**1. Introduction**

Automotive powertrains are being electrified to achieve lower emissions and higher fuel efficiency. Along with battery-powered trucks, fuel cell-powered electric trucks (FCETs) are a promising candidate to replace conventional vehicles [1]. Researches done in California have shown feasibility of this technology for certain types of medium- and heavy-duty trucks [2]. Interest in FCETs for medium-duty vocational trucks such as parcel or package delivery has increased. United Parcel Service (UPS) has unveiled its first prototype for a fuel cell-powered van, and FedEx Express has started delivery using FCETs, which in this case are fuel cell range extenders (FCRExs). FCRExs rely primarily on a battery for power and energy, and they carry a fuel cell to extend the range of the battery pack [3]. The range extender enables the vehicle to cover longer distances that would be difficult with the battery pack alone. In addition, the battery is also used as a buffer for high power and for collecting regenerative energy like a hybrid electric vehicle.

A great deal of work has been done on fuel cell electric vehicle (FCEV) control strategies to improve overall fuel efficiency. In [4], the authors proposed control strategies ruled by fuel cell power. Hames et al. [5] compared different control strategies. However, hybrid powertrains with two or more power sources should optimize powertrain component sizes before developing their energy management control strategy. Fuel efficiency and vehicle performance are always dependent on the sizes of vehicle components. Moreover, improper component sizes can increase vehicle cost, which makes the vehicle unattractive for the consumer to purchase. It is important to define the component

system. Fauvel et al. [6] and Kim et al. [7] proposed and validated component sizing processes for hybrid electric vehicle (HEV) powertrain configurations. Marcinkoski et al. [8] optimized component sizes to replace diesel trucks with FCETs while ensuring equivalent performance. Bendjedia et al. [9] presented a methodology to size the energy storage system for different batteries by considering weight, cost, and battery volume. Unlike the presented rule-based sizing processes, Lee [10] proposed a sizing process to minimize fuel consumption with an optimization algorithm to search for an optimum value. It is called POUNDERS (practical optimization using no derivatives for sums of squares), and was developed by Argonne National Laboratory [11]. Using this process, we focused on vehicle ownership costs, including the cost of fuel consumption. Eren et al. [12] sized FCEVs based on, but they did not consider costs that occur when a vehicle is purchased and is being used.

Consumers want to know how much a vehicle will cost throughout the period of ownership; knowing this will help them decide which vehicle to purchase because they know how much money they need to own, purchase, sustain, and operate each vehicle. Total cost of ownership (TCO) is all costs for these. TCO has been used for the estimation of market penetration and the market forecasting [13]. Some researchers have attempted to quantify this cost. The TCO varies in the definition. Mock et al. [14] specify a measure of relevant ownership cost (RCO). Simeu et al. [15] and Rousseau et al. [16] analyzed energy consumption and the costs of plug-in electric vehicles using RCO.

FCEVs use two different energy sources: a battery pack and a hydrogen tank. Properly sizing the fuel cell and the battery can reduce the overall cost of the vehicle while sustaining vehicle performance. The objective of component sizing is to help minimize the overall ownership cost of the FCEV. This paper seeks the optimal component size to minimize RCO for fuel cell hybrid vehicles. We use FCEV models developed in Autonomie and an optimization algorithm from POUNDERS to simulate and optimize a medium- and heavy-duty trucks. The paper is organized as follows. In Section 2, we review rules based on design assumptions from an earlier study. In Section 3, we propose a sizing process based on the cost of ownership and on performance. Sections 4 and 5 describe case studies for a class 4 delivery van and a class 8 linehaul truck, respectively. We analyzed how the sizing result that minimizes the ownership cost changes when some assumptions change. Finally, Section 6 provides a conclusion.
