Effects of Fuel Cell Size and Dynamic Limitations on the Durability and Efficiency of Fuel Cell Hybrid Electric Vehicles under Driving Conditions

Abstract

In order to enhance the durability of fuel cell systems in fuel cell hybrid electric vehicles (FCHEVs), researchers have been dedicated to studying the degradation monitoring models of fuel cells under driving conditions. To predict the actual degradation factors and lifespan of fuel cell systems, a semi-empirical and semi-physical degradation model suitable for automotive was proposed and developed. This degradation model is based on reference degradation rates obtained from experiments under known conditions, which are then adjusted using coefficients based on the electrochemical model. By integrating the degradation model into the vehicle simulation model of FCHEVs, the impact of different fuel cell sizes and dynamic limitations on the efficiency and durability of FCHEVs was analyzed. The results indicate that increasing the fuel cell stack power improves durability while reducing hydrogen consumption, but this effect plateaus after a certain point. Increasing the dynamic limitations of the fuel cell leads to higher hydrogen consumption but also improves durability. When considering only the rated power of the fuel cell, a comparison between 160 kW and 100 kW resulted in a 6% reduction in hydrogen consumption and a 10% increase in durability. However, when considering dynamic limitation factors, comparing the maximum and minimum limitations of a 160 kW fuel cell, hydrogen consumption increased by 10%, while durability increased by 83%.

1. Introduction

Currently, due to the increasing use of fossil fuels, global energy consumption and environmental pollution are intensifying. Researchers worldwide are exploring renewable and environmentally friendly energy solutions. Hydrogen, based on renewable energy sources, is widely regarded as a promising green energy solution for the future [1,2]. In the realm of transportation, hydrogen fuel cell hybrid vehicles serve as a pivotal means to attain low-carbon and low-pollution mobility. Particularly, when hydrogen gas is generated via renewable energy sources, the overall greenhouse gas emissions associated with the entire life cycle of the vehicle, from production to operation, approach negligible levels [3].

However, hydrogen fuel cells face significant economic disadvantages compared to internal combustion engines, even though they meet emission requirements. Currently, the global infrastructure for hydrogen refueling stations is relatively limited, resulting in higher costs associated with the production and distribution of hydrogen gas [4]. Additionally, the application of proton exchange membrane fuel cells (PEMFCs) in vehicles suffers from the drawback of poor dynamic response. To overcome this limitation, a hybrid power system combining PEMFCs with a battery pack is required [5]. Therefore, the parameter matching and energy allocation strategies for dual power sources have been a longstanding research focus [6]. Currently, the most commonly used architecture is the parallel configuration of PEMFCs and batteries. During vehicle operation, the fuel cells serve as the primary power source, while the batteries compensate for the power demands that the fuel cells cannot meet [7]. Weiguang Zheng et al. performed parameter matching for heavy-duty fuel cell commercial vehicles, considering fuel economy and the cost of the propulsion system. Their findings suggested that a power source system consisting of a 70 kW fuel cell and 696 battery cells demonstrated the best overall economic performance throughout the vehicle’s lifecycle [8]. Jianhui Zhang et al. employed a multi-objective optimization approach to match parameters for fuel cell buses, considering both the economic and durability aspects of the fuel cell. The results indicated that a 100 kW fuel cell exhibited the best performance for fuel cell buses [9]. Samuel Filgueira da Silva et al. optimized the topology of a bus system incorporating fuel cells, batteries, and supercapacitors. Using the Interactive Adaptive-Weight Genetic Algorithm, they determined that a 90 kW fuel cell exhibited the best economic performance over the vehicle’s entire lifecycle [10]. Literature research indicates that parameter matching for fuel cell vehicles has primarily focused on buses, with limited calculations for heavy-duty commercial vehicles or trucks. Additionally, the calculation of economic performance does not precisely account for fuel cell lifespan. Despite fuel cells being an important means to reduce greenhouse gas emissions as a substitute for internal combustion engines, their durability is relatively low [11]. As early as 2020, the U.S. Department of Energy set a target for fuel cell lifespan in stationary applications at over 40,000 h and 5000 h under actual driving conditions. When fuel cells are in operation, their voltage is not fixed due to the influence of activation, ohmic, and concentration losses. Therefore, quantifying the impact of losses on voltage is crucial. The degradation mechanisms of fuel cells differ between vehicle applications and laboratory testing due to the influence of load variations. When fuel cells and batteries jointly supply power to a vehicle, energy management strategies need to correctly identify the degradation state of the fuel cell to provide accurate energy consumption. As fuel cells operate, electrochemical losses increase, which can lead to changes in their output performance. Hence, the development of fuel cell degradation models is of paramount importance [12].

