JBCS

INTRODUCTION

As the global demand for renewable energy continues to rise, fuel cell technology has attracted significant attention as an efficient and environmentally friendly energy conversion device. Proton exchange membrane fuel cells (PEMFCs), in particular, are considered as a promising direction for future energy development due to their high energy density, rapid response, and zero emissions. However, a critical technical challenge for PEMFCs lies in their performance during startup in low-temperature environments, especially in applications such as automotive and mobile devices. The cold-start issue has thus become a key bottleneck restricting their widespread adoption.

Under low-temperature conditions, water management and reaction efficiency face numerous challenges. The electrolyte membrane in PEMFCs is prone to freezing, which impedes effective proton conduction and significantly reduces the overall reaction efficiency of the cell.¹ Furthermore, the removal of water produced by reactions becomes difficult at low temperatures, leading to water accumulation and subsequent freezing within the cell - this further blocks gas diffusion and hinders electrochemical reactions.² These issues result in increased startup overpotential, heightened mass transfer resistance, and reduced reaction rates, ultimately impairing the startup process.³ Water management under low-temperature conditions is critical to the startup challenges of fuel cells. In PEMFCs, protons are conducted through the proton exchange membrane, and water generated from redox reactions must be promptly expelled from the reaction layer. Ineffective water removal can cause accumulation in the electrodes and gas diffusion layer, obstructing gas transport and disrupting the reaction process.⁴ This problem is exacerbated at low temperatures, as frozen water can further block microporous channels in the gas diffusion layer, significantly reducing the efficiency of electrochemical reactions.⁵

In recent years, researchers have proposed various water management optimization strategies to address this issue. For example, using hydrophobic gas diffusion layer materials can enhance water discharge capability and reduce water accumulation at low temperatures.⁶ Additionally, optimizing flow channel design to improve water expulsion effectiveness is another viable approach.⁷ Increasing the width and depth of flow channels can promote the uniform distribution of gas and liquid, thereby reducing local water buildup.⁸ During cold-starts, the electrolyte membrane in PEMFCs is prone to freezing, which drastically diminishes proton conduction across the membrane. This freezing effect not only prolongs startup time but may also degrade the mechanical properties of the membrane material, shortening its lifespan.⁹ To tackle this issue, researchers have proposed various strategies. A common approach involves using external preheating devices to warm the fuel cell system, preventing electrolyte membrane freezing.¹⁰ However, while preheating strategies can effectively improve startup efficiency, they increase operational costs and design complexity due to additional energy consumption and system intricacies.¹¹ Consequently, researchers are developing electrolyte membrane materials with superior low-temperature performance to reduce reliance on external preheating. For instance, certain perfluorosulfonic acid ion-exchange membranes exhibit enhanced proton conductivity at low temperatures, making them suitable for extreme environments.¹²

At low temperatures, the catalytic activity within the cell declines, significantly slowing the electrochemical reaction rate during startup. This is attributed to the poor reaction kinetics of catalysts at low temperatures, which hinders their ability to effectively catalyze redox reactions.¹³ To address this issue, researchers have proposed various strategies for optimizing catalyst design to enhance low-temperature catalytic activity. Nanostructured catalysts, with their large specific surface area and high surface energy, are widely utilized in fuel cell catalyst design. Nanoscale noble metal catalysts, such as platinum (Pt)-based catalysts, exhibit significantly higher activity at low temperatures compared to traditional catalysts.¹⁴ Additionally, the introduction of bifunctional catalysts offers new possibilities for cold-starts. Bifunctional catalysts can simultaneously promote oxidation and reduction reactions, alleviating the issue of insufficient catalyst activity during startup.¹⁵ For example, Pt-Ru bimetallic catalysts demonstrate greater resistance to CO poisoning and higher reaction activity in low-temperature environments, thus being widely employed in low-temperature fuel cell research.¹⁶

