# Energy balance and hydrogen exhaust emissions of the second-generation Toyota Mirai

Breno Mendes Alves, Pierre Savignac, Pierre Leduc

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Breno Mendes Alves, Pierre Savignac, Pierre Leduc. Energy balance and hydrogen exhaust emissions of the second-generation Toyota Mirai. International Journal of Hydrogen Energy, 2025, 156, pp.150411. 10.1016/j.ijhydene.2025.150411. hal-05215154

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# Energy balance and hydrogen exhaust emissions of the second-generation Toyota Mirai

Breno Mendes Alves*, Pierre Savignac, Pierre Leduc

IFP Energies nouvelles, Institut Carnot IFPEN Transports Énergie, 1 et 4 avenue de Bois-Préau, 92852, France

## ARTICLE INFO

Handling Editor: Dr M Djukic

**Keywords:**

Toyota Mirai II

Fuel cell

Fuel cell electric vehicle system

Vehicle test bench

Hydrogen consumption

$H_2$ emissions

## ABSTRACT

Fuel Cell Electric Vehicles (FCEVs) stand as a promising alternative to conventional Internal Combustion Engine Vehicles (ICEVs), offering lower greenhouse gas emissions and more efficient onboard energy utilization, while presenting an extended range in comparison to Battery Electric Vehicles (BEVs). This paper delves into the performance evaluation of the *Toyota Mirai II* FCEV, a leading model in the market. It emphasizes key performance metrics such as energy consumption, power balance, and tailpipe emissions on controlled test-bench experiments, including its response to varying driving conditions and energy demands. Many variables of the powertrain were assessed, including electrical measurements, as well as measurements of the cooling loops and of the exhaust gases. The energy transformation processes happening within this architecture can then be analyzed, detailing the performances of the fuel cell system. Fuel cell stack LHV efficiency peaked at low power demands at around 70 %, which dropped to 54 % near maximum output stack power at around 130 kWe. These values drop to 62 % and 46 %, respectively, when considering efficiency at the fuel cell system level. Hydrogen consumption on a WLTC driving cycle was accounted at 0.8 $kg_{H_2}$/100 km. At steady-state power demands, hydrogen purges were measured between 0.8 % and 2.4 % of the total amount of fuel used. This study enriches the ongoing dialogue surrounding sustainable transportation solutions by conducting a data-driven analysis of the *Toyota Mirai II*.

## 1. Introduction

Associated to a low-carbon hydrogen production, Hydrogen Fuel Cell Electric Vehicles (FCEVs), integrating Polymer Electrolyte Membrane Fuel Cells (PEMFCs), are relevant candidates to inflect global Green House Gases (GHG) emissions not only in passenger and freight intensive and heavy-duty road transport sectors, but also off-road, maritime and rail transport domains [1].

Bearing in mind that the overall efficiency (from the electrolysis for hydrogen production to the propulsive mechanical energy production) of FCEVs is two to three times less than their battery-powered counterparts [2], the vehicle efficiency and the hydrogen consumption are key performance indicators to assess their environmental impact.

In addition to the hydrogen consumption evaluation, it is important to evaluate the in-use GHG emissions of FCEVs, as the exhaust gases may contain purged hydrogen. Hydrogen has an indirect impact on global warming, with recent studies highlighting different Global Warming Potentials (GWPs) for different time horizons [3–5]. The 100-year time horizon GWP of $H_2$ has been reported at $11.6 \pm 2.8$ [5], but in the

literature values as high as $12.8 \pm 5.2$ [6] and as low as $3.3 \pm 1.4$ [7] have been published [3]. Therefore, calculations based on a value with such a wide range with high uncertainties must be done cautiously, even when a value is stated.

At the tailpipe, air coming from the cathode (hot, moist and oxygen-starved) encounters a mix of gaseous water, nitrogen and hydrogen periodically purged from the anode. Due to the proton exchange membrane gas permeability, some nitrogen content migrates from the cathode to the anode, progressively reducing the partial pressure of hydrogen. Anode purges are periodically triggered to evacuate nitrogen and water from the hydrogen circuit and recover a nominal hydrogen concentration.

The publications acknowledge the need and the existence of these purges but provide limited figures for these emissions [8–10]. In 2013, a simulation study was carried out on a fuel cell system that purges at a given nitrogen accumulation, and typical hydrogen emissions were observed at 0.8 % for steady state operation and 1.2 % for transient load [11].

According to Ref. [12], other hydrogen emission sources in fuel cell transport applications are leakage from compressed gas tank (0.06 %–0.72 % for a storage window between 0.5 and 3 days), hydrogen

<footnote>* Corresponding author.</footnote>

<footnote>E-mail addresses: breno.mendes-alves@ifpen.fr (B.M. Alves), pierre.savignac@ifpen.fr (P. Savignac), pierre.leduc@ifpen.fr (P. Leduc).</footnote>
crossover to the cathode (if no recombination with oxygen is considered) and venting during start-up and shutdown (0.04 %–0.7 % in a 2–5 min window). Total hydrogen leakage rates by 2050 should reach between 1.0 % and 2.3 % for fuel cell electric road vehicles [13].

The topic of hydrogen emissions is receiving increasing attention. Recently the IEA explicitly cited the lack of empirical purge/leakage data in vehicles and infrastructure [14]. These emissions occur throughout the value chain, from hydrogen production to its final use by vehicles, including the stages of processing, transport, and distribution. To assess the impact of all these emissions, a precise evaluation of hydrogen emissions at each phase is necessary [14].

The present work participates in the assessment of fuel cell passenger car emissions, as it has been recently the case with the publication of figures regarding city bus emissions [10]. Moreover, since anode purges are the main source of in use FCEV emissions, firstly they need to be qualified (frequency, intensity), as well as the conditions under which they occur (power demand, operating temperature, etc.).

The literature on fuel cell vehicle chassis dynamometer testing is rather deficient. In 2018, the Argonne U.S. DOE laboratory exhaustively tested a *Toyota Mirai I* FCEV on a roller test bench, assessing electrical variables and hydrogen consumption. On the EPA 5-cycle label fuel economy procedures, it was measured at 1.06 $kg_{H_2}$/100 km [15]. Likewise, IFPEN carried out a study in 2022 on the *Hyundai Nexo*, with fuel consumption reported from 0.67 $kg_{H_2}$/100 km for urban-type driving conditions to 1.24 $kg_{H_2}$/100 km for very dynamic cycles [16].

Then, in 2024, the Joint Research Centre from the European Commission tested a light-duty FCEV under both chassis dynamometer and on-road conditions. The study evaluated the vehicle’s efficiency and its hydrogen consumption, which ranged between 0.975 and 1.5 $kg_{H_2}$/100 km [17]. Finally, an on-road evaluation of several FCEVs was also performed by NREL but with anonymized and normalized data [18].

Following the previous study focused on the energy analysis of the *Hyundai Nexo* [16], the present work aims at supplementing the topic through the analysis of the *Toyota Mirai II* (the 2020 model, also known as the second generation of the vehicle) on a roller test bench at IFPEN and adapted for accommodating FCEVs.

Although allowing for higher flexibility for instrumenting vehicles, this type of experiment has drawbacks in not being able to reproduce the exact real-world driving conditions, such as seasonality, traffic and driver behavior. In addition, the refueling events occurred at the station that was closest to the test bench, among the possible stations. This study then cannot account for differences in hydrogen quality, which would arise if the stations used were from various suppliers with potentially different hydrogen production methods.

Compared to the first generation, the *Mirai II* has seen improvements on fuel cell stack compactness and performance, on driving performance, on cruising range [19] and finally on vehicle aerodynamic performance [20].

Fuel cell stack and system efficiencies, as well as electrical fluxes onboard have been monitored. That allows for an investigation of the power consumption of the components of the fuel cell system. As it will be discussed in this study, the eCompressor of the air loop is the most power consuming auxiliary.

