Open AccessArticle

Water Status Detection Method Based on Water Balance Model for High-Power Fuel Cell Systems

Yiyu Zhong

¹,

Yanbo Yang

^1,2,*

Naiyuan Yao

¹,

Tiancai Ma

^1,2

and

Weikang Lin

School of Automotive Studies, Tongji University, Shanghai 201804, China

Institute of Carbon Neutrality, Tongji University, Shanghai 200092, China

Author to whom correspondence should be addressed.

Energies 2024, 17(21), 5410; https://doi.org/10.3390/en17215410

Submission received: 7 September 2024 / Revised: 9 October 2024 / Accepted: 25 October 2024 / Published: 30 October 2024

(This article belongs to the Collection Batteries, Fuel Cells and Supercapacitors Technologies)

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Browse Figures

Figure 1
Power system diagram. "> Figure 2
Schematic diagram of exhaust gas water content detection device. "> Figure 3
Comparison of flow rate of water flowing out of hydrogen side at different operating temperatures ((a) 120 A; (b) 210 A; (c) 300 A; vertical axis shows water flow; horizontal axis shows temperature; data from top to bottom show flow rates of 1.8/2.0/2.2/2.4). "> Figure 4
Comparison of flow rate of water flowing out of air side at different operating temperatures ((a) 120 A; (b) 210 A; (c) 300 A; vertical axis shows water flow; horizontal axis shows temperature; data from top to bottom show flow rates of 1.8/2.0/2.2/2.4). "> Figure 5
Comparison of flow rate of water flowing out of air side under different air metering ratios ((a) 120 A; (b) 210 A; (c) 300 A; vertical axis shows water flow; horizontal axis shows air flow rate; data from top to bottom show temperatures of 63/65/68/70/73 °C). "> Figure 6
Comparison of water flow rate flowing out of hydrogen side under different air metering ratios ((a) 120 A; (b) 210 A; (c) 300 A; vertical axis shows water flow; horizontal axis shows air flow rate; data from top to bottom show temperatures of 63/65/68/70/73 °C). "> Figure 7
Comparison chart of internal water content of fuel cell system under different conditions ((a) 120 A; (b) 210 A; (c) 300 A). "> Figure 8
Selection of fuel cell OS operating environment (working environment surrounded by dots; (a) 120 A; (b) 210 A; (c) 300 A). ">

Versions Notes

Abstract

With the gradually accelerating pace of global decarbonization, highly efficient and clean proton exchange membrane fuel cells (PEMFCs) are considered to be an energy solution for the future. During the operation of a fuel cell, it is necessary to keep the internal proton exchange membrane in a good state of hydration, so an appropriate method of detecting the hydration state is essential. At present, fuel cell systems are rapidly developing towards high power, but methods for detecting the hydration state of high-power fuel cell systems are still relatively lacking. Therefore, this paper studies the hydration state of high-power fuel cell systems and builds a condensation tail-gas water collection device for calculating the water flow out of a fuel cell system, deriving the hydration status inside the high-power fuel cell system. To verify the proposed water balance model, a series of experiments were conducted based on controlled variables such as working temperature, air metering ratio, and load current. Experiments were conducted on a 100 KW fuel cell system to collect water flow from the fuel cell system. Finally, based on the experimental data, the change rate of the internal water content of the fuel cell system under different conditions was calculated. The results show that, under the same load current, as the working temperature and air metering ratio increase, the change rate of the internal water content of the fuel cell system gradually decreases. Therefore, at low power, it is necessary to maintain an appropriate working temperature, while at high power, maintaining an appropriate air metering ratio is more important.