To address the cold-start issue of PEMFCs, researchers have proposed various system-level startup strategies. Preheating startup is a common method that uses external heating devices to raise the fuel cell to an appropriate operating temperature, preventing electrolyte membrane and water freezing. However, this approach increases system complexity and energy consumption, which is particularly disadvantageous for mobile fuel cell applications.¹⁷ Another strategy involves using advanced control algorithms to optimize the startup process. By monitoring parameters such as temperature, water content, and current in real time, the control system can dynamically adjust operating conditions during startup to achieve more efficient initiation.¹⁸ The effectiveness of these methods depends, in part, on the response speed of the hardware system and the low-temperature performance of cell materials. Therefore, dual optimization of materials and systems is crucial for achieving rapid startup.^19-21

Multi-objective optimization is a mathematical and computational method used to simultaneously optimize multiple conflicting objective functions. In the design and optimization of fuel cells, it is often necessary to balance multiple performance indicators such as conductivity, corrosion resistance, cost, and lifespan.^22-25 Thus, multi-objective optimization methods provide powerful tools for fuel cell system design. In fuel cell system optimization, common multi-objective optimization methods include genetic algorithms, particle swarm optimization, and simulated annealing. These methods can search for optimal solutions in complex design spaces, balancing different design objectives. Fernández et al.²⁶ applied genetic algorithms to fuel cell system optimization, aiming to maximize cell efficiency while minimizing system cost. The study demonstrated that multi-objective optimization methods can effectively enhance the overall performance of fuel cells and provide multiple design options. In the design of metallic bipolar plates, multi-objective optimization can be used to balance different design requirements, such as optimizing flow channel structures to enhance heat transfer while reducing pressure drop, or considering factors like conductivity, cost, and durability when selecting materials.

In conclusion, when addressing the cold-start issue of proton exchange membrane fuel cells, auxiliary heating strategies can effectively reduce water freezing by raising the initial cell temperature, thereby accelerating the startup process. However, auxiliary heating requires a trade-off between energy consumption and efficiency, and optimizing this process is crucial for improving overall system efficiency. In this regard, multi-objective optimization algorithms show great potential, as they can balance multiple conflicting performance indicators to optimize auxiliary heating strategies. Through multi-objective optimization algorithms, factors such as startup time, energy consumption, and heating efficiency can be considered simultaneously to design more efficient auxiliary heating strategies. This approach enables dynamic adjustment of heating power under different operating conditions, effectively preventing electrolyte membrane and water freezing while minimizing energy consumption. Accordingly, this paper focuses on optimizing fuel cell auxiliary heating cold-start strategies based on multi-objective optimization. By fully considering key factors such as positive temperature coefficient (PTC) heating power, temperature rise rate, and cold-start time, it provides a theoretical basis for formulating cold-start strategies.

 

EXPERIMENTAL

Fuel cell one-dimensional multi-phase cold-start single-cell model

The cold-start model primarily consists of electrochemical reaction equations, various conservation equations, and equations pertaining to the five states of water: membrane dissolved water, membrane-bound ice, supercooled water, ice, and water vapor. The equations involved in the proposed model have been given in previous studies.^27-30 Referring to previous studies, this paper gives a detailed modeling process of the simulation model, as shown in Figure 1.

 

 

One-dimensional multiphase single-cell model

The one-dimensional multiphase single-cell model serves as the foundation for fuel cell stack modeling. As shown in Figure 1, the modeling process for the one-dimensional multiphase cold-start fuel cell stack is detailed as follows.

Model assumptions

To reduce computational load while ensuring model reliability, a series of assumptions are made. These include:

(i) All gases within the model are considered ideal gases, and gravitational effects are neglected.

(ii) Water produced by the electrochemical reaction is initially treated as membrane-bound water.

(iii) Only heat and mass transfer within the vertical plane of the cell are considered.

(iv) The influence of internal pressure changes on cell performance is ignored.

(v) The presence of liquid water and ice in the gas channels is neglected.

(vi) Sublimation from ice to water vapor is not considered.