Additionally, characterizing an FCEV requires being capable of measuring the hydrogen fuel consumption, among others. Yet, the most straightforward method consisting of measuring the hydrogen mass flow rate could not be used in this work due to safety constraints on the hydrogen loop of the fuel cell. Thus, other measuring methods were implemented such as the fuel cell current method and the tank pressure method.

Chassis dynamometer experimental research on FCEVs has focused so far on assessing fuel consumption and efficiency at different levels of the vehicle powertrain [15–18]. This study bridges a gap in current literature presenting data about the *Mirai II* and enriching the understanding of FCEVs’ behavior through an extensive set of measured physics.

Notably, heat losses have been evaluated to assess an exhaustive

<figure><img src="image_4.png" /><figcaption>Fig. 1. Powertrain electrical diagram of the *Toyota Mirai II*.</figcaption></figure>

energy balance of the vehicle powertrain on various mission profiles. Additionally, a dedicated gas analyzer has been installed at the vehicle exhaust to monitor the purged hydrogen emissions. These measurements were then analyzed to draw conclusions about in-use FCEVs hydrogen emissions. The air loop is also explored in detail, including an analysis of cathode stoichiometry levels.

## 2. Vehicle presentation and test campaign

### 2.1. Powertrain layout and electrical measuring equipment

FCEVs are electric vehicles, with the specificity that the energy source for the powertrain comes from both a fuel cell and a battery. In the case of the *Toyota Mirai II*, the powertrain electrical architecture is depicted in Fig. 1.

For this vehicle, the 128-kW fuel cell stack [21] takes the role of the prime mover, whereas the 1.24-kWh high voltage Li-ion battery contributes to help the fuel cell during transient loads and to unlock regenerative braking, further improving the vehicle global efficiency. To supply the fuel cell with hydrogen, the vehicle is equipped with a set of three type-IV hydrogen tanks with a total storage capacity of 5.6 kg.

The vehicle was equipped with multiple clamp-type electrical current sensors to monitor the following currents:

* High voltage battery output (1 in Fig. 1).

* High voltage battery DC/DC converter output (2 in Fig. 1).

* Coolant heater DC input (3 in Fig. 1).

* Compressor Electric Motor (CEM) inverter AC output (4 in Fig. 1).

* Electric traction motor AC input (5 in Fig. 1).

* Fan motor DC input (6 in Fig. 1).

* Fuel cell DC/DC boost converter output (7 in Fig. 1).

* Low voltage auxiliary battery (8 in Fig. 1).

The following voltages were also monitored:

* High voltage battery output (1 in Fig. 1).

* High voltage battery DC/DC converter output (2 in Fig. 1).

* Compressor Electric Motor (CEM) inverter AC output (4 in Fig. 1).

* Electric traction motor AC input (5 in Fig. 1).

The different sensors described above were connected to an electrical Power Analyzer Hioki PW3390.

The Balance of Plant (BoP) includes all auxiliary components necessary for the fuel cell stack operation, encompassing air, hydrogen, and cooling loops. The air loop ensures proper stoichiometry, pressure, and humidity at the cathode (see Section 2.3). The hydrogen loop manages hydrogen injection and recirculation, with consumption
<figure><img src="image_5.png" /><figcaption>Fig. 2. Diagram of the exhaust system in the test bench.</figcaption></figure>

measurement methods detailed in Section 2.4. The cooling loop maintains optimal operating temperatures, described in Section 2.6. This work considers the following BoP components:

* Intake air electric compressor (eCompressor).

* Hydrogen pump (for hydrogen recirculation in the anode).

* Coolant pump dedicated to the FC cooling circuit (High-Temperature Loop).

* Coolant pump dedicated to the other circuits (Low-Temperature Loop).

* Fan in front of the vehicle.

* Fuel cell electric heater (for cold starts).

The BoP power consumption can then be defined by the following equation:

$$ \mathcal{P}_{\text{BoP}} = \mathcal{P}_{\text{eCompressor}} + \mathcal{P}_{\text{H}_2 \text{ pump}} + \mathcal{P}_{\text{radiator fan}} + \mathcal{P}_{\text{HT coolant pump}} + \mathcal{P}_{\text{LT coolant pump}} + \mathcal{P}_{\text{heater}} \quad (1) $$

The individual measurement of each auxiliary consumption is complicated due to the integration of the powertrain in the vehicle. Still, the CEM, the radiator fan and the electric heater were assessed with the measuring equipment cited before. The other auxiliaries' individual power consumption values are obtained using the vehicle on-board diagnostics data, as described in Section 2.5.

The ensemble of the BoP power consumption throughout this paper is going to be evaluated by Eq. (2), referring to 1 and 2 in Fig. 1.

$$ \mathcal{P}_{\text{BoP}} = \mathcal{P}_{\text{eCompressor}} + (\mathcal{P}_1 - \mathcal{P}_2) \quad (2) $$

As seen in Fig. 1, the measurement between points 1 and 2 includes not only the components cited above, but also all of the auxiliaries depending on the 14V auxiliary battery in the BoP power consumption (Eq. (2)). At the roller test bench, they consisted mainly of the computer systems that ensure a proper functioning of the vehicle. This added consumption was seen to amount to 200 W, which is much lower than the BoP components consumption. This effect is then neglected.

Another complication for installing the electrical measurement equipment is the compact integration of the battery DC/DC converter. The obtained BoP consumption levels are therefore increased by a factor equivalent to the efficiency of this component.

## 2.2. Tailpipe gas emissions instrumentation

The vehicle was installed on the roller test bench and its exhaust connected to the bench emissions monitoring system. To account for the tailpipe gas emissions, firstly the air mass flow is measured using a pitot tube flow meter downstream of the exhaust pipes. Then, three sensors have been tested to assess the tailpipe emissions, notably of $H_2$. These are the following:

<table><caption>Table 1
$H_2$ tailpipe emissions sensors (General presentation).</caption><thead><tr><td>Sensor</td><td>Brand</td><td>Model</td><td>Technology</td></tr></thead><tbody><tr><td>1</td><td>Messkonzept</td><td>FTC300</td><td>Thermal conductivity</td></tr><tr><td>2</td><td>SICK</td><td>Thermor 615</td><td>Thermal conductivity</td></tr><tr><td>3</td><td>Riken Keiki</td><td>FSD-753</td><td>Catalytic reaction method</td></tr></tbody></table>

<table><caption>Table 2
$H_2$ tailpipe emissions sensors (Details).</caption><thead><tr><td>Sensor</td><td>Range</td><td>Response time</td></tr></thead><tbody><tr><td>1</td><td>0–100 % (gas volume)</td><td>&lt;1 s</td></tr><tr><td>2</td><td>0–100 % (gas volume)</td><td>&lt;20 s</td></tr><tr><td>3</td><td>0–40000 ppm</td><td>&lt;0.5 s</td></tr></tbody></table>

Both technologies used by the sensors are inherently affected by the presence of liquid water and must be used in dry conditions. A sampling line was extracted from the exhaust and equipped with a cooling unit, included in the bench emissions monitoring system. It switches the flow to a dry base, condensing and eliminating water. The three sensors were installed after this drier, as depicted in Fig. 2.

The sensor 3, from Table 1 and Table 2, is used primarily for safety applications, detecting when thresholds are exceeded. Conversely, the sensors 1 and 2, based on the thermal conductivity technology, can provide reliable measurements. Nonetheless, the response time of the second sensor is too long (see Table 2).

Therefore, sensor 1 was the most appropriate option to quantify the hydrogen purges. It should be noted that both thermal conductivity sensors present a significant cross-sensitivity to $O_2$. This leads to offsets in $H_2$ levels and sometimes to artificial peaks, when the $O_2$ levels change quickly.

Since the corrective factors to other gases than $H_2$ were not made available by the sensor constructors, sensor 3 was used to detect the $H_2$ purges and sensor 1 to quantify them, according to the methodology presented in Appendix B.