Keywords:

PEMFC; water content; water balance; high-power fuel cell system

1. Introduction

Proton exchange membrane fuel cells (PEMFCs), henceforth denoted as fuel cells, facilitate the direct conversion of chemical energy present in hydrogen into electrical energy. These fuel cells are characterized by their high energy utilization rate, low operating temperature, and production of water as the sole reaction byproduct. Their versatility allows them to function not only as a small-scale distributed power supply but also as an energy source for high-power transportation systems, thus demonstrating their broad applicability [1]. Nevertheless, the reliability, stability, and durability of the fuel cell stack, as the central component of the fuel cell power system, have emerged as critical factors influencing the extensive commercialization of fuel cell products. During the operation of the fuel cell, it is crucial to keep the proton exchange membrane (PEM) in an optimal state of hydration to ensure that the proton conduction capability is at its zenith, thereby facilitating efficient and stable output performance. Hydration state failure is the most common failure mode in fuel cells, representing approximately half of total failures, and is primarily characterized by conditions of drying and flooding. Short-term hydration state failures can lead to fluctuations and reductions in the fuel cell’s output performance, and if such conditions are prolonged, they may result in irreversible performance degradation. A deficiency of water in PEMFC can lead to a decrease in proton conductivity, as noted in the literature [2,3,4,5,6], which underscores the importance of monitoring and managing the hydration state to prevent operational inefficiencies and long-term damage to the fuel cell system.

In the event of a dry failure, the water content within the fuel cell stack is insufficient to maintain a properly hydrated state, leading to an increase in internal resistance and elevated heat production due to regions of the PEM not being fully hydrated. Prolonged dry conditions can potentially cause mechanical damage to the PEM, resulting in irreversible harm [7,8]. This highlights the critical need to maintain adequate water content to prevent performance degradation and structural integrity loss in the fuel cell system. In the event of a flood failure, the water content inside the stack is too high, and the liquid water gradually blocks the flow channel or reaction area, preventing the reaction gas from reaching the reaction site, causing a local “starvation” phenomenon [9,10]. In severe instances, additional side reactions can occur within the fuel cell under these conditions, leading to damage to the carbon carrier [10,11,12,13]. This emphasizes the importance of preventing extreme dry failures to safeguard the structural and functional integrity of the fuel cell components, thereby ensuring long-term reliability and performance.

In addition to the direct impact on output performance, the internal hydration state also indirectly affects environmental adaptability and durability [14,15]. In low-temperature conditions, especially in sub-zero environments, the free water inside the fuel cell will freeze, thereby blocking the reactant channels, and even causing structural damage to the catalyst layer and diffusion layer [16,17]. In addition, it will also affect the aging characteristics of the catalyst [7,18]. Flooding conditions will accelerate the loss of Pt surface area, while dry conditions will accelerate the corrosion of the carbon carrier [19,20].

Research on fuel cell hydration states utilizes indicators like water content, electrical signals, and neutron imaging [21,22,23,24], but high costs and complexity limit neutron imaging’s adoption. Instead, the law of conservation of mass is employed to compute water content during stable operation, validated by comparing the calculated rates with the observed water distributions [25,26,27].

The output voltage of a fuel cell is a direct indicator of hydration state faults, influencing voltage fluctuations or drops, especially in high-power systems where the Cell Voltage Monitoring module (CVM) is a common standard [28,29]. Electrical signal-based recognition standards, such as polarization curves and voltage fluctuation signals, show that severe water flooding leads to more pronounced voltage decay at higher current densities [30]. Additionally, the pressure drop between the fuel cell’s inlet and outlet, which increases with liquid water content, reflects water flooding severity and is diagnosed through various indicators and analysis methods [31].

The detection methods based on electrochemical signals mainly include electrochemical impedance spectroscopy, the current interruption method, cyclic voltammetry, etc. Among them, electrochemical impedance spectroscopy is the most common hydration state detection method because it can distinguish different electrochemical processes and can be tested online [19,20,32,33,34]. As the air humidity decreases, the value of the high-frequency impedance segment (i.e., the intercept of the impedance spectrum with the real axis) gradually increases, the impedance spectrum moves to the right, and the radius of the low-frequency arc segment also gradually increases [21,35,36], which can be used as an indicator of the hydration state of the fuel cell.