Mathematical equation construction

The mathematical model primarily consists of electrochemical equations and various conservation equations.

(i) Electrochemical equations: the output voltage is expressed as the sum of the Nernst voltage, the activation overpotentials at the anode and cathode, the concentration overpotentials at the anode and cathode, and the ohmic overpotential.

(ii) Conservation equations: the model includes conservation equations for mass, momentum, species, charge, liquid water, ice, membrane-bound water, and membrane-bound ice.

Source term determination

The cold-start process at low temperatures involves multiple source terms, each expressed differently in various regions of the fuel cell. The mass and species conservation equations include source terms derived from hydrogen, air, and water vapor. The momentum conservation source terms are defined based on the specific regions within the cell. The electron and proton conservation source terms also vary depending on the region. Determining these source terms is crucial for accurately representing the physicochemical processes occurring within the fuel cell.

Phase change source term analysis

Water undergoes phase transitions under specific conditions, making it essential to analyze the variation of cold-start phase change source terms under different conditions. For example, the water vapor-liquid water phase change source term is determined based on the comparison between water vapor pressure and the saturation vapor pressure, along with temperature conditions. Other phase change source terms, such as water vapor-ice and liquid water-ice, also have their own condition-based calculation formulas.

These formulas reflect the governing rules of water phase transitions during the cold-start process.

Set model parameters

Basic parameters of the fuel cell like size, material physical properties, etc., are shown in Table 1.

 

 

One-dimensional multiphase reactor model

Based on the one-dimensional multiphase single-cell model, the model is extended to the stack level. This process mainly considers the following aspects:

Energy exchange between single cells

(i) Heat transfer via cooling channels: adjacent single cells exchange heat through the cooling channel layer (with shared flow field plates on the anode/cathode side). The heat transfer is calculated using the following formula:

where, Q_ij is the heat transfer rate between the cell, k_cp (W m^-2 K^-1) is the heat transfer coefficient between two adjacent battery flow channel layers, T (K) is the temperature, δ_cp (m) is the thickness of adjacent flow channel layer.

(ii) Heat transfer between end plate and edge battery: the edge single battery is thermally conducted to the reactor through the end plate. The calculation formula is as follows:

where, k_{cp_ep} (W m^-2 K^-1) is the heat transfer coefficient between adjacent flow channel layer and edge flow channel layer, δ_ep (m) is the thickness of the edge plate, T_ep and T_cp (K) are the temperature of adjacent flow channel layer and edge flow channel layer, respectively.

Coolant system modeling

(i) Coolant flow channel module: this module includes the inlet manifold, outlet manifold, PTC (positive temperature coefficient) electric heater, and connecting pipes. The internal temperature loss due to fluid flow is neglected.

(ii) Energy conservation equation: taking the heat transfer between the inlet pipe and the inlet manifold as an example, the inlet pipe accounts for both PTC heating and convective heat transfer with air. The calculation formula is as follows:

where, m_in (kg) is the total mass of coolant in the inlet pipe, C_{p_w} (J kg^-1 K^-1) is the specific heat capacity of the coolant, q_m (kg s^-1) is the mass flow of coolant, T_PTC (K) is the temperature of the PTC heater, T_in (K) is the temperature of the coolant in the inlet pipe, A_{pape_in} (m²) is the side surface area of the inlet pipe, T_bd (K) is the external ambient temperature, h_{cp_air} (W m^-2 K^-1) is the natural convective surface heat transfer coefficient between the pipe surface and the external air.

The inlet manifold is considered to be exchanged with the end plate for heat transfer. The calculation formula is:

where, m_{m_in} (kg) is the total mass of coolant in the inlet manifold, T_{m_in} (K) is the temperature of the coolant in the inlet manifold, A_mani (m²) is the side area of the manifold, T_ep (K) is the end plate temperature, h_{cp_m} (W m^-2 K^-1) is the convective heat transfer coefficient between the coolant and the manifold.