Finally, even though in this study there is an emphasis on measuring hydrogen emissions, several gases are measured on the test bench. Here is a non-exhaustive list:

* $H_2$: sensors 1, 2 and 3 in Table 1 and in Table 2.

* $H_2O$: sensor 1 in Table 1 and in Table 2.

* Euro 6 standard regulated and non-regulated gases (including $CO_2$ for the first and $O_2$ for the latter): emissions monitoring system already installed in the bench.

## 2.3. Air loop instrumentation

To feed the cathode with oxygen, the air loop is comprised of an air filter, a compressor and a Water Charge Air Cooler (CAC). No humidifier is installed in this specific air loop architecture [22].

Air pressure and temperature were monitored in the air loop at 3 different locations depicted in Fig. 3 by the P and T marks: compressor inlet (1), compressor outlet (2) and stack inlet (3). Moreover, the

<figure><img src="image_6.png" /><figcaption>Fig. 3. Diagram of the intake fuel cell system air loop.</figcaption></figure>
<figure><img src="image_7.png" /><figcaption>Fig. 4. Cooling loops instrumentation.</figcaption></figure>

laboratory ambient pressure and temperature were also tracked.

The air properties used in computations throughout this paper, including water saturation, were obtained using the library CoolProp [23], unless explicitly stated.

## 2.4. Cooling loops instrumentation

In the *Mirai II*, two cooling loops can be identified: firstly, a High-Temperature Loop. The fluid in this loop works at around 333 K, reaching almost 363 K in high power demands. Its main purpose is to cool the fuel cell stack, also going through a deionization filter and a radiator.

Secondly, a Low-Temperature Loop can be identified, which fluid works at around 303 K, but can reach almost 318 K. It aims at cooling the power electronics, notably the Fuel Cell Power Converter (FCPC) and the Power Control Unit (PCU) from Fig. 1. It also passes through the Compressor Electric Motor (CEM) from Fig. 3 and a radiator.

To further characterize the FCEV efficiency, both loops were studied in the test campaign. It should also be noted that the traction motor is cooled by a dedicated oil circuit [20], whose characterization was not in the scope of this study.

Considering the High-Temperature loop, pressure and temperature were monitored at four different locations depicted by the *P* and *T* marks in Fig. 4: upstream and downstream the stack and Water CAC ensemble, and upstream and downstream the radiator. The volumetric flow was measured in the main loop and in the de-ionizer filter bypass, represented by the *F* marks.

The Low-Temperature loop is more straightforward since no deionization filter is present. The volumetric flow was monitored, as well as pressure and temperature upstream and downstream of the radiator, being depicted respectively by the *F*, *P* and *T* marks in Fig. 4.

Each one of the cooling loops contains a different fluid, as that which goes through the fuel cell stack needs to be of a very low electrical conductivity. Both fluids were characterized in density and in heat capacity as a function of the temperature between 293 and 353 K. Therefore, the coolant mass flow and the heat exchanges between two temperature measurement points can be estimated.

$$ 
\begin{array}{l}
\dot{Q}_{\text{coolant}} = \dot{m}_{\text{coolant}} \cdot \Delta h = (\rho \cdot \dot{V}) \cdot (\overline{Cp} \cdot \Delta T) \\
\text{with } \rho = f(T), \overline{Cp} = C_p \left( \frac{T_{in} + T_{out}}{2} \right) \\
\text{and } \Delta T = T_{out} - T_{in}
\end{array}
\qquad (3) $$

The two radiators presented in the HT and LT cooling loops in Fig. 4 are cooled by a single fan located at the front of the vehicle, also depicted in Fig. 1.

## 2.5. Vehicle on-board diagnostics data

Along with the electrical equipment described before, the *Toyota GTS TechStream* software has been used to collect 55 signals from the Controller Area Network (CAN) of the vehicle. Among these signals, the following were of particular interest:

* Stack inlet air mass flow rate.

* Stack coolant inlet and radiator outlet temperature.

* CEM inverter DC power.

* Stack voltage and current.

* Hydrogen pressure at anode and upstream the injectors.

* Fuel cell resistance.

* Pressure and temperature in each of the 3 hydrogen tanks.

As described in Section 2.1, no current measurements in the fuel cell stack output were done, due to the implementation of the DC/DC boost converter in the same housing as the FC stack. Access difficulties prohibiting current sensor installation, the values mentioned for FC in this work were obtained thanks to the CAN.

As it can be noticed, some variables exploited in this paper are exclusively accessible within the CAN of the vehicle. This presents a limitation due to their monitoring frequency, at approximately 4 Hz, compared to the bench data acquisition frequency of 10 Hz. To address this discrepancy, the data underwent cross-correlation and re-sampling treatments allowing the comprehensive utilization of both data sets.

Throughout this manuscript, instances where CAN variables are utilized are explicitly denoted with a superscript. Finally, unless otherwise specified, data is presumed to be obtained from the bench instrumentation.

## 2.6. Fuel consumption measuring methods

The primary equation that governs the functioning of a fuel cell, involving the conversion of hydrogen and oxygen into electricity and water, is as follows:

$$ 
\begin{array}{l}
1\text{H}_2 \rightarrow 2\text{H}^+ + 2\text{e}^- \qquad \text{(anode)} \\
\frac{1}{2}\text{O}_2 + 2\text{H}^+ + 2\text{e}^- \rightarrow 1\text{H}_2\text{O} \qquad \text{(cathode)} \\
1\text{H}_2 + \frac{1}{2}\text{O}_2 \rightarrow 1\text{H}_2\text{O} \qquad \text{(global)}
\end{array}
\qquad (4) $$

The *Mirai II* stack being composed of 330 cells [21] and knowing the produced current, the hydrogen mass flow can then be obtained from Eq. (4). Throughout this paper, this will be the preferred method for computing the hydrogen mass flow.

$$ \dot{m}_{\text{H}_2} = N_{\text{cell}} \frac{MM_{\text{H}_2} I_{\text{stack}}^{\text{CAN}}}{2F} \qquad (5) $$

As stated in Section 1, some purges happen in the hydrogen loop to eliminate undesirable species that may be present in the circuit, such as water and crossover nitrogen. The consumption measuring method cited above cannot take these H₂ purges into account. Therefore, a specific instrumentation was prepared to measure them, as discussed in Section 4.
<caption>**Table 3**</caption>

Relative difference between H₂ WLTC consumption estimated by various methods and consumption stated by the manufacturer.

<table><caption>**Table 4**</caption><thead><tr><th>Method</th><th>Current-based</th><th>PT<sub>IR-based</sub></th><th>PT<sub>CAN-based</sub></th><th>Dashboard</th></tr></thead><tbody><tr><td>Relative difference</td><td>4.5 %</td><td>28.8 %</td><td>6.9 %</td><td>3.2 %</td></tr></tbody></table>

Vehicle test mass and road-load parameters.

<table><thead><tr><th>Vehicle mass</th><th>2076</th><th>kg</th></tr></thead><tbody><tr><td>f<sub>0</sub></td><td>170</td><td>N</td></tr><tr><td>f<sub>1</sub></td><td>0.734</td><td>N/(km/h)</td></tr><tr><td>f<sub>2</sub></td><td>0.02639</td><td>N/(km/h)<sup>2</sup></td></tr></tbody></table>

## 2.2.

The ISO 23828 and SAE J2572 [24,25] are the two most commonly used standards in terms of hydrogen fuel consumption measurements. The gravimetric method and the hydrogen flow method, two of the methods they advocate, were put aside in this study as the first requires using an external hydrogen tank system, while the second requires intruding into the hydrogen pipes, which was not permitted in this case for safety reasons.

Another method these norms advocate is based on the tank pressure and temperature levels. These variables were obtained both from the vehicle CAN and from the infrared communication present in the hydrogen refueling port. Knowing the tanks volumes, Eq. (6) can then be applied to determine the fuel consumption via the hydrogen equation of state:

$$ \dot{m}_{H_2} = \sum_{tanks} \frac{V \cdot \rho_{H_2} (P_{ini}, T_{ini}) - V \cdot \rho_{H_2} (P_{end}, T_{end})}{t_{end} - t_{ini}} \quad (6) $$

Finally, the hydrogen consumption was estimated in this study for various driving cycles cited in Section 2.7 via the following methods:

* Current-based: instantaneous measurement (Eq. (5)).