When analyzing the relationship between impedance spectra and the internal hydration state of fuel cells, an equivalent circuit model is often introduced. The model generally includes resistors, capacitors, inductors, and Warburg elements [37]. The model is capable of quantitatively analyzing the electrochemical process. The key to this method is the establishment of equivalent models and parameter identification. Fouquet et al. [38] extended a standard capacitor to a constant phase element, proving that the three resistance values of the model are related to the relative humidity of the air supply. Zhang et al. [27] used a neural network method to complete parameter identification, and the predicted Nyquist plot almost completely coincides with the measured value, and by directly predicting the parameters of the equivalent circuit, they detailed the degree of influence of different processes on fuel cell performance. BMW proposed a method for the online monitoring of impedance, which requires collecting five frequency points divided into three groups to fit the Randles circuit, obtaining ohmic impedance, polarization resistance, and double layer capacitance [38].

However, the above methods are mostly suitable for single cells or low-power fuel cells. Applying them to high-power fuel cell does not lead to any noticeable improvements [37,39,40,41,42], since the assembly structure, flow field structure, and operating conditions of high-power fuel cell stacks are significantly different from those of single cells and low-power stacks [43].

Therefore, researchers have considered utilizing the law of conservation of mass to compute the water content within fuel cells. When the fuel cell is operating stably, the flow rate of residual water can be calculated by measuring the discharged water. Zhao et al. [44] employed a single transparent fuel cell to conduct tests under varying operating conditions. By comparing the calculated rate of change in water content within the fuel cell and the water distribution in the flow channel, the accuracy of the model was validated.

In addition, research has indicated that smaller-scale fuel cell stacks exhibit reduced sensitivity to gas flow rates [45,46], which can also cause a difference between small and big stacks.

Additionally, the variation in the number of cells within a fuel cell stack can significantly influence its power generation performance, leading to temperature imbalances [41]. This, in turn, further exacerbates the uneven distribution of water present throughout the stack. Consequently, there exists a pronounced distinction between smaller and larger stacks regarding these phenomena. Research indicates that there may exist notable differences in the water generation mechanisms between large-scale and small-scale proton exchange membrane fuel cell (PEMFC) stacks [47]. Therefore, traditional approaches relying on electrochemical analysis and similar techniques may not be applicable to large-scale stacks. Due to the fact that large-scale fuel cell stacks frequently operate at lower power densities [48], this could potentially have an impact on the water generation mechanisms involved, further differentiating them from their smaller-scale counterparts.

This study is dedicated to exploring the hydration state of high-power fuel cell systems and developing a validated water balance model. This research begins by examining the water balance model of a high-power fuel cell system and introduces a condensation-type exhaust water collection device to accurately measure the flow rate of water exiting the system. To validate the constructed water balance model, controlled variable experiments were conducted across different operating temperatures, air-to-fuel ratios, and load currents. The experimental results show that with increasing operating temperature and air-to-fuel ratio, the water flow rate from the air side increases, while the water flow rate from the hydrogen side decreases. Additionally, as the load current increases, the water flow rate from both sides increases. Based on the experimental data, the rate of change in the internal water content of the fuel cell system under various conditions was calculated. The findings indicate that at the same load current, as the operating temperature and air stoichiometric ratio increase, the rate of change in the internal water content of the fuel cell system decreases. Conversely, as the load current increases, the influence of the air stoichiometric ratio also increases. Thus, at low power, maintaining an appropriate operating temperature is crucial, whereas at high power, managing an appropriate metering ratio becomes more significant. This research provides valuable insights into optimizing the operational parameters of high-power fuel cell systems to ensure efficient water management and system performance.

2. Experiment

To verify the reliability of the water balance model for high-power fuel cell systems, it is necessary to record the water-containing state of the high-power fuel cell system when it reaches water balance under different operating conditions. Therefore, the experimental conditions should meet the following three requirements:

The selected operating parameters should be within the normal operating range of the fuel cell system, reducing the effects of faults in the FC (fuel cell) system other than water content faults (gas supply insufficiency, air compressor surge, proportional valve failure, etc.).
By designing experiments that manifest more pronounced phenomena under both dry and flooded conditions, the study should investigates the effects of water content faults in fuel cell systems.
The steady-state operation time should be long enough to ensure that the water content inside the fuel cell is in dynamic balance during this period, avoiding the impact of dynamic characteristics on the experimental results.