Simulation termination conditions

The one-dimensional multiphase stack model is developed based on Matlab R2024a/Simulink (The MathWorks Inc., USA, 2024), and includes the stack module, current/voltage input module, temperature/voltage output module, and state judgment module. The judgment criteria are defined as follows:

(i) The failure condition is when the voltage of any single cell drops to 0 V.

(ii) The success condition is when the minimum temperature among all single cells exceeds 0 ºC.

The simulation ends when the cold start succeeds or a failure occurs.

Model validation

The model validation was performed using experimental data under a specific operating condition, where the fuel cell stack is started from a relatively low temperature (263.15 K) up to the normal operating coolant temperature. The initial temperatures of both the stack and the coolant were approximately 263.15 K. A linear loading strategy was adopted: the current was ramped linearly from 0 A to approximately 80 A within 15 s, and then held constant for about 185 s. Throughout the entire test, the coolant circulated in a small loop, and no heater was activated. The comparison between experimental and simulation data is shown in Figure 2. It can be observed that the simulation results match the experimental data well throughout the test, indicating that the model is suitable for further studies on coolant-assisted heating during cold start.

 

 

RESULTS AND DISCUSSION

Cold-start without PTC successful boundary identification

To investigate the effectiveness of auxiliary heating strategies during cold start, this study first identifies the minimum successful cold-start boundary of a fuel cell stack composed of 30 single cells. This step establishes the lowest self-start boundary without auxiliary heating. Using a cold-start stack model, we analyze the performance under temperatures ranging from 251.15 to 271.15 K and load rates from 0.005 to 0.040 A cm^-2. By assessing the minimum single cell voltage, we determine whether the cold start is successful, thereby establishing the minimum temperature boundary for self-starting. As illustrated in Figure 3, the minimum single cell voltage decreases with decreasing temperature. This is due to the increased rate of ice formation at the three-phase interface of the catalyst layer (CL) at lower temperatures. With a constant load rate, the CL gradually becomes covered with ice, obstructing gas transport and hindering electrochemical reactions, leading to a voltage drop.

 

 

As the load rate increases, the minimum single cell voltage decreases, and the self-start temperature is reduced. Figure 3 shows that the minimum successful self-start boundary is 256.15 K at a load rate of 0.040 A cm^-2, compared to 261.15 K at 0.005 A cm^-2, highlighting the impact of load rate on cold start. This phenomenon occurs because higher load rates lead to faster increases in current density, causing voltage to drop more rapidly due to voltage-current characteristics. However, the increased load rate also accelerates the temperature rise rate, facilitating ice melting and thus supporting successful cold start.

Further increasing the load rate continues to enhance the temperature rise rate but also increases water production at high currents, thereby accelerating the ice formation rate. Figure 3 also indicates that higher load rates result in lower minimum single cell voltages, increasing the risk of reverse polarization, which is detrimental to cold start of fuel cells. Consequently, this study focuses on a maximum load rate of 0.040 A cm^-2 for further investigation.

Analysis of the influencing factors of auxiliary heating and cold start

Based on the analysis of Figure 3, it is evident that the minimum successful cold-start temperature at a load rate of 0.040 A cm^-2 is 256.15 K. Consequently, this temperature is selected as the research condition for the auxiliary heating strategy. In this strategy, the PTC power serves as the primary external heat source, providing significant temperature elevation for the fuel cell, thereby enhancing its success rate. The flow rate of the coolant, which acts as the heating medium for the PTC, is crucial for the distribution of heat among individual cells. Simultaneously, the load rate, as a significant factor influencing the cell self-heating rate, must also be considered in the auxiliary heating strategy. Therefore, this section focuses on investigating the effects of various auxiliary heating factors, such as load rate, coolant flow rate, and PTC heating power-on cold-start characteristics. Additionally, the impact of these three factors on cold-start performance will be quantified to support the subsequent application of the NSGA-II algorithm.