* Tanks pressure and temperature, using IR-read values (Eq. (6)).

* Tanks pressure and temperature, using CAN values (Eq. (6)).

* Vehicle dashboard display information.

The relative difference with the WLTC consumption announced by Toyota is enclosed in Table 3 for each one of the cited methods. Given that we need to estimate the hydrogen consumption in instantaneous conditions, the most appropriate method is to use the current-based method.

## 2.7. Driving cycles

The vehicle was put on a roller test bench built at IFPEN and adapted for testing FCEVs from 283 K to 308 K (10–35 °C), with the following road-load parameters originating from the European CE-type certificate of conformity (see Table 4).

Multiple driving cycles were tested on the chassis dynamometer, including WLTC, US06, RDE compliant cycles, JC08, BAB130 and FTP75 cycles. All tests were driven at ambient temperatures that range from 283 K to 303 K (10 °C–30 °C) and controlled humidity. To assess transient responses, the vehicle also underwent cycles comprised of a maximum accelerator pedal demand on steep slopes.

In order to evaluate fuel cell efficiency and BoP components performances during steady-state operation, the vehicle was also submitted to a series of increasing and decreasing load steps within a pyramid-shaped load cycle.

A first cycle was assessed at a constant speed of 120 km/h with varying-slope profiles from 1.5 % to 8.5 % and each step fixed for 180 s. Another cycle consisted of keeping the vehicle at 50 km/h varying the

<figure><img src="image_8.png" /><figcaption>**Fig. 5.** Toyota Mirai II Fuel Cell stack and system efficiencies. The scattered points represent instantaneous measurements, with upward triangles denoting mean values during increasing power steps and downward triangles during decreasing power steps. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)</figcaption></figure>

slope in steps from 0 % to 11.3 %, with each step also fixed for 180 s. That allowed an assessment for stack output power values from 5 to about 105 kW, complemented eventually with points at the maximum pedal demand.

In conclusion, a database of results over about 100 cycles was generated and the repeatability of some cycles was assessed. In this paper, the whole database gathering the running points of the vehicle during these 100 mission profiles (about 1 million running points) is used only when required (for example in Section 3.2.2).

# 3. Fuel cell system analysis

The vehicle underwent a series of increasing and decreasing load steps as described in Section 2.7, completed with a maximum accelerator pedal demand cycle. This established steady-state conditions over power steps for the analyses described in this chapter. They cover the fuel cell system and auxiliaries, from hydrogen consumption to electric power generation and its associated losses, as well as an in-depth analysis of the air loop.

## 3.1. Fuel cell stack and system efficiencies

The fuel cell stack efficiency is calculated using the following equation:

$$ \eta_{stack} = \frac{U_{stack} \cdot I_{stack}}{LHV_{H_2} \cdot \dot{m}_{H_2}} = \frac{2F}{LHV_{H_2} \cdot MM_{H_2} \cdot N_{cell}} \cdot U_{stack}^{CAN} \quad (7) $$

with $\dot{m}_{H_2}$ the hydrogen consumption estimated with the electric current-based method (Eq. (5)). The calculation of the stack efficiency is then purely based on voltage values extracted from vehicle CAN.

On the other hand, the fuel cell system efficiency is determined considering the hydrogen consumption calculated with the electric current-based method (Eq. (5)) and the BoP power consumption:

$$ \eta_{FCS} = \frac{(U_{stack}^{CAN} \cdot J_{stack}^{CAN}) - \mathcal{J}_{BoP}^{Bench}}{LHV_{H_2} \cdot \dot{m}_{H_2}} \quad (8) $$

The obtained efficiencies are presented in Fig. 5 and tend to slightly overestimate the fuel cell efficiency, as Eq. (5) does not take into account the hydrogen consumption associated with the purges operated by the hydrogen loop. A proper analysis of the H₂ purges is done in Section 5.

In this figure, all the running points gathered during the pyramid-
<table><caption>**Table 5**
System efficiencies of the Nexo [16], Mirai I [15] and Mirai II.</caption><thead><tr><td>FCEV</td><td>Maximum system efficiency</td><td>Efficiency at maximum power</td></tr></thead><tbody><tr><td>Hyundai Nexo [16]</td><td>67 % @ 8 kWe</td><td>48 % @ 82 kWe</td></tr><tr><td>Toyota Mirai I [15]</td><td>63.7 % @ around 10 kWe</td><td>40 % @ 90 kWe</td></tr><tr><td>Toyota Mirai II</td><td>62.1 % @ 8.7 kWe</td><td>46.3 % @ 110 kWe</td></tr></tbody></table>

<figure><img src="image_9.png" /><figcaption>**Fig. 6.** Toyota Mirai II BoP power consumption.</figcaption></figure>

shaped test presented in Section 2.7 are depicted. The scattered points represent the instantaneous measurements in Fig. 5, while the triangle-shaped markers indicate the mean value calculated over steps of 180 s.

Please note that each load step was tested twice: once with increasing load (depicted by upward triangles) and once with decreasing power (depicted by downward triangles).

A particular behavior of the fuel cell can be observed when operating at 35 kW output system power. Indeed, there is a notable system efficiency gap between the increasing (57.5 %) and decreasing (53.8 %) power steps, while the stack efficiency is almost constant, varying from 62.5 % to 62.2 %.

To verify the repeatability of this phenomenon, cycle assessments were conducted, confirming its dependency to the power point history. It will be further explored in Section 3.2 by analyzing the power distribution between the auxiliaries' components.

Another specific behavior can be noticed around maximum output power. During the test, a maximum system output power of 110 kW has been reached but it cannot be maintained for more than 50 s. The power output then progressively decreases and falls back to just under 100 kW.

Table 5 compares the fuel cell system efficiencies of the Hyundai Nexo, the Toyota Mirai I and the Toyota Mirai II. Although these vehicles belong to different categories, their use of similar hydrogen fuel cell technology for converting hydrogen into electricity allows for an informal comparison, aiming to inform rather than rank the performances.

## 3.2. Balance of Plant (BoP)

Concerning the individual analysis of the auxiliaries involved in Eq. (1), bench data is available for *P*<sub>eCompressor</sub>, *P*<sub>radiator fan</sub> and *P*<sub>heater</sub>. The CAN data was then used for assessing *P*<sub>HT coolant pump</sub>, *P*<sub>LT coolant pump</sub> and *P*<sub>H<sub>2</sub> recirculation pump</sub>. The power consumption values of the four most demanding auxiliaries are exposed in Fig. 6.

As expected, the electric air compressor turned out to be the most

<figure><img src="image_10.png" /><figcaption>**Fig. 7.** FCPC efficiency measurements.</figcaption></figure>

<figure><img src="image_11.png" /></figure>

<figure><img src="image_12.png" /><figcaption>**Fig. 8.** Air loop response and eCompressor efficiency.</figcaption></figure>

energy consuming device among the BoP components, with a particular behavior at 35 kW output power that is also noted in Fig. 5. Its maximum DC electric power consumption reached 14 kWe on steady-state conditions and got as far as 17 kWe during transient operation.

The radiator fan reached an almost constant power consumption of around 600 W from 45 kWe system net power output. The coolant pump and the H<sub>2</sub> recirculation pump together reached 1.5 kW at the maximum measured system net power output of 110 kW. The heater was not found to consume any parasitic power on steady state operation, keeping in
<figure><img src="image_13.png" /><figcaption>Fig. 9. Cathode stoichiometry according to different measurements.</figcaption></figure>

mind that no cycles under 10 °C were assessed.