The membrane electrode assembly (MEA) is a crucial component of a fuel cell. All electrochemical reactions occur within it. It consists of a gas diffusion layer (GDL), a cathode catalyst layer (CCL), an anode catalyst layer (ACL), and a membrane. The catalyst layer is a crucial part of it, mainly used to enhance the rate of the oxygen reduction reaction (ORR). The energy loss that occurs in the catalyst layer is called activation loss. The energy lost in the catalyst not only dissipates as heat but also leads to catalyst degradation, resulting in a loss of electrochemical surface area (ECSA) [13]. Catalyst degradation mainly involves the dissolution of platinum-based nanoparticles and the degradation of the catalyst support material. Specifically, the dissolution process can be further divided into platinum dissolution and redeposition, formation and reduction in platinum oxides, carbon corrosion, and the membrane precipitation of platinum ions [14]. All of these reactions are influenced by temperature.

The proton exchange membrane (PEM) is a component in fuel cells that facilitates the transport of hydrogen ions from the anode to the cathode. The ohmic losses in a fuel cell are primarily caused by the ion conductivity of the membrane, which is influenced by the moisture content of the membrane [15]. The failure of the proton exchange membrane can be classified as either physical failure or chemical failure. Physical failure refers to damages such as cracks or ruptures that occur due to physical factors like airflow impact or stresses caused by changes in moisture content within the cell [16]. These damages are typically evident in the early stages of cell operation. Chemical failure, on the other hand, occurs over time due to the membrane’s degradation caused by high temperature, high humidity, and acidic or alkaline conditions. It takes longer periods of usage to manifest chemical failure.

The gas diffusion layer (GDL) in a fuel cell serves multiple functions. Its primary role is to distribute reactants evenly to the catalyst layer while providing mechanical support to both the proton exchange membrane and the catalyst. Additionally, the GDL facilitates electron conduction, heat dissipation, and water transport. In a fuel cell, concentration loss refers to the inability of the gas diffusion layer to meet the high mass flow requirements promptly. However, typically, fuel cells do not operate at current densities that result in concentration loss, and therefore, its impact on the overall fuel cell performance is minimal. Hence, when considering the rated power degradation of a fuel cell, the main focus is on catalyst layer degradation and proton exchange membrane degradation [17].

Researchers have conducted extensive work on identifying and predicting the degradation and decay of fuel cells. Currently, two main methods are used for fuel cell degradation modeling: semi-empirical methods and physical methods. Semi-empirical methods typically involve collecting a set of data in a reference state and directly fitting coefficients to be applied across all operating conditions of the fuel cell. These coefficients are often fixed values and independent of the actual operating conditions and electrochemical behavior of the fuel cell. As a result, these models cannot accurately predict degradation under different driving conditions. Physical methods, on the other hand, are based on transport equations and electrochemical reactions. These models require more detailed data compared to semi-empirical methods, but they provide more accurate results. However, certain parameters, such as the evolution of hydrogen gas content within the membrane over time, are difficult to measure and accurately estimate. Therefore, while physical models offer improved accuracy, some parameters remain challenging to measure or predict accurately [18].

The empirical and semi-empirical models currently used in the literature are mostly derived from the studies of Pei et al. [19] and Lu et al. [20]. In their research, they conducted degradation tests on fuel cells, developed degradation models based on constant degradation rates, and validated them using actual operational data from buses. However, the specific sources of the coefficients used in the models were not explained, including their relationship with temperature, humidity, and operating conditions.

Another approach to fuel cell degradation modeling is based on the establishment of equations derived from physical principles. Due to their foundation in physical phenomena, models built upon these equations have higher accuracy compared to empirical methods and are more widely applicable across different fuel cell models. However, current research in this area mainly focuses on catalyst degradation [21] or membrane degradation [21]. When considering parameters such as current density, load variations, temperature, humidity, etc., the computational cost increases, making it challenging to apply these models in practical applications.

In this study, a hybrid semi-empirical and semi-physical model was developed by combining the principles of both the physical and empirical approaches. This degradation model utilizes the degradation rate of the fuel cell measured under reference conditions as a baseline and scales it using a physical model. Similar methods can be found in the research conducted by Chen et al. [22], where they also accounted for the effects of current density, temperature, and relative humidity to correct significant deviations in the empirical model’s degradation rate. However, their results showed a linear trend in predicting the fuel cell degradation rate. Although it exhibited low error when applied to the fuel cell hybrid electric vehicle discussed in the paper, it cannot guarantee the same level of accuracy when replacing the fuel cell, as the scaling coefficients were obtained via fitting using artificial intelligence algorithms rather than derived from physical equations.