2.1. Experimental Design

Our literature review highlights that the air-to-fuel ratio, operating temperature, and load current are the predominant factors affecting water content within a fuel cell [29]. Given that the temperature inside a stack cannot be measured during operation, the inlet temperature of the coolant is treated as the working temperature in this research, and the working temperature in the following section refers to the inlet temperature of the coolant. According to the operating conditions recommended by the system side, a three-factor five-level water content experiment was designed. The parameters of the experiment are shown in Table 1.

Reference [30] indicates that the time required for the fuel cell system to reach water balance is generally a few seconds to ten minutes. Therefore, each test point ran for 20 min, and it was assumed that the fuel cell was in the process of establishing water balance within the first 15 min; no data were recorded for this process, and the data obtained in the last 5 min were recorded. During the test, if a single cell voltage is too low or other faults cause the fuel cell system to shut down, the data of this operating point will be removed.

2.2. Test Platform Introduction

The high-power fuel cell system used in this article is shown in Figure 1, manufactured by AT&M Environmental Engineering Technology Co., Beijing, China With a rated net output power of 100 kW, the stack is composed of 410 single cells. High-pressure dry hydrogen gas enters the anode of the reaction stack after being depressurized by the solenoid valve and proportional valve. The liquid water in the residual hydrogen is separated by the gas–water separation device and intermittently discharged through the drain valve.

For the above fuel cell system, the water balance model can be represented as

\frac{d m_{w, s y s}}{d t} = Q_{v, i n, s y s} + Q_{w, g e n, c a} - Q_{w, o u t, c a} - Q_{w, o u t, a n}

(1)

In Formula (1) [9], the elements are defined as follows:

$m_{w, s y s}$ represents the water content inside the fuel cell system, in grams;
$Q_{v, i n, s y s}$ represents the flow rate of water vapor entering the fuel cell system, in g/s;
$Q_{w, g e n}$ represents the water flow generated by the electrochemical reaction, in g/s;
$Q_{w, o u t, c a}$ represents the water flow out of the system from the air subsystem, in g/s;
$Q_{w, o u t, a n}$ represents the water flow out of the system from the hydrogen subsystem, in g/s;

Taking the fuel cell system during steady-state operation as the research object, the change in the water content of the auxiliary system of the fuel cell system can be ignored, that is,

\frac{d m_{w, s t k}}{d t} = \frac{d m_{w, s y s}}{d t}

(2)

Each part of the equation required for the water balance model is described below.

2.2.1. Water Flow into the System

Since the hydrogen entering the system is high-pressure hydrogen with a purity of 99.99%, water vapor mainly enters the system with air. By recording the temperature, humidity, and pressure of the environment during the reaction process, and the air flow entering the system, the water flow entering the system can be calculated.

Q_{v, i n, s y s} = \frac{Q_{a i r; i n, s y s} \cdot P_{v a m b} \cdot M_{v}}{M_{a} \cdot P_{a m b}} = \frac{Q_{a i r; i n, s y s} \cdot (P_{a m b} - P_{s a t} * R H) \cdot M_{v}}{M_{a} \cdot P_{a m b}}

(3)

In Formula (3), the elements are defined as follows:

$Q_{a i r; i n, s y s}$ stands for air flow into the system, in g/s;
$P_{a m b}$ stands for environmental pressure, in kPa;
$R_{v}$ represents the relative humidity of the environment;
$P_{s a t}$ represents the saturated vapor pressure of the environment, which can be calculated using the saturated water vapor pressure formula

p_{s a t} = exp (9.3876 - \frac{3826.36}{T_{a m b} - 45.47}) \times 10^{3}

(4)

$T_{a m b}$ represents the environmental temperature, K;
$M_{v}$ represents the water’s relative molecular mass, in g/mol;
$M_{a}$ represents the water’s relative molecular mass, in g/mol;

2.2.2. Water Flow Produced by Electrochemical Reaction

The water flow produced by the electrochemical reaction can be presented as in the formula below:

Q_{v, g e n, c a} = \frac{N \cdot M_{v} \cdot I_{s t}}{2 F}

(5)

N represents the number of single cells in the fuel cell stack.
$I_{s t}$ represents the load current, in A.
F stands for the Faraday constant, which is 96,485 C/mol.