Finally, the Fuel Cell Power Converter (FCPC) serves the purpose of boosting the FC output voltage to the level of the vehicle HV DC network voltage. This voltage is around 350 V but may reach up to 650 V during higher power demands. Its efficiency, calculated with Eq. (9), decreases with the FC power increase as the voltage ratio of the DCDC conversion increases. Its value has been measured ranging from 96 % to 99 % (see Fig. 7).

$$ \eta_{FCPC} = \frac{U_{FCPC}^{CAN} \cdot I_{stack}^{Bench}}{U_{stack}^{CAN} \cdot I_{stack}^{CAN}} \qquad (9) $$

### 3.2.1. Air loop analysis

The maximum stack pressure reached 0.25 MPa and the maximum air mass flow rate was measured at 96 g/s (Fig. 8). The fuel cell system cathode stoichiometry $\lambda_{O_2}$ went as low as 1.2 and reached almost 2 at 40 kW net power output on steady-state operation. The stoichiometry was calculated using CAN data for both air flow and current levels and will be further explored in Section 3.2.2.

Firstly, one can note that the cathode stoichiometry values are relatively lower than other FC solutions. Furthermore, a sudden change in the stoichiometry control was observed around 40 kWe FC stack output with a steady-state value measured at either 1.4 or 2 depending on the previous step load value (ascending or descending).

The temperature and pressure measurements up and downstream the air compressor allowed to determine the compressor isentropic efficiency, with $T_{2,ls}$ being the isentropic outlet temperature.

$$ \eta_{ls} = \frac{h_2(T_{2,ls}, P_2) - h_1(T_1, P_1)}{h_2(T_2, P_2) - h_1(T_1, P_1)} \qquad (10) $$
with $T_{2,ls} = T_1 \cdot \left(\frac{P_2}{P_1}\right)^{\frac{\gamma-1}{\gamma}}$

The compressor overall efficiency reached 43 % at maximum steady-state fuel cell system output power, around 90 kWe. This efficiency considers the electrical losses in the inverter, the losses associated with the electrical machine and the isentropic losses.

This value went as high as 51 % on maximum system net output power 110 kWe in transient conditions. The coupled mechanical and electrical efficiency of the Compressor Electric Motor $\eta_{EM}$ also includes the mechanical efficiency of the planetary step-up gear located in between the motor shaft and the compressor wheel. Thus, the mechanical

losses in the gear are likely to account for the surprisingly low values of $\eta_{EM}$.

### 3.2.2. Cathode stoichiometry

The results obtained in Fig. 8 concern the steady-state cycles mentioned in the introduction of Section 3, using CAN current and air flow measurements and according to the following equation:

$$ \lambda_{O_2}^{\text{CAN}} = \frac{\dot{m}_{O_2}}{\dot{m}_{O_2}(\lambda_{O_2} = 1)} = \frac{\dot{m}_{O_2}}{\dot{m}_{O_2}^{\text{sto}}} $$
with $\dot{m}_{O_2} = X_{O_2} \cdot \rho_{air} \cdot V_{air}^{\text{CAN}}$ \qquad (11)
and $\dot{m}_{O_2}^{\text{sto}} = \frac{MM_{O_2} \cdot N_{\text{cells}}}{4F} \cdot I_{stack}^{\text{CAN}}$

During the load step test, $\lambda_{O_2}$ reached lower values at high power outputs compared to low demands, with a peak at medium load. Further analyses have been made to confirm this unexpected behavior. Using the whole database of available tests, as presented in Section 2.7, a 2D histogram was generated with respect to the cathode stoichiometry and FC stack power and represented by the blue circles in Fig. 9. In this figure, the size of the marks is proportional to the occurrence of the running point in the whole database, which represents about 1 million points, with points occurring less than 1 % being ignored.

A second method to compute the cathode stoichiometry is based on the bench instrumentation described in Sections 2.1 and 2.2. With the electrical measurements, the FCPC output current and power values are obtained. Supposing the efficiency for this component $\eta_{FCPC} = 97 \%$, in accordance to Fig. 7, it is possible to recalculate the stack current. From this current and the tailpipe air flow measurement, $\lambda_{O_2}$ values are obtained and represented in Fig. 9 by the orange star markers.

$$ \lambda_{O_2}^{\text{Bench}} = \frac{\dot{m}_{O_2}}{\dot{m}_{O_2}^{\text{sto}}} $$
with $\dot{m}_{O_2} = X_{O_2} \cdot \rho_{air} \cdot V_{\text{tailpipe}}^{\text{Bench}}$ \qquad (12)
$$ \dot{m}_{O_2}^{\text{sto}} = \frac{MM_{O_2} \cdot N_{\text{cells}}}{4F} \cdot I_{\text{stack}} $$
and $I_{\text{stack}} = \frac{I_{\text{FCPC}}^{\text{Bench}} U_{\text{FCPC}}^{\text{CAN}}}{\eta_{\text{FCPC}} U_{\text{stack}}^{\text{CAN}}}$

Finally, a third method of computing the cathode stoichiometry is based on the exhaust gases concentration levels, according to the instrumentation detailed in Section 2.2. With the bench exhaust instrumentation, $O_2$ and $H_2$ concentrations are measured after the cooling unit, where water condensates and is eliminated. Water vapor values did not exceed 0.5 % in the tests assessed.

Expanding Equation (4) to consider non-consumed $H_2$, $O_2$ and $N_2$ in the products and then re-computing concentrations in the dry environment downstream the cooling unit, the following equation can be derived to compute $\lambda_{O_2}$ from the measured concentrations. The air is simplified to a $N_2$ and $O_2$ mixture.

$$ \lambda_{O_2}^{\text{Exhaust}} = \frac{1 - Y_{H_2} - Y_{O_2}}{1 - Y_{H_2} - (1 + \chi) \cdot Y_{O_2}} \qquad (13) $$
with $\chi = \left(\frac{Y_{N_2}}{Y_{O_2}}\right)^{\text{air}} = \frac{0.78}{0.21}$

Neglecting the $H_2$ concentration in the exhaust gases, one can infer that when $\lambda_{O_2} = 1$, all available oxygen in air has been consumed. When $\lambda_{O_2} \to \infty$, no $O_2$ has been consumed and thus the $O_2$ to $N_2$ ratio is equal to the ambient air one. The stoichiometry levels obtained with this method are represented by the green cross markers in Fig. 9.

The three methods depicted in Fig. 9 represent the same behavior for
<figure><img src="image_14.png" /><figcaption>Fig. 10. Fuel cell normalized resistance (data extracted from the vehicle CAN) as a function of the fuel cell stack power.</figcaption></figure>

the cathode stoichiometry as a function of the fuel cell stack power, notably the low levels of stoichiometry in the 85 to 120 kWe FC stack power output range. As stated in Section 3.2.1, the unique response at around 40 kWe FC stack output infers that there may be other variables that affect the stoichiometry control of the vehicle.

To ensure stable performance and a longer stack lifetime, one of the key parameters is the membrane hydration which must be kept in an optimal range as it may otherwise lead to flooding, reducing of the electro-chemical active surface, and cause mechanical and chemical degradations [26,27]. Evacuating water is essential to mitigate flooding phenomena, hence there is active research on water management methods [28,29].

In a fuel cell system with no external humidifier, such as the case of the Mirai II [21], controlling the cathode stoichiometry seems the best way to control the hydration level of the membrane, in combination with a proper control of the recirculation at the anode thanks to the hydrogen pump.

A key research topic on PEMFCs is the development of estimators of membrane water content, as it is complex to measure this variable [30]. They usually explore the link between the membrane electrical resistance and its hydration level. It should also be noted that abnormally high values on ohmic resistance may indicate an advanced aging [31].

Consequently, the CAN fuel cell resistance is depicted in Fig. 10 for the power steps presented in the beginning of Section 3. There seems to be a strategy to control the resistance around the normalized value of 0.3, which may be linked to the cathode loop calibration. It increases at maximum power output, which probably indicates a difficulty to keep the membrane well hydrated. Hence, this demand can only be reached in transient conditions.