1.1. Problem Statement

Through a comprehensive review of previous research, there are still some unresolved issues:

• There has been no research conducted on the durability variation of high-power fuel cells exceeding 100 kW.
• Current empirical and semi-empirical models do not account for variations in fuel cell electrochemistry and operating conditions, as they uniformly apply the same trends on polarization curves.
• Most studies on fuel cell durability lack experimental data support.
• There is a lack of literature regarding the durability variation of fuel cells when applied in vehicles.
• Existing fuel cell durability models proposed in the literature are only applicable to laboratory testing conditions and lack adaptability for real vehicles.

1.2. Contribution

The main focus of this study is as follows:

• An analysis is conducted to examine the impact of fuel cell stack rated power and fuel cell dynamic response on both the durability of the fuel cell and the overall vehicle performance. By performing a cross-analysis, the study aims to uncover the coupling relationship between these factors to aid in the development of fuel cell hybrid electric vehicles. Secondly,
• A method is proposed to estimate the degradation rate coefficient of the fuel cell. This method utilizes empirical formulas and data to reflect the degradation of the fuel cell on the polarization curve.
• A degradation model based on real driving cycles is developed, which assesses the degree of fuel cell degradation by distinguishing the working conditions during operation. This model can be applied to establish fuel cell degradation models and predict fuel cell lifespan. Overall, the study focuses on analyzing the impact of power and dynamic response, proposing a method to estimate degradation rate coefficients, and developing a degradation model based on actual driving cycles for fuel cell durability modeling and lifespan prediction.

2. Simulation Model

In this section, we provide a detailed introduction to the key components of FCHEV. To conduct accurate research on the rated power and dynamic limitations of fuel cell stacks, we conducted detailed modeling and validation of both the fuel cell and the vehicle used. Furthermore, we developed and integrated energy management strategies and fuel cell degradation models and performed simulations under actual operating conditions of heavy-duty trucks. The vehicle simulation architecture is illustrated in Figure 1.

2.1. Fuel Cell Hybrid Tractor Model

2.1.1. The Architecture of Tractor

The vehicle in the article is a heavy-duty truck consisting of an expandable fuel cell, a 212 Ah lithium battery, and four 70 kW drive motors. The fuel cell is connected to the DC bus via a DC/DC converter, while the power battery is directly connected to the bus. This configuration serves the dual purpose of protecting the fuel cell from voltage fluctuations on the bus and reducing energy losses during DC/DC conversion. The specific configuration is illustrated in Figure 2.

2.1.2. Fuel Cell Model

The fuel system model includes the fuel cell stack and its associated components. When the fuel cell operates, energy losses inevitably occur due to chemical reactions. These irreversible losses are reflected in the polarization overpotential, and the polarization overpotential, along with the ideal electromotive force, determines the actual output voltage of the fuel cell. The output voltage of a single fuel cell is represented by the following equation:

$$V_{cell}=E_{nernst}-V_{act}-V_{ohm}-V_{con}$$

(1)

The ideal electromotive force ($E_{nernst}$) is related to pressure and temperature. It represents the electromotive force of the fuel cell at equilibrium when no current is flowing internally. The Nernst equation provides the formula for the ideal electromotive force:

$$E_{nerst}=\frac{∆G}{2F}+\frac{∆S}{2F}\left(T-T_{ref}\right)+\frac{RT}{2F}\left[\mathrm{l}\mathrm{n}\left(P_{H_2}\right)+\frac{1}{2}\mathrm{l}\mathrm{n}\left(P_{O_2}\right)\right]$$

(2)

$$V_{act}=\frac{R\cdot T}{\alpha \cdot n\cdot F}log\left(\frac{\left(i_{stack}+i_n\right)}{i_0}\right)$$

(3)

$$V_{ohm}=R_{memb}\cdot i_{stack}$$

(4)

$$V_{cons}=-B\cdot log\left(1-\frac{i_{stack}}{i_1}\right)$$

(5)

To account for the actual output performance of a fuel cell, the fuel cell accessories are integrated into the fuel cell stack, forming a fuel cell system. These accessory components are collectively referred to as the Balance of Plant (BoP), which includes the anode, cathode, and cooling circuit. The anode’s main function is to supply sufficient hydrogen to the fuel cell while also facilitating hydrogen recirculation and purging. The cathode includes a compressor that supplies air, which is humidified and then enters the fuel cell cathode flow channels. The exhausted air and generated water pass through a condenser before being released into the atmosphere. Changes in the gas excess ratio of the cathode and anode can result in variations in the performance output of the fuel cell. Reducing the gas excess ratio leads to a decrease in fuel cell performance and output voltage. The purpose of establishing a fuel cell model is to simulate the actual working process of the fuel cell and investigate its degradation mechanisms. The schematic diagram of the fuel cell system’s composition is shown in Figure 3.