Effect of load rate on auxiliary-heating cold start

Figure 4 illustrates the cold-start characteristics at various loading rates. As depicted in Figure 4a, an increase in the loading rate results in a faster growth rate of the cathode ice volume fraction, with the onset of icing occurring earlier. This phenomenon can be attributed to the fact that the cold-start process is essentially an electrochemical reaction within the fuel cell. As the loading rate increases, the rate of current density growth accelerates, directly reflecting the intensity of the electrochemical reaction. Consequently, the reaction rate and water production rate increase, leading to a higher rate of ice formation. Additionally, the faster generation rate of membrane-dissolved water in the catalyst layer (CL) facilitates reaching the maximum non-freezing water content, which hastens the onset of icing.³¹

 

 

Figure 4b shows that as the loading rate increases, the rate of temperature rise also increases. A higher loading rate enhances the self-heating rate of the stack, allowing the temperature to rise above the freezing point before the ice completely covers the three-phase boundary, thereby increasing the likelihood of a successful cold start.

In Figure 4c, it is evident that with higher loading rates, the voltage drops to a lower value before reaching zero. This indicates that an increased loading rate causes the voltage to decrease rapidly with the swift increase in current. During the cold-start process, if the loading rate is excessively high, the voltage may quickly fall below zero, resulting in a reverse polarity and ultimately leading to cold-start failure. Furthermore, an increase in the loading rate accelerates the icing rate, which quickly occupies the three-phase boundary and causes a voltage drop.

Figure 4d demonstrates that as the loading rate increases, the growth rate of the coefficient of variation (Cv) of voltage fluctuation also increases. Voltage fluctuation reflects the voltage differences between individual cells, calculated using Equation 5. Higher loading rates result in a faster rate of voltage decline between cells. Due to the end plate effect, the operating conditions vary among individual cells, leading to differences in the magnitude and frequency of voltage decline, ultimately causing fluctuations in coefficient of variation (Cv). Moreover, increasing the loading rate enhances the icing rate, and the differences in icing at the three-phase boundary among individual cells also contribute to Cv fluctuations.

where, sd is voltage standard deviation and mean is voltage average.

In summary, both excessively high and low loading rates are detrimental to the success of cold starts. At lower loading rates, the temperature rise is insufficient to effectively prevent icing, thereby increasing the likelihood of cold-start failure. Conversely, increasing the load rate accelerates both the temperature rise and the icing rate. This requires a careful balance of the effects of loading rate on temperature and icing to identify the optimal range. As illustrated in Figure 4, the impact of the loading rate on temperature rise progressively decreases, indicating that there is a limit to how much loading rate can influence temperature rise. Therefore, determining the appropriate loading rate requires a comprehensive assessment of the relationship between icing and temperature rise, taking into account voltage, temperature, ice volume fraction, and changes in the Cv curve.

Effect of coolant flow rate on auxiliary heating during cold start

In the process of auxiliary heating during a cold-start, the fluidity of the coolant is crucial for ensuring uniform thermal distribution within the system. During the operation of the fuel system, maintaining an appropriate coolant pump speed is essential to achieve uniform temperatures across the individual cells of the fuel stack, thereby enhancing the balance of its electrochemical performance. Additionally, this prevents the formation of local hotspots that could damage the proton exchange membrane and cause localized short circuits. During the low-temperature cold-start phase, the coolant flow rate is a critical factor for successful operation. An appropriate flow rate can effectively mitigate the "end plate effect", preventing rapid freezing of cells near the end plates, which could lead to system shutdown.

Figures 5a-5c illustrate that the coolant flow rate has minimal impact on system temperature rise, voltage, and freezing. However, Figure 5d shows that as the coolant flow rate increases, the coefficient of variation (Cv) gradually decreases. This indicates that increasing the coolant flow rate effectively promotes uniform temperature distribution among the individual cells, thereby improving Cv. Nevertheless, it is also evident from Figure 5d that the improvement in uniformity diminishes with further increases in coolant flow rate, suggesting a limited benefit from higher flow rates. Based on these considerations, this study concludes that selecting a coolant flow rate in the range of 0.1-0.5 kg s^-1 is reasonable, and subsequent optimization strategies can be developed within this range.