2.2.3. The Water Flow Out of the System from the Air Side and the Hydrogen Side

To measure the water flow out of the system from the air and hydrogen sides, this article designed an exhaust water content detection device centered on condensation.

Figure 2. Schematic diagram of exhaust gas water content detection device.

The exhaust water content detection device (Figure 2) on the air side is composed of a heat exchanger, a water separator, a temperature sensor, and a water collection device with a liquid level sensor. The basic principle is to condense the high-temperature supersaturated exhaust gas on the air side, and then separate the liquid water inside from the exhaust gas through the water separator, thus obtaining saturated low-temperature exhaust gas and liquid water. Then, we must collect the separated liquid water and determine the liquid level with a liquid level sensor. Therefore, the water flow out of the system from the air side is composed of two parts: the liquid water collected in the air side collection device and the water vapor carried in the saturated steam after water vapor separation, that is,

Q_{w, o u t, c a} = \frac{d m_{w, c a c o l l e c t}}{d t} + \frac{Q_{a i r, o u t, s y s} \cdot p_{v, s a t} \cdot M_{v}}{M_{a} \cdot P_{a m b}}

(6)

In Formula (6), the elements are defined as follows:

$m_{w, c a c o l l e c t}$ represents the mass of the liquid collected by the exhaust water collection device on the air side, in grams (g);
$Q_{a i r, o u t, s y s}$ represents the air flow out of the system, in g (gram)/s (second), which can be calculated by the following formula.

The

Q_{a i r, o u t, s y s}

is represented as below:

Q_{a i r, o u t s y s} = Q_{a i r, i n, s y s} - Q_{o, r e c a t, c a} + Q_{v, g e n, c a} - \frac{d m_{w, c a c o l e c t}}{d t}

(7)

Since the hydrogen return circuit of the system is equipped with a water separator, the water content detection device on the hydrogen side mainly collects liquid water and a small amount of hydrogen, with less gaseous water, which does not significantly affect the experimental results. Therefore, the exhaust water content detection device on the hydrogen side only has a water collection device with a liquid level sensor, which is used to record the water flow discharged from the hydrogen side.

Q_{w, o u t, a n} = \frac{d m_{w, a n c o l l e c t}}{d t}

(8)

m_{w, a n c o l l e c t}

represents the mass of the liquid collected by the exhaust water collection device on the hydrogen side, in grams (g).

2.2.4. Test Methods

In sequence, turn on the host computer, system controller, electronic load, auxiliary devices, and impedance testing system. Turn on the water pump, solenoid valve, proportional valve, back pressure valve, air compressor, drain valve, and hydrogen circulation pump in sequence, setting the anode inlet gas pressure 10 kPa higher than the cathode inlet gas pressure (

Δ p = 20

kPa).

Gradually load the system to 120 A; adjust the speed of the air compressor and the opening angle of the back pressure valve, so that the air flow rate reaches the air metering coefficient of 2.8 corresponding to the target current; gradually raise the working temperature to

55 \pm 1 ° C

; and start the temperature closed-loop control program to maintain this temperature. After the working temperature is stable at

55 \pm 1 ° C

, start timing and run the system for a total of 15 min. Adjust the speed of the air compressor and the opening angle of the back pressure valve, so that the air metering ratio gradually decreases in the range of 2∼2.8 with a step size of 0.2. Raise the working temperature to

60 \pm 1 ° C

65 \pm 1 ° C

, and

70 \pm 1 ° C

73 \pm 1 ° C

. Repeat the testing phase and record the experimental data.

Load up to 210 A and 300 A, and repeat all the recording steps until all operating point water content detection experiments are completed.

Gradually reduce the load to 0 A, purging the circuit with nitrogen; turn off the machine; and power down the system in sequence.

3. Results and Discussion

3.1. Effect of Operating Temperature on Water Flow Rate Outflow from Air Side

Figure 3 shows the change in the water flow out of the air side at different working temperatures. As can be seen from Figure 3a, as the temperature rises, the water content in the air side exhaust gas generally shows an upward trend. The higher the temperature, the higher the saturation vapor pressure of the fuel cell. Under the same water content, the relative humidity will decrease at this time, which is equivalent to the generation of less liquid water inside the fuel cell, and the ability of the gas to carry water is improved. This change applies to both the air side and the hydrogen side, which is shown in Figure 4b,c. Therefore, when the other conditions are the same, the water flow out of the fuel cell stack cause by the air increases with an increase in temperature, and more liquid water is collected by the air side exhaust gas collection device.

It is worth noting that when the load current is 120 A, the impact of the working temperature on the water flow of the air side is slightly different under different metering ratios. As the air metering ratio increases, the growth rate of the water flow on the air side gradually decreases. This is because at a small current density, the fuel cell produces less water due to the electrochemical reaction, and at the same time, the high-speed high-temperature reaction gas has a strong ability to carry water, and the water produced by the fuel cell is completely carried out by the reaction gas. Therefore, even if the air metering ratio increases, the reaction gas cannot carry out more water. For the working conditions of low working temperature and large load current, the ability of the reaction gas to carry water is low or the fuel cell produces more water, so there is still some water vapor or liquid water remaining in the system. At this time, if the air flow is increased, the water flow out of the system will also increase accordingly.

Figure 3a shows that as the temperature rises, the water content in the hydrogen side exhaust gas generally shows a downward trend, and even at 120 A/70

° C

, the water content in the hydrogen side exhaust gas is 0. The same result appears at 210 A (Figure 3b) and 300 A (Figure 3c). There are two main reasons for this phenomenon. First, according to the principle of proton exchange membrane fuel cell reactions, the reaction product water is generated at the cathode (that is, the air side), and the fuel used by the fuel cell system is 99.99% pure hydrogen. Therefore, the water inside the hydrogen side is mainly the water that migrates from the air side to the hydrogen side under the action of concentration diffusion and pressure diffusion. Since the hydrogen–air pressure difference is basically consistent (20 kpa) during the experiment, the influence of pressure on water migration can be ignored when comparing them. Second, the exhaust gas collected on the anode side needs to first pass through the water separator built into the fuel cell system to separate the unreacted hydrogen from the liquid water, and then it can be collected by the exhaust water collection device on the hydrogen side. And at higher working temperatures, the saturation vapor pressure of the gas on the hydrogen side rises, and the content of liquid water decreases relatively. These two factors cause the working temperature to rise and the content of water flowing out of the hydrogen side to decrease.

3.2. Influence of Air Metering Ratio on the Water Flow Out of the Cathode and Anode

We compared the water flow out of the air side and the hydrogen side at 120 A, 210 A, 300 A load currents, different coolant inlet temperatures, and different air metering ratios, as shown in Figure 5. Similar to the impact of working temperature on the water flow out of the air side, under the same load current, the higher the air metering ratio, the more water is carried out of the stack by the unreacted air, which also applies to load currents of 210 A (Figure 5b) and 300 A (Figure 5c). It should be noted that this growth is not unlimited. After reaching a certain air metering ratio, the growth of the water content in the air side exhaust gas slows down, especially when the load current is small and the working temperature is high. This is because at this time, the water produced by the electrochemical reaction of the fuel cell has been completely carried out of the fuel cell by high-temperature high-speed air. At this time, even if the air metering ratio continues to increase, the water content of the exhaust gas will not continue to increase.

For the hydrogen side (Figure 6), similarly, as the air metering ratio increases, the water flow out of the hydrogen side basically continues to decrease. After the above analysis, as the air metering ratio increases, the water stored in the cathode is taken out of the stack by the high-speed airflow, and the water flow diffused to the hydrogen side through concentration difference becomes less, so relatively speaking, the water collected on the hydrogen side will become reduced. However, the degree of decline is different. Under low temperature (120 A/60

° C

, 210 A/60

° C

, and 300 A/63

° C

), they all show a relatively gentle decline. As the temperature rises, the water flow out of the hydrogen side is also gradually affected by the air metering ratio.