2.2. Energy Management Strategy

Given that FCHEVs utilize both fuel cells and battery packs as power sources, an energy management strategy is required to coordinate the outputs of these two power sources [23]. The goal is to ensure that the fuel cell or battery pack operates within its efficient output range while maintaining the system’s economy and power. Rule-based control strategies are widely used in vehicle applications due to their simplicity and ease of implementation. However, traditional control methods often require precise mathematical models of the controlled objects. In engineering practice, a complex system can often achieve good control results based on practical operational experience. Based on a certain empirical basis, researchers have proposed the concept of fuzzy control. Fuzzy logic control consists of four main components: fuzzification, fuzzy inference, knowledge base, and defuzzification. The workflow diagram of fuzzy control is shown in Figure 4.

Fuzzification is the primary task in designing fuzzy logic control. It involves converting the received data into easily understandable information using human-like thinking. For a specific problem, different membership functions are used to determine the membership degree of each precise input variable (such as the state of charge of the battery and the difference between the demanded power and the lower limit of power in the fuel cell’s efficient range) within their respective domains. Then, based on which fuzzy subset the element belongs to, the accurate value of that variable is represented.

The knowledge base primarily stores the fuzzy subsets of the input and output variables after fuzzification, as well as the fuzzy control rules generated based on expert experience. These two components are typically stored in a database and a rule base, respectively.

The main purpose of logical inference is to deduce the output values of a fuzzy control system based on fuzzy rules. It uses a relatively broad language variable value as a working criterion to represent specific numerical values.

Defuzzification is primarily performed because the variables obtained after fuzzy inference are still in a fuzzy form. Therefore, the defuzzification process is used to convert these fuzzy variables into precise numerical values.

2.3. Fuel Cell Degradation Model

The purpose of establishing the degradation model is to quantify and predict the voltage decay issue in fuel cell operation that was not considered in the original fuel cell model. The degradation model used in the paper is based on reference [24]. To apply this model in both real-world and simulation scenarios, two implementation methods are provided. The first method involves analyzing the degradation and its influencing factors of the fuel cell under specific operating conditions by acquiring the fuel cell’s operational data. The second method involves incorporating the degradation model in parallel with the aforementioned fuel cell model, enabling the real-time optimization of the fuel cell’s output state. This approach can also be applied in practical applications.

In practical applications, the degradation behavior of a fuel cell is primarily reflected in its voltage. Therefore, when calculating the actual output voltage of the fuel cell at the same current density, the equation should be as follows:

$$V_a=V_{fc,int}\left(1-\delta \right)$$

(6)

To calculate the degradation rate of the fuel cell, a semi-empirical and semi-physical approach is proposed, combining empirical models and physical methods based on previous research on fuel cell degradation models. This approach combines the empirical knowledge and physical understanding of fuel cell degradation, providing a more comprehensive and accurate estimation of the degradation rate.

The degradation of a fuel cell’s voltage output is influenced by activation polarization, ohmic polarization, and concentration polarization. Therefore, the degradation of the fuel cell’s voltage is divided into low-power degradation, high-power degradation, and moderate-power degradation (natural degradation). According to reference [24], the degradation trends for moderate-power and high-power degradation are consistent, so they are unified as normal power degradation. When the operating conditions of a fuel cell change, there is also a significant impact on the stack [25]. Therefore, it is necessary to separately analyze the effects of load changes and start–stop operations on fuel cell voltage degradation. However, voltage is only a result of fuel cell operation, and it requires analysis of deeper influencing factors. The operating temperature of the fuel cell, relative humidity of hydrogen/air, current density, and other factors can affect the voltage output of the fuel cell. The commonly defined performance output characteristics of a fuel cell are represented by polarization curves, where the dependent variable is the current density. Therefore, defining the load variation in a fuel cell based on the intensity of the current density is more scientifically accurate. In the proposed model, based on four operational conditions of the fuel cell, the analysis of fuel cell degradation is divided into three layers: reference degradation rate, electrochemical changes, and physical factor changes. The overall calculation of fuel cell degradation can be determined using the following equation:

$$\delta =k_{lp}{\delta }_{lp}+k_{np}{\delta }_{np}+k_{lc}{\delta }_{lc}+n_{ss}{\delta }_{ss}$$

(7)

2.3.1. Reference Degradation Model

Most of the current models for determining the degree of fuel cell degradation are based on the Pei test data from reference [19]. However, due to the differences in the fuel cells used and the operating conditions, the degradation rates should not be consistent. They are expected to vary with changes in temperature, humidity, and working conditions. The degradation rates of fuel cells under different operating conditions obtained from this literature are shown in

Table 1. Fuel cell baseline degradation rate.