Moreover, there seems to be a hysteresis phenomenon when points are reached from higher or lower power demands. From lower demands, the resistance $R_{FC}^{CAN}$ is lower as the membrane humidity is easier to control. From higher demands, membrane is in a drier state and $R_{FC}^{CAN}$ is higher.

To conclude, the cathode stoichiometry levels seen on the Toyota Mirai II are quite low, especially in comparison to the 1st generation model [22]. It can be attributed to the extensive improvements that are claimed by Toyota for the Mirai II [21] in the gas channels design to increase $O_2$ concentration in the gas diffusion layer (GDL) and in the ionomer of the catalyst layer design so that it is more permeable to $O_2$. Moreover, the air and hydrogen flows inside the Mirai II stack are in counter-flow, allowing it to be operated without an external air inlet humidifier. That may also require low air mass flow rates to ensure a

proper self-hydration of the membrane.

### 3.3. Power balance at stack level

The power balance was firstly analyzed at stack level, concerning the conversion from $H_2$ heating value to electrical energy. As described in Section 2.4, the HT cooling loop circulates through the stack, to dissipate the losses involved in the electrochemical reaction, the de-ionizer filter and a radiator.

Focusing on the coolant temperature measurements up and downstream the fuel cell stack, the heat exchanged between the stack and the coolant was determined with Equation (3). Neglecting the diffusive losses, this heat exchange is then considered to be equal to the losses during the conversion of $H_2$ calorific value to electrical energy.

The obtained value in Fig. 4 also takes into account the heat exchanges in the Water Cooled Charge Air Cooler. To provide more accurate results, this contribution needs to be deducted from the obtained losses values.

As pressure and temperature measurements were available for the air flow up and downstream the Water CAC, referring to Section 2.3, the change in enthalpy can be computed. Inside this component, the air is considered to exchange solely with the coolant fluid, so the heat exchanges between them were obtained and deducted from the heat losses estimated with Eq. (3).

The $H_2$ rate of heat flow associated to both Lower Heating Value and Higher Heating Value were calculated using the available hydrogen mass flow values, and are referred to as $\mathcal{P}_{H_2HV}$ in Eq. (14).

$$ \epsilon = \frac{(\mathcal{P}_{\text{electrical}} + \mathcal{P}_{\text{heat losses}})^{\text{FC Stack}}}{\mathcal{P}_{\text{H}_2\text{HV}}} $$ 
with $\mathcal{P}_{\text{electrical}} = U_{\text{stack}}^{\text{CAN}} \cdot I_{\text{stack}}^{\text{CAN}}$ 
$\mathcal{P}_{\text{heat losses}} = -(\dot{Q}_{\text{coolant}}^{\text{Bench}} - \dot{Q}_{\text{Water CAC}}^{\text{Bench}})$ 
$= -(\dot{m} \cdot \Delta h)_{\text{coolant}}^{\text{FC Stack}} - (\dot{m} \cdot \Delta h)_{\text{coolant}}^{\text{Water CAC}})$ 
$= -(\dot{m} \cdot \Delta h)_{\text{coolant}}^{\text{FC Stack}} + (\dot{m} \cdot \Delta h)_{\text{air}}^{\text{Water CAC}})$ 
and $\mathcal{P}_{H_2HV} = \dot{m}_{H_2} \cdot HV$

Logically, the electrical power and the heat losses should sum to $\mathcal{P}_{H_2HV}$, which is not the case neither for the LHV nor HHV. They correspond to the energy released during the dissociation of hydrogen and the formation of water (Eq. (4)). To further exploit this observation, the power balance for the fuel cell energy conversion is then calculated with respect to both heating values.

The actual heating value that would make the balance be equal to

<figure><img src="image_15.png" /><figcaption>Fig. 11. Fuel cell stack power balance.</figcaption></figure>
<figure><img src="image_16.png" /><figcaption>**Fig. 12.** Power distribution at stack and system levels for fuel cell stack running points at 42 and 105-kWe.</figcaption></figure>

100 % is between the LHV and the HHV for every fuel cell power point. The LHV takes into account water in the vapor state in Eq. (4), corresponding to the subtraction of the heat of vaporization from HHV. The latter treats then the produced water in the liquid state.

This result is unsurprising considering that within the stack, water exists in both its liquid and vapor phases. Moreover, the proportion of vapor to liquid water is not constant along the pipes downstream of the stack. This will be further explored at the system level in Section 3.4 and Appendix A, as the temperature reduces downstream the fuel cell until ambient conditions and some of the water condenses.

<table><caption>**Table 6**

Hydrogen consumption correction factors on a WLTC cycle.</caption><thead><tr><th>WLTC Phase</th><th>Low</th><th>Medium</th><th>High</th><th>X-High</th><th>Cycle</th></tr></thead><tbody><tr><td>K<sub>H2</sub> [kgH<sub>2</sub>/100Whe]</td><td>4.98</td><td>4.85</td><td>5.32</td><td>2.59</td><td>3.25</td></tr></tbody></table>

<figure><img src="image_17.png" /><figcaption>**Fig. 13.** Toyota Mirai II H₂ consumption at 10 °C and 23 °C on WLTC. Fuel consumption values were obtained using fuel cell current measurements. Approval data come from standard WLTP tests carried out at 23 °C.</figcaption></figure>

### 3.4. Power balance at system level

Power balances were then analyzed for multiple levels of the powertrain, from the stack level H₂ heating value to electrical energy conversion mentioned before, to the available power at the electric machine, heat losses included. Hence, in this section a global comprehension of the heat generated and exchanged either at the radiators or in the air loop is done. The latter is described in Appendix A.

Three levels of energy balance are presented in Fig. 12 for two fuel cell stack operating points. The nested pie charts show and compare the distributions of the available power inside the powertrain.

The conversion of H₂ heating value to electrical energy and its associated losses is depicted from the innermost level to the middle one. For better understanding, the dark blue wedge at the innermost level, corresponding to the graphical representation of the power associated to the H₂ HHV, represents actually the difference between the HHV and the LHV.

The analysis of the conversion of energy cited above for two fuel cell stack power points agree with what was exposed in Fig. 11: the power balance is between the HHV and the LHV for both levels. It is also closer to the LHV for the 105-kWe operating point than the 42-kWe one.

From the middle level to the outer one, the availability of electrical power for the traction motor is rendered, as well as the heat exchanges at the radiators on both cooling loops and the change in air enthalpy from the intake to the exhaust.

The calculation of this enthalpy change is explained in Appendix A. It is firstly computed with respect to the exhaust gases temperature and rendered at the Δ*H*<sub>air</sub> green wedge in Fig. 12. Secondly, it is computed at the ambient conditions and the obtained difference corresponds to the reduction that can be seen graphically by the white dots.

Since temperature lowers in the tailpipe until the laboratory ambient conditions are reached, a higher fraction of water condenses. So, as expected the power balance on the outer level is closer to the LHV associated H₂ power when considering water condensation.

### 4. Hydrogen consumption measurements on driving cycles

Homologation data accounts for a 0.81 kgH₂/100 km consumption on the WLTC cycle for the second-generation Mirai [32]. As a part of a comprehensive study of the Toyota Mirai II, a consumption analysis has been performed to appraise this value.

The HV battery may variate in SOC during a cycle, so to reduce its influence the use of a correction coefficient K<sub>H₂</sub> [16] has been accounted
<figure><img src="image_18.png" /><figcaption>Fig. 14. Instantaneous H₂ tailpipe emissions on several cycles (blue lines). WLTC: A @ 23 °C (cold start), B @ 23 °C (hot start), C @ 10 °C (cold start) D: Steady-state fuel cell power cycle. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)</figcaption></figure>

for and it is defined as follows:

$$ \mathcal{F}_{C_{H_2}} = \mathcal{F}_{C_{raw,H_2}} + K_{H_2}EC \quad (15) $$

with $\mathcal{F}_{C_{H_2}}$ [kgH₂/100 km] being the corrected hydrogen consumption, $K_{H_2}$ [kgH₂/100 Whe] the correction factor, EC [Whe/km] the electrical energy consumption at HV battery level.