 

 

Effect of PTC heating power on auxiliary during heating cold start

In low-temperature environments, fuel cell stacks encounter challenges such as voltage instability, ice formation, and insufficient temperature rise during startup. The implementation of PTC heating-assisted startup strategy significantly mitigates these issues.

Firstly, in cold environments, water within the stack may freeze, leading to ice formation. This ice can obstruct the pathways for reactive gases and hinder mass transfer within the stack. The PTC heater can heat the air or directly affect the surrounding environment of the stack, accelerating the melting of ice. This prevents startup delays and output instability caused by ice formation, thereby enhancing the power performance under low-temperature conditions. As demonstrated in Figure 6a, increasing the PTC heating power effectively suppresses the rate of ice formation, allowing more time for the temperature to rise. If the temperature at the triple-phase boundary reaches the freezing point before significant ice formation occurs, the ice will begin to melt, ultimately ensuring a successful cold start.

 

 

Moreover, the PTC heater effectively increases the temperature rise of the stack, thereby improving the success rate of cold starts. Figure 6b illustrates that as the PTC power increases, the rate of temperature rise improves significantly.

Secondly, at low temperatures, the chemical reaction rates within the stack slow down, leading to considerable fluctuations in output voltage. The PTC heater provides rapid heating, helping the stack quickly reach the optimal temperature for reactions. This stabilization of the stack voltage ensures normal output during the startup phase. As shown in Figure 6c, the use of the PTC heater effectively increases the stack voltage, offering better protection for the stack. Additionally, Figure 6d indicates that as the PTC heating power increases, the coefficient of variation (Cv) is effectively suppressed.

Optimization of assisted heating strategy based on NSGA-II

Acquisition of the training data

Through Matlab calculations, 125 datasets were obtained as training data for NSGA-II, some of which are shown in Table 2, the overall datasets shown in Table 1S (Supplementary Material).

 

 

NSGA-II was used to optimize the corresponding relationship between 125 independent variables and dependent variables, and the objective function of the model is defined as:

The NSGA-II program was written using Matlab to optimize the four outputs obtained for different cold-start conditions using the above objective function. According to the analysis of the section "Analysis of the influencing factors of auxiliary heating and cold start", the accuracy of the three independent variables coolant flow rate, PTC heating power and loading rate were determined to be 10, 1 and 0.1% respectively. The Pareto optimal solution set for this multi-objective optimization was obtained after 1000 generations of evolution at a population size of 400, a crossover probability of 0.9 and a variance probability of 0.05, as shown in Table 3.

 

 

In selecting the optimal solution for fuel cell cold-start performance, the 10^th solution was identified as the most effective. This solution was chosen based on the highest minimum single-cell voltage, the smallest Cv value, and the lowest maximum ice volume fraction. A higher minimum single-cell voltage indicates a higher voltage threshold during the cold-start process, effectively preventing reverse polarity phenomena and enhancing the success rate of cold starts. This ensures that the fuel cell stack can be successfully initiated at lower temperatures, thereby extending its operational lifespan. A lower maximum ice volume fraction suggests a larger space for ice formation, allowing for a more prolonged temperature rise and consequently improving the success rate of cold starts. The Cv value is critical to maintaining the stability of the fuel cell stack performance during cold starts; reducing Cv effectively enhances the overall performance of the stack, ensuring a smooth cold-start process. As shown in Table 3, the time differences among the 10 optimal solutions for cold-start are negligible, with the maximum and minimum durations differing by only 4.38 s. Therefore, when prioritizing cold-start performance, the duration of the cold start can be considered a secondary factor.