Operating Condition	$\frac{\mathit{d}\mathsf{\delta }}{\mathit{d}\mathit{t}}$
Idle Power (%/h)	$1.26\cdot 10^{-5}$
Load Power (%/cycle)	$5.93\cdot 10^{-7}$
High Power (%/h)	$1.47\cdot 10^{-5}$
Start–Stop (%/cycle)	$1.96\cdot 10^{-5}$

.

2.3.2. Modeling Based on Empirical Parameters

• Low power

Under this operating power, the fuel cell operates primarily in the activation overpotential regime. The degradation in this region is primarily caused by the degradation of the proton exchange membrane and the cathode catalyst. By analyzing the activation voltage formula, it is known that the main factors affecting the activation polarization voltage are the stack current density $i_{stack}$, the exchange current density $i_0$, and the internal current density $i_n$. Among them, $i_0$ has a functional relationship with ECSA as follows [26]:

$$i_0=i_0^{Pt}ECSA$$

(8)

$$ECSA=S_0\times e^{-k_{c}t}$$

(9)

In the equation, A represents the ratio of the catalyst’s active surface area to the single-cell area of the fuel cell. As shown in Figure 5, the typical active surface area of a fuel cell exhibits exponential characteristics [27]. Therefore, the activation voltage formula is as follows:

$$V_{act}=\frac{RT}{\alpha \cdot n\cdot F}ln\left(\frac{i_{stack}+i_n}{i_0\times S_0\times e^{-k_{c}t}}\right)=V_{act,0}-A\times k_c\times t$$

(10)

According to the reference model, the voltage decay in idle mode is determined by measuring the current density at 10 mA/cm². Therefore, at this current density, the polarization voltage coefficient is normalized to 1 [19]. The calculation of the polarization voltage coefficients at other current densities is as follows:

$${\tau }_{lp}\left(i\right)=0.0006i+0.9937$$

(11)

2.

Medium power

When operating in moderate power conditions, fuel cells experience more pronounced degradation factors. At this stage, the fuel cell stack exhibits higher ohmic losses. The ohmic resistance, which contributes to the ohmic losses, consists of three main components: ionic resistance $R_{ion}$, electronic resistance $R_{elec}$, and contact resistance $R_{contact}$. The overall ohmic resistance can be determined via high-frequency resistance (HFR) experiments. Therefore, the formula for ohmic resistance is expressed as

$$R_{ohm}=R_{ele}+R_{ion}+R_{contact}$$

(12)

According to the results from reference [28], the ohmic resistance is a function that varies with time. Considering the degradation rate from the reference model, the coefficient for the high-power point can be set to 1. Therefore, the calculation of the ohmic resistance coefficient for fuel cells under moderate power conditions is as follows:

$${\tau }_{mp}\left(i\right)=0.0002i+0.8592$$

(13)

3.

High power

When fuel cells operate at high power levels, the ohmic losses and electrochemical losses in the fuel cell stack increase, leading to an elevated temperature. At this stage, the increased temperature in the fuel cell can potentially accelerate degradation phenomena. Degradation primarily occurs due to phenomena such as partial oxygen starvation, membrane flooding, and increased losses in kinetics, ohmic resistance, and mass transport. All these losses are directly proportional to the increase in current density. In the absence of temperature and humidity considerations, the degradation mechanisms in this scenario can be scaled with the current density:

$${\tau }_{hp}\left(i\right)=0.0002i+0.7674$$

(14)

4.

Load Change

The degradation caused by load variations is primarily a result of multiple factors interacting together. The main phenomena leading to membrane and catalyst degradation are associated with cathode and anode starvation, gas flow, water management, and thermal management issues. Due to the unpredictable nature of load variations, the voltage degradation rate caused by load changes differs under different operating conditions. Consequently, there is no fixed cycle that can characterize the voltage degradation caused by load variations. Currently, researchers often detect current density oscillations as indicators of load change and apply the corresponding degradation rate under reference test conditions for each load change period [28]. However, in practical operational settings, the changes in current density often occur slowly, and the voltage oscillations may differ from laboratory testing conditions. Therefore, this degradation model monitors the changes in current density at each time step.

The corresponding analytical expression for a is as follows:

$${\tau }_{lc}\left(\frac{di}{dt}\right)=\frac{d{n}_{lc}}{dt}\frac{\frac{d\delta }{dt}}{{\frac{d\delta }{dt}}_{lc,ref}}=\frac{{\left|∆i\right|}_{dt}}{2{\left|∆i\right|}_{ref}}$$

(15)

2.4. Integration of Degraded Models

As mentioned earlier, this model can be used in parallel with a fuel cell model to achieve online estimation in a simulation model. It can also be applied to fuel cell power control to achieve degradation control of the fuel cell. By using this model for real-time monitoring and estimation, the degradation status of the fuel cell can be detected promptly, and corresponding control strategies can be implemented to mitigate the degradation rate, improve the fuel cell’s lifespan, and enhance its performance stability. This control approach can help optimize the operation of the fuel cell system, improving its reliability and efficiency.