The correction factor $K_{H_2}$ was determined by fitting linear regressions on multiple fuel consumption measurements and it was obtained for each WLTC phase. The relevant $K_{H_2}$ is then considered to adjust the fuel consumption of the cycle depending on its driving type (urban, extra-urban or highway, etc.) and the values are exposed in Table 6.

Multiple WLTC cycles were driven to compare measurements with approval data. Some of the tests were carried out in a test bench at ambient air temperature of 283 K (10 °C). Fig. 13 shows that IFPEN hydrogen consumption measurements at 296 K (23 °C) are 5 % lower than the approval data yet the trend is well reproduced. This fuel consumption underestimation is likely to be explained by the uncertainties in the fuel consumption measuring method (based on fuel cell current in Fig. 13) and to a lesser extent to the hydrogen purges that are not taken into account with this fuel consumption estimation method.

## 5. Tailpipe hydrogen emissions

To optimize the stack performance, it is essential to fine-tune the anode structure. Depending on the chosen architecture, performance losses resulting from byproduct accumulation at the anode side can be

<figure><img src="image_19.png" /><figcaption>Fig. 15. Tailpipe hydrogen emissions on three steady-state operation cycles.</figcaption></figure>

detrimental to stack efficiency.

The sealing of the anode causes two major issues. Firstly, $N_2$ accumulation due to the proton exchange membrane permeability, which dilutes hydrogen and results in a reversible voltage decay. Secondly, liquid water aggregation, which can result in the phenomenon known as flooding.

An integral aspect of maintaining optimal performance involves then the implementation of anode purges, crucial for the removal of accumulated nitrogen and liquid water [33]. Nevertheless, opening the anode to the exhaust comes with an $H_2$ loss, which calls for careful optimization of purge duration and frequency.

Furthermore, re-circulation, a complementary technique, entails redirecting a portion of the anode content back into the system. This re-circulation process contributes to an improved overall efficiency of the fuel cell by fostering a more uniform distribution of the hydrogen partial pressure and facilitating better control over operating conditions [34].

To measure hydrogen losses at the exhaust due to purges, several sensors were installed (Section 2.2). The hypothesis and method used to quantify these losses are detailed in Appendix B. Instantaneous plots of hydrogen emission values in comparison to vehicle speed or to fuel cell stack power provide a visual indication of the purge strategy (Fig. 14).

Two types of driving cycles are analyzed in this section (described previously in Section 2.7). Firstly, three WLTC (cycles A, B and C), with hydrogen emissions being compared to the vehicle speed.

Secondly, one steady-state cycle at a constant vehicle speed of 120 km/h and varying slope (cycle D), with hydrogen emissions being compared to fuel cell stack power. Two power steps have been set: one at 40 kW (assessed twice) and one at 80 kW.

In the tests, purge events were observed when the vehicle is in one of the following situations:

* Vehicle acceleration and high fuel cell stack power demand.

* High vehicle speed, corresponding to the extra-high phase on the WLTC cycles (A, B, C) after 1480 s, where fuel cell stack power was found to be of at least 20 kW.

* Vehicle deceleration and no fuel cell power demand (at the end of each phase of the WLTC cycles).

* High and constant vehicle speed and fuel cell stack power of at least 30 kW (cycle D).

When it comes to lower temperatures (cycle C, Fig. 14), the frequency (number of purges in a cycle) and the emissions values are higher than for cycles at 296 K (23 °C) (cycles A and B). During the first 1000 s (phases 1 and 2), thirteen purges occur on cycle C, when there are respectively eight and six for tests A and B. It also comes with higher levels and longer duration for each purge. Then, when the vehicle is warm, numbers, duration and levels become similar.

It should be noted that the purge strategy of the fuel cell is related to the power requirement: in test D, at a steady-state power of 80 kW, a
<table><caption>**Table 7**
Purge strategy on steady-state test, in continuous operation (Cycle D – Fig. 14).</caption><thead><tr><th>Fuel cell stack power</th><th>33 kWe (up)</th><th>80 kWe</th><th>33 kWe (down)</th></tr></thead><tbody><tr><td>H<sub>2</sub> purge mass rate</td><td>0.8 %</td><td>1.3 %</td><td>1.4 %</td></tr><tr><td>Purge frequency</td><td>0.14 Hz</td><td>0.06 Hz</td><td>0.14 Hz</td></tr></tbody></table>

constant purge regime is reached after about 200 s (at global time around 400 s). It is also observed that emission “rebounds” occur at high-power demand, with two occurring between each purge at 80 kW on cycle D in Fig. 14.

This phenomenon has been observed in other steady-state tests, with varying numbers of rebounds (from one to four), dependent on the power demand but consistent throughout the power step.

Therefore, it is relevant to compare the specific hydrogen emissions (Eq. (16)) with the power supplied by the fuel cell. This analysis was done in Fig. 15, where two specific emissions values coexist for every point, whether the fuel cell is in an increasing (upward triangle) or decreasing power step (downward triangle).

$$H_2 \text{ specific emissions } [\text{g/kWh}] = \frac{m_{H_2\text{purged}}}{\int \rho_{\text{FC}} dt} \qquad (16)$$

Two different behaviors can be observed in Fig. 15, below and above fuel cell stack power outputs of 60 kW. Below, the specific emissions remain almost constant at around 0.4 g/kWh from 30 to around 50 kW, while from 60 to 80 kW they were seen at 0.8 g/kWh. Above 80 kW, there is a linear dependency on power.

Hydrogen emissions can also be expressed as a mean purge mass rate, as a function of the hydrogen consumption, via Equation (17). The purge rate of a steady-state power point of 105-kWe, evaluated during a 400 s period, is approximately 2.4 %, while for a medium-power output of 53-kWe it ranges from 0.8 % to 1.0 %.

$$H_2 \text{ purge mass rate } [\%] = 100 \cdot \frac{m_{H_2\text{purged}}}{(m_{H_2\text{consumed}} + m_{H_2\text{purged}})} \qquad (17)$$

As previously mentioned, a hysteresis phenomenon was seen in the purge strategy. Table 7 highlights this observation for the cycle D evaluated above, which repeatability was seen in Fig. 15. For most steady-state conditions, a decreasing power step will produce higher specific emissions than an increasing one of equivalent power.

For the future, progress is expected in the PEMFC technology and in the control of its systems, for example through proton exchange membranes with reduced permeability to nitrogen, or improved nitrogen estimators at the anode for more precision in the purge management. This progress could lead to reducing purge frequency, and hence lower H₂ emissions from the vehicles in the future.

## 6. Conclusion

Following a previous energy benchmark dedicated to the FCEV Hyundai Nexo [16], a complementary study has been carried out at IFPEN on the 2020 generation of the Toyota Mirai (Mirai II). The aim of this study was to examine the behavior of its powertrain at various levels, including stack and system efficiencies, auxiliaries power consumption and hydrogen exhaust emissions. The scope of the energy analysis of the vehicle has been improved with respect to the Nexo study, thanks to the measurements of heat losses at vehicle level, both in the high temperature and the low temperature coolant circuits. Finally, the fuel consumption was assessed in different driving cycles.

