VSI input capacitor is given by where dT and d are the maximum peak values of the MPI top and differential duty cycles.The ripple voltages of the HVport and LV-port capacitors are set to 1% of the rated catenary voltage and BESS voltage, respectively.The rms current in either capacitor is derived based on (34).
Once the required capacitance and rms current rating are derived, a number N cap of dc film capacitors with sufficient voltage and current rating to be connected in parallel are chosen from the catalog of the manufacturer TDK [53].The volume and mass of the capacitor bank are calculated on the basis of N cap and the size and weight data of each capacitor.

C. Heatsinks Sizing
Heatsinks are often sized considering a fixed operating point of the power converter and the corresponding steadystate thermal network [38], [54].However, traction power converters operate under highly variable loads and rarely reach thermal equilibrium, so a steady-state approach for the heatsink design would be too conservative and lead to oversizing.Therefore, a different procedure is implemented.The catalog of 300-mm heatsinks produced by ABL [55] is used as a database for the following iterative design procedure.An initial candidate is selected based on the maximum converter power.Furthermore, the most demanding segment of the converter mission profile is identified.Based on the selected IGBT modules, the converter dynamic electrothermal model is built in PLECS and simulated for an ambient temperature of 45 • C, air-forced cooling at 5 m/s, and under the condition of periodic thermal steady state, that is, with equal initial and final temperatures in all components of the system.If the maximum temperature of a junction in the simulated mission segment is above or below the limit value of 125 • C, a different heatsink with lower or higher thermal resistance is selected and the procedure is repeated.Otherwise, the procedure is terminated, and the mass and volume of the selected heatsink are recorded.

APPENDIX B
See Table VI.

Fig. 5 .
Fig. 5. Experimental results for a typical traction cycle of the QSS propulsion system.(a) Motor speed.(b) d − q axis current control.(c) DC and ac power flows.(d) Currents in the HV dc-link.(e) Currents in the LV dc-link.(f) DC and ac voltages.(g) Modulating signals of the first MPI phase.

Fig. 6 .
Fig.6.Flowchart of the procedure implemented to design and compare the semiactive and QSS power conversion systems.

Fig. 9 .Fig. 10 .
Fig. 9. Efficiency of the traction inverter in the semiactive and QSS systems.(a) Round-trip losses (normalized with respect to the semiactive system).(b) Efficiency points.

Fig. 14 .
Fig. 14.Estimated cost of power switches, filters, cooling components, and control electronics of the traction inverter and dc-dc converters in the semiactive and QSS systems.

TABLE I OVERVIEW
OF EXISTING LITERATURE ON THE NPC-MPI

TABLE IV SIZING
SPECIFICATIONS OF POWER SWITCHES, INDUCTORS, CAPACITORS, AND HEATSINKS Fig. 8. Weight and volume requirements of passives and heatsinks of the power converters in the semiactive and QSS systems.

TABLE VI VALUES
FOR THE COST MODELS OF FILTERS AND HEATSINKS