In the first scenario, integrating this model into the energy management strategy allows for optimal energy control. In this case, the energy management strategy can receive feedback on the degree of fuel cell degradation, which can be reflected in hydrogen consumption and power output. The fuel cell voltage degradation can be applied to either the voltage or power.

In the second scenario, this model can be directly applied to the fuel cell power demand as a power degradation factor, guiding the operation of the fuel cell.

$$P_{fc}=P_{fc,ref}\left(1-\delta \right)$$

(16)

In this case, due to the influence of the power degradation factor on the fuel cell’s power output, the energy management strategy is unable to distinguish whether the insufficient power output is caused by the degradation of the fuel cell itself or by other factors such as load demand or system faults. As a result, the energy management strategy may incorrectly assess the fuel cell’s state and hydrogen consumption.

To validate the accuracy of the degradation model proposed in the study, actual vehicle operational data was used for simulation and analysis. The fuel cell operating current during real-world driving cycles was collected and used as input for conducting durability tests on an actual operating bench. The actual operating current of the fuel cell is shown in Figure 6. After 5323 h of cyclic operation, polarization curve measurements were performed to evaluate the actual degradation rate of the fuel cell. To verify the accuracy of the proposed degradation model, a fuel cell degradation model and a fuel cell system model were built using SIMULINK, and the experimental data were used as input. The results are shown in Figure 7. From the figure, it can be observed that the simulation model can effectively represent the initial characteristics of the fuel cell. The model also follows the experimental values for the polarization curve of the fuel cell after durability testing, with an average error of 0.51%. The maximum error, reaching 1.5%, occurs at a high current density of 1.52 A/cm².

After completing the 5323 h durability test, the fuel cell’s power degradation is determined to be 2.3%. Based on calculations, it is estimated that it would take 23,143 h for the fuel cell system to degrade by 10%, which aligns with the target set by DOE2020.

3. The Impact of Size and Dynamic Limitations

In this section, we conducted simulations using a comprehensive fuel cell vehicle model. The detailed parameters used are listed in

Table 2. FCHEV parameters.

Parameter	Unit	Value
Vehicle Mass	kg	12,150
Windward area	m2	8.32
Radius	mm	542.5
Air drag coefficient	-	0.6
Rolling resistance coefficient	-	0.015
Battery capacity	kW·h	123.1
Initial SOC	%	72
Battery voltage	V	600

:

3.1. Impact on Fuel Cell Performance

The maximum power and dynamic response of a fuel cell system can significantly impact the performance output of the fuel cell, leading to different trends in current density variations. Therefore, considering the degradation and output performance of the fuel cell system under real-world operating conditions, this section analyzes the trends in fuel cell output performance with changes in power and dynamic response. Figure 8 illustrates the current density variations for fuel cells rated at 100 kW and 200 kW. In the figure, the analysis of maximum power and minimum power design for fuel cell stack performance and degradation is conducted by introducing the change rate of fuel cell current density as a comparative condition. The study selects current density change rates of 0.001 A/cm², 0.01 A/cm², 0.1 A/cm², and 1 A/cm², corresponding to strict power limitations and ideal conditions with no limitations.

In Figure 8a, where the fuel cell current density change rate is controlled at 1 A/(cm²·s), it corresponds to no control over the fuel cell’s output performance (only existing in the simulation). The energy management strategy aims for power performance and charge maintenance without considering the fuel cell’s aging and dynamic response. When increasing the fuel cell power, it can be observed that the time for the fuel cell to reach its rated power output decreases. This is because high-power fuel cells can instantly deliver a large amount of power to meet the power demand and energy storage requirements of the power battery, whereas low-power fuel cells need to sustain themselves at high power levels for a longer time to meet the power demand. Since fuel cell systems are primarily composed of individual fuel cells, the shorter the time they operate at maximum power, the higher their efficiency and economic performance. Therefore, fuel cells with lower rated power cannot simultaneously balance efficiency and economic performance while meeting power requirements.

Figure 8b represents setting the fuel cell’s current density change rate to 0.1 A/(cm²·s). Although this limitation is still low compared to the actual dynamic characteristics of the fuel cell, a comparison between Figure 8a,b reveals that some high-power points in Figure 8a cannot be achieved. In order to meet the power demand, the fuel cell also tends to reduce the time spent operating at minimum power. These phenomena are more pronounced in the fuel cell curve with a maximum power of 100 kW. In addition, due to this dynamic limitation, the power changes of 200 kW and 100 kW fuel cells become relatively stable. Combined with the fuel cell degradation model, it can be seen that a gentle load change in fuel cells will increase durability.