It has been observed that the fuel cell stack LHV efficiency peaked at around 70 % at low power demands, while system efficiency was

<table><caption>**Table 8**
Main findings of the experimental work on the Toyota Mirai II.</caption><tbody><tr><td><strong>Efficiencies</strong></td></tr><tr><td>Stack efficiency: 55%–64% for power values from 20 to 100 kWe<sub>stack</sub></td></tr><tr><td>System efficiency: 47%–61% for power values from 20 to 90 kWe<sub>system</sub></td></tr><tr><td><strong>Auxiliaries</strong></td></tr><tr><td>Highest electrical consumption: eCompressor</td></tr><tr><td>Up to 14 kW at 90 kWe<sub>system</sub></td></tr><tr><td>75%–90% of the BoP total consumption</td></tr><tr><td>Hysteresis phenomenon at mid-loads</td></tr><tr><td><strong>Energy balance</strong></td></tr><tr><td>∫<sub>H₂,LHV</sub> < ∫<sub>electrical</sub> + ∫<sub>heat losses</sub> < ∫<sub>H₂,HHV</sub></td></tr><tr><td><strong>H₂ emissions at tailpipe</strong></td></tr><tr><td>At 33 kWe-stack: 0.3 gH₂/kWh<sub>stack</sub> or 0.8% purge mass rate</td></tr><tr><td>At 105 kWe-stack: 1.3 gH₂/kWh<sub>stack</sub> or 2.4% purge mass rate</td></tr><tr><td>Hysteresis phenomenon</td></tr></tbody></table>

assessed at 62 %. These values drop to respectively around 54 % and 46 % near maximum output power, around 130-kWe for the stack and 110-kWe for the fuel cell system.

The most energy-consuming auxiliary was the eCompressor, reaching values as high as 17 kWe on transient maximum power operation. A particular behavior for the eCompressor occurs near 35 kW fuel cell system output, with power consumption and cathode stoichiometry varying depending on whether the running point was reached from higher or lower power demands.

When adding the electric output of the fuel cell stack to the heat loss of the stack, the sum of these two amounts of energy is somewhere in between the lower and higher heating values of the hydrogen consumed by the stack. Typically for a medium power output of the fuel cell, around 50 kW, stack electrical output plus heat loss represents 95 % of HHV and 105 % of the LHV. This is interpreted because of the formation of liquid water at stack level during the electrochemical reaction.

Hydrogen emissions at vehicle exhaust have also been examined and quantified. These emissions are due to periodic purge of the anode of the fuel cell to eliminate nitrogen and water accumulation that reduces hydrogen partial pressure and then stack efficiency. It has been observed that hydrogen emissions increase with fuel cell power output.

Running several WLTC cycles has shown quite a similar shape of purge profile with an increased purge frequency during the extra-high phase of the cycle. Nevertheless, the purge profile is not exactly the same for each WLTC, revealing a complex purge management strategy, probably based on numerous parameters. Hydrogen loss represents about 1 % of the hydrogen consumed by the vehicle at medium power outputs (53 kW) and up to 2 % at 100 kW.

The data gathered from this roller bench test campaign provides figures that can help future studies for advancing discussions on hydrogen’s role in transportation applications. Therefore, this study serves as a benchmark in the Tank-to-Wheel (TtW) analysis of the Mirai II. The key findings are resumed in Table 8.

The present work can support Life Cycle Assessment (LCA) studies, which commonly assess the environmental impact of FCEVs with a primary focus on hydrogen production, distribution, and end-use, from an energy and fuel consumption point of view [35,36]. Nowadays hydrogen emissions all along the whole supply chain (hydrogen production, processing, transport, distribution, end-use) is getting increased attention.

Additional work on this topic could help in the foreseeable elaboration of future hydrogen emission reporting frameworks or even regulatory thresholds. As purges contribute to operational hydrogen losses of FCEVs, this study extends recent assessments for the vehicle in-use phase by providing additional figures regarding H₂ emissions at tailpipe [10].
This article can also facilitate the development of models for simulating vehicle behavior or specific components, such as the fuel cell stack. Furthermore, it can aid in refining simulation tools that enhance the performance evaluation and optimization of FCEVs.

To progress on the topic of FCEVs' testing, it is recommended to further assess fuel consumption and hydrogen emissions in real-world driving conditions, as it is the case for example in the work detailed in Ref. [37]. Other constraints arise when considering a fleet of vehicles in real use, such as fuel quality and hydrogen refueling standards. In contrast to the scenario outlined in this study, drivers typically refuel their vehicles at various stations from different providers.

## CRediT authorship contribution statement

**Breno Mendes Alves:** Writing – original draft, Visualization, Methodology, Investigation, Formal analysis, Conceptualization. **Pierre Savignac:** Writing – original draft, Visualization, Methodology, Investigation, Formal analysis, Conceptualization. **Pierre Leduc:** Writing – review & editing, Supervision, Methodology, Conceptualization.

## Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## Acknowledgements

The authors express their gratitude for the valuable contributions of Jules Sery, in charge of the early work described in this paper. Additionally, the efforts of Xavier Dunand, Tony Klein, and Philippe Pauvert, whether in the domain of roller test bench operation or measuring equipment implementation, are duly recognized and appreciated.

## Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j.ijhydene.2025.150411.

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Nomenclature

List of abbreviations

AC: Alternating Current

BAT: Battery

BoP: Balance of Plant

CAN: Controller Area Network

CEM: Compressor Electric Motor

DC: Direct Current

EM: Electric Motor

EPA: U.S. Environmental Protection Agency

FC: Fuel Cell

FCEV: Fuel Cell Electric Vehicle

FCPC: Fuel Cell Power Converter

FTP-75: EPA Federal Test Procedure

GB: Gearbox

GHG: Green House Gases

GWP: Global Warming Potential

HT: High Temperature

HV: High Voltage

HVAC: Heating, Ventilation and Air-Conditioning

HWFET: Highway Fuel Economy Test

INV: Inverter

IR: Infrared

LCA: Life Cycle Assessment

LT: Low Temperature

LV: Low Voltage

PEMFC: Polymer Electrolyte Membrane Fuel Cell

PCU: Power Control Unit

RDE: Real Driving Emissions

RH: Relative Humidity

Water CAC: Water Cooled Charge Air Cooler

WLTC: Worldwide Harmonized Light Vehicles Test Cycles

WLTP: Worldwide Harmonized Light Vehicles Test Procedures

List of notations

P<sub>BOP</sub>: Balance of Plant Power Consumption (Bench)

P<sub>eCompressor</sub>: eCompressor Power Consumption (Bench)

P<sub>H2 recirculation pump</sub>: Recirculation Pump Power Consumption (CAN)

P<sub>heater</sub>: eHeater Power Consumption (Bench)

P<sub>HT coolant pump</sub>: HT Loop Cooling Pump Power Consumption (CAN)

P<sub>Radiator fan</sub>: Radiator Fan Power Consumption (Bench)

I<sub>FCPC</sub>: FCPC Current (Bench)

I<sub>stack</sub>: Stack Current (CAN)

U<sub>FCPC</sub>: FCPC Output Voltage (CAN)

U<sub>stack</sub>: Stack Voltage (CAN)

List of symbols

ΔH: Change in enthalpy rate (J/s)

ṁ: Mass Flow (kg/s)

Q: Heat flow rate (W)

V̇: Volumetric flow rate (L/min)

η: Efficiency (%)

γ: Heat Capacity Ratio (–)

λ<sub>O₂</sub>: Cathode O₂ stoichiometry (–)

F̄ ∈ H₂: Hydrogen fuel consumption (kgH₂ /100 km)

P̄: Power (kW)

ρ: Density (kg/m3)

E: Energy (J)

EC: Electrical energy consumption (Whe/km)

F: Faraday's constant (96 485 As/mol)

h: Specific enthalpy (J/kg)

HHV<sub>H₂</sub>: H₂ Higher Heating Value (142 MJ/kg)

I: Current (A)

K<sub>H₂</sub>: Fuel consumption correction factor (kgH₂ /100Whe)

LHV<sub>H₂</sub>: H₂ Lower Heating Value (120 MJ/kg)

m: Mass (kg)

MM<sub>H₂O</sub>: H₂O molar mass (18 g/mol)

MM<sub>O₂</sub>: O₂ molar mass (32 g/mol)

N<sub>cell</sub>: Number of cells in the stack (330)

P: Pressure (MPa)

R: Resistance (Ω)

T: Temperature (°C, K)

t: Time (s)

U: Voltage (V)

V: Volume (m³)

X: Mass concentration (%)

Y: Volume concentration (%)