Optimized cold-start performance improvement analysis

Cold-start performance improvement

Figure 7 illustrates the cold-start performance of a fuel cell at 256.15 K using an auxiliary heating strategy, compared to previous strategies. Strategy "a" represents the prior self-start method with a load rate of 0.04 A cm^-2, while strategy "b" employs auxiliary heating with a coolant flow rate of 0.45 kg s^-1, PTC heating power of 2375 W, and a load rate of 0.02268 A cm^-2.

 

 

As depicted in Figure 7a, the implementation of the auxiliary heating strategy effectively suppresses the ice formation at the three-phase boundary of the cathode catalyst layer, reducing the ice volume fraction from 0.94 to 0. This is attributed to the optimal combination of coolant flow rate and PTC heating power, which significantly enhances the internal temperature rise of the fuel cell. The load rate of 0.02268 A cm^-2 is intermediate within the 0-0.04 A cm^-2 range. As analyzed earlier, at this rate, the heat generation outpaces the ice formation, maximizing heat production without excessively increasing water production, thereby facilitating the cold-start process.

Figure 7b shows a marked improvement in the temperature rise rate with the auxiliary heating strategy, as evidenced by the red curve surpassing the black curve, highlighting the contributions of PTC and coolant. Meanwhile, Figure 7c indicates that the voltage does not significantly decrease with the auxiliary heating strategy, demonstrating its effectiveness in compensating for voltage losses caused by increased current density and ice formation at the three-phase boundary. Additionally, Figure 7d shows that the coolant effect significantly improves stack uniformity.

Increase in the minimum starting temperature

Figure 8 illustrates that implementing the optimized auxiliary heating strategy effectively reduces the cold-start temperature from 256.15 to 247.15 K, thereby demonstrating the efficacy of the strategy. This approach facilitates lower temperature startups by enhancing the temperature rise, freezing rate, and balance among individual cells.

 

 

CONCLUSIONS

This study develops a one-dimensional multi-phase cold-start stack model to investigate cold-start performance under auxiliary heating strategies. The NSGA-II algorithm was applied to comprehensively optimize coolant flow rate, PTC heating power, and load rate, thereby determining the optimal auxiliary heating strategy and enhancing fuel cell cold-start performance. The main conclusions are as follows:

(i) The study identifies the minimum self-start temperature boundaries for a 30-cell fuel cell stack under various temperature (251.15-271.15 K) and load rate (0.005-0.040 A cm^-2) conditions. The lowest successful cold-start temperature was 256.15 K at a load rate of 0.040 A cm^-2, compared to 261.15 K at 0.005 A cm^-2, indicating that a higher load rate facilitates cold start.

(ii) Increasing the load rate enhances the growth of the cathode ice volume fraction and the temperature rise rate, though it may also lead to polarity reversal during cold-start. The optimal range for load rate was 0 to 0.04 A cm^-2. A coolant flow rate of 0.1 to 0.5 kg s^-1 significantly improves temperature uniformity and reduces voltage fluctuations. The PTC heater increases the temperature rise rate, improves voltage stability, and raises the temperature to the freezing point before ice covers the three-phase boundary, thus improving cold-start success rate.

(iii) The optimal solution, determined through NSGA-II algorithm optimization, includes a coolant flow rate of 0.45 kg s^-1, PTC heating power of 2375 W, and a load rate of 0.02268 A cm^-2. Using this optimized auxiliary heating strategy at 256.15 K reduces the cathode catalyst layer ice volume fraction from 0.94 to 0, significantly increases the temperature rise rate, and effectively mitigates voltage drop and stack uniformity issues. The optimized auxiliary heating strategy reduces the minimum cold-start temperature from 256.15 to 247.15 K, demonstrating significant improvement under ultra-low temperature conditions.

 

SUPPLEMENTARY MATERIAL

Complementary material for this work (training data of NSGA-II algorithm) is available at http://quimicanova.sbq.org.br/, as a PDF file, with free access.

 

DATA AVAILABILITY STATEMENT

The authors declare that all data are available in the text.

 

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Associate Editor handled this article: Eduardo M. Richter