Figure 8c,d illustrate the variations in fuel cell output power when the current change rate is limited to 0.01 A/(cm²·s) and 0.001 A/(cm²·s), respectively. In these cases, due to the stringent restrictions on the fuel cell’s dynamic response, it can be clearly seen that the power output of the fuel cell becomes smoother. In Figure 8c, both fuel cells with different maximum power settings reduce the time spent operating at the minimum power point. As the power demand increases, the 100 kW fuel cell increases the time spent operating at the rated power point. At this higher current density, the fuel cell generates more heat, leading to noticeable high-power degradation. Moreover, as observed in the experimental results in Figure 7, the degradation rate of the fuel cell is higher under high-power conditions. In Figure 8d, strict current density limitations result in a longer time for the fuel cell to reach its maximum power. For both power designs, an increase in the minimum operating power and a decrease in the intensity and amplitude of power changes can be observed. Based on the analysis in Figure 8c, it can be inferred that the degradation rate of the fuel cell decreases in this case, but the equivalent hydrogen consumption increases. According to the simulation results, low-power fuel cells are unable to maintain the charge characteristics of the power battery.

3.2. Impact on the Performance of Fuel Cell Hybrid Vehicles

The previous analysis discussed the impact of size and dynamic limitations on the performance output and degradation rate of fuel cell systems. However, in practical applications, it is more important to consider the changes in overall vehicle power performance and economy.

The overall energy consumption of a fuel cell hybrid electric vehicle is ultimately provided by hydrogen gas. From the perspective of energy conversion, electrical energy consumption can be equivalently translated into the mass of hydrogen consumed by the fuel cell. In this case, the hydrogen consumption of the vehicle can be calculated using the following formula:

$$m_{veh}=m_{fc}+\frac{∆SOC\cdot Q_{bat}}{\eta H_L}$$

(17)

In this section, hydrogen consumption was normalized in order to visually compare its relationship with power. Figure 9 illustrates the impact of the current variation rate and maximum power on the overall vehicle hydrogen consumption. As mentioned earlier, a higher-rated power of the fuel cell leads to lower current density and higher efficiency when operating at the same power. The hydrogen consumption presented here is the actual hydrogen consumption of the fuel cell, converted and compared with the variation in the power battery’s state of charge (SOC). Due to the limitations in the fuel cell’s current density variation rate, there are cases where the power battery’s SOC at the end of the operation does not return to its initial state. To account for this, this portion is converted into equivalent hydrogen consumption for comparison. From Figure 9, it can be observed that the equivalent hydrogen consumption for a fuel cell hybrid vehicle is the lowest at 160 kW. Increasing or decreasing the fuel cell’s rated power will affect the hydrogen consumption economy of the entire vehicle. This is because when the fuel cell’s size is reduced, it tends to operate in the high current density region to meet the vehicle’s energy demands, resulting in decreased efficiency. Compared to a fuel cell with a power rating of 160 kW, a 100 kW fuel cell exhibits an increase in hydrogen consumption ranging from 6% to 33%. On the other hand, increasing the power of the fuel cell does not proportionally increase hydrogen consumption, even though the fuel cell operates more efficiently. Increasing the power of the fuel cell stack necessitates higher power consumption by accessories such as the compressor, leading to a higher increase in the overall hydrogen consumption of the fuel cell vehicle compared to the increase in power. As a result, a fuel cell with a rated power of 200 kW exhibits a hydrogen consumption that is 1% to 7% higher than that of a 160 kW fuel cell. Regarding the current density variation rate of the fuel cell, an unrestricted state (1 A/(cm²·s)) does not correspond to the lowest hydrogen consumption. By limiting the current density variation rate to 0.01 A/(cm²·s), the hydrogen consumption of the 160 kW fuel cell can be further reduced by 1%. Combined with the analysis in Figure 8c, it can be observed that when the current density variation rate is limited, the fuel cell tends to operate in a steady-state region, achieving a balance between economy and power under conditions with relatively minimal changes. This also ensures the maintenance of charge capability. However, when the current density variation rate is limited to 0.001 A/(cm²·s), the fuel cell’s power output is insufficient, resulting in more energy being supplied by the power battery. At the end of the operation, the power battery’s charge maintenance capability is insufficient, resulting in a maximum difference of 29.8%. The lack of energy from the power battery needs to be converted into equivalent hydrogen consumption. This conversion leads to an increase of 32.6% in hydrogen consumption for a vehicle equipped with a 100 kW fuel cell. In vehicles equipped with a 160 kW and 200 kW fuel cell, hydrogen consumption increases by 7% and 10%, respectively.

The equivalent hydrogen consumption at a current density change rate of 0.01 A/cm² is shown in

Table 3. Equivalent hydrogen consumption at a current density change rate of 0.01 A/cm².