3.3. Effects of Operating Temperature and Air Metering Ratio on Internal Water Content of Fuel Cell System

According to the working principle of the fuel cell, during the reaction process, water mainly comes from the electrochemical reaction and the water vapor that enters the fuel cell with the reaction gas. Then, some of the water is discharged from the fuel cell with the exhaust gas after the reaction, and the rest of the water stays inside the fuel cell. In this article, the change rate of the water remaining in the fuel cell will be used as the research object to evaluate the water content status inside the fuel cell.

\frac{d m_{w, s t k}}{d t} = Q_{w, i n, s y s} + Q_{w, g e n} - Q_{w, o u t, c a} - Q_{w, o u t, a n}

(9)

In Formula (9),

m_{w, s t k}

is the water content inside the fuel cell, in g,

Q_{w, i n, s y s}

is the water flow rate entering the fuel cell system, in (g/s),

Q_{w, g e n}

represents the water flow rate generated by the electrochemical reaction, in (g/s),

Q_{w, o u t, c a}

represents the water flow rate flowing out of the system from the cathode, in (g/s), and

Q_{w, o u t, a n}

represents the water flow rate flowing out of the system from the anode, in (g/s).

During the reaction process, under the effects of concentration diffusion and electro-osmotic drag, water at the cathode will migrate to the anode. However, the research object of the water balance method is the entire fuel cell, so the internal water migration process will not have an impact.

Using the method described above, the rate of change in the water content inside the fuel cell system under different load currents, working temperatures, and air metering ratios can be calculated. In the process of making the graph, to maintain the integrity of the graph, we use (Load current/Temperature/Coefficient) as the format of the test environment description. The data of (210 A/55

° C

/1.8) and (210 A/55

° C

/2.0) are replaced with the (210 A/55

° C

/2.2) test’s data. The obtained results are compared, as shown in Figure 7a–c, where positive values indicate an increase in water content (represented in blue), and negative values indicate a decrease in water content (represented in red). For the convenience of subsequent discussions, the blue part is defined as flooding, the red part is defined as drying, and the green part is defined as the normal state.

As can be seen from Figure 7, under the same load current, as the working temperature increases and the air metering ratio increases, the rate of change in the water content inside the fuel cell system gradually decreases. When it is (120 A/73

° C

/2.8), (210 A/73

° C

/2.4), and (300 A/73

° C

/2.4), the rate of change in the water content inside the fuel cell system reaches the minimum value under this load current. However, the degree of influence of the working temperature and the air metering ratio on the rate of change in the water content inside the fuel cell system is slightly different. When the load current is 120 A or 210 A, too low a working temperature is more likely to cause flooding than too low an air metering ratio. For example, at 120 A, when the working temperature is 55

° C

, even if the air metering ratio reaches 2.8, the fuel cell system is still in a relatively flooded state; and when the working temperature is 73

° C

, even if the air metering ratio is only 2.0, the fuel cell system is in a normal state. In a dry state, the degrees of influence of working temperature and air metering ratio are not much different. However, when the load current is 310 A, the trend is the opposite. Too low a working temperature and too low an air metering ratio will cause flooding, and too high an air metering ratio is more likely to cause drying than too high a working temperature.

Furthermore, this paper uses the method of linear regression to analyze the impact of working temperature and air metering ratio on the water content inside the fuel cell system. Before this, the data need to be standardized. This paper uses the Z-score normalization method [49,50], which is

x^{*} = x - μ σ

(10)

Table 2 shows the results of the analysis: Similar to the phenomenon described above, the impact of working temperature is more significant when the load current is 120 A or 210 A, while the impact of the air metering ratio is more significant when the load current is 300 A. The reason for this phenomenon may be that the air metering ratio is related to the load current. Under different load currents, the air metering ratio changes to the same magnitude, but the change in