Power (kW)	100	160	200
H2 Consumption (g)	3401.7	3380.4	3386.9

. It can be observed that the fuel cell with the highest hydrogen consumption is the 100 kW power cell, with an equivalent hydrogen consumption of 3401.7 g. The 160 kW fuel cell has the lowest equivalent hydrogen consumption at 3380.4 g, with a difference of 21.3 g. The 200 kW fuel cell falls in the middle in terms of equivalent hydrogen consumption, which aligns with the previous economic analysis.

3.3. Impact on the Durability of Fuel Cells

In this section, we will analyze the impact of fuel cell rated power and current density variation rate on the durability of the fuel cell. Durability refers to the ability of the fuel cell to maintain its performance and lifespan during long-term operation.

Based on the analysis results from the previous section, we can infer that the rated power and current density variation rate also have an impact on the degradation rate of fuel cells. Figure 10 illustrates the variations in degradation factors of fuel cells under different rated powers and current density variation rates. By considering the analysis in Figure 11, we can observe their combined effects. According to the lifespan termination criteria established by the Department of Energy, the fuel cell’s lifespan reaches its endpoint when the power relative to the nominal voltage decreases by 10%. In this experiment, the fuel cell’s nominal power was used, corresponding to a current density of 1.6 A/cm².

When increasing the rated power of the fuel cell system there is a significant impact on the degradation distribution of the fuel cell. From Figure 11, it can be observed that, in the absence of dynamic limitations, the 100 kW designed fuel cell has a 15% increase in lifespan compared to the 200 kW fuel cell. Combining this with Figure 10, it becomes apparent that this is due to lower degradation caused by load variations in the lower-power fuel cell. Figure 8a indicates that higher-power fuel cells exhibit more pronounced load variations in the unrestricted state, leading to an increased proportion of degradation caused by load changes. The proportion of degradation caused by load variations increases from 43.1% to 48.1%. Additionally, from Figure 10, it can be seen that start–stop events are the second-largest contributing factor to degradation, and they are not influenced by cycling conditions but rather by the number of start and stop cycles. As the rated power of the fuel cell system increases, the proportion of low-power operation increases while the duration of high-power operation decreases.

From Figure 10, it can be observed that as the restriction on current density variation rate becomes more stringent, the proportion of degradation caused by load variations increases. Therefore, imposing dynamic variation restrictions on the fuel cell system is the most effective way to increase its lifespan. Figure 11 also demonstrates that reducing the current density variation rate can effectively extend the fuel cell’s lifespan. Comparing the working conditions of the fuel cell with no dynamic restrictions to the most stringent dynamic restriction, the durability of the 100 kW and 200 kW fuel cells increases by 106% and 101%, respectively. Although it may not be feasible to apply such strict restrictions in practical situations, limiting the current density to 0.1 A/cm²·s and 0.01 A/cm²·s can still yield improvements of approximately 20% and 50%, respectively. This increase in lifespan is primarily attributed to the reduction in degradation caused by load variations. Under a rated power of 160 kW, the degradation caused by load variations ranges from 5.7% to 43.9% of the total degradation. Combining this with Figure 11, it can be observed that the projected lifespan of the fuel cell increases incrementally, with a maximum increase of 106%.

4. Conclusions

In this study, we developed a semi-physical and semi-empirical degradation model for onboard proton exchange membrane fuel cells (PEMFCs) and investigated the impact of fuel cell rated power and dynamic limitations on fuel cell hybrid electric vehicles (FCHEVs). Subsequently, the proposed degradation model was applied to an FCHEV. We conducted simulations on the China Heavy-duty Commercial Vehicle Test Cycle (CHTC) using fuel cells with different rated powers while controlling the dynamic responsiveness of the fuel cell via energy management strategies. The simulation results demonstrate the following findings:

Increasing the fuel cell’s rated power can improve the overall vehicle efficiency, resulting in an average reduction of around 6% in hydrogen consumption.

Increasing the dynamic response limitations of the fuel cell leads to an approximately 3% increase in hydrogen consumption. However, it effectively enhances the durability of the fuel cell, and the projected lifespan is expected to increase by approximately 27% compared to a current density change rate of 0.001 A/cm²·s.

From the analysis of fuel cell degradation under different operating conditions, it is observed that when the dynamic variation rate is low, the proportion of degradation caused by load changes increases, accounting for approximately 48% of all degradation factors.

In the design of the powertrain system for fuel cell hybrid electric vehicles, it is important to consider the degradation of fuel cells as part of the evaluation. Simply increasing the fuel cell power to improve efficiency does not significantly enhance durability or reduce hydrogen consumption. When comparing a 200 kW fuel cell to a 100 kW fuel cell, the hydrogen consumption increases by 1%, and the projected lifespan decreases by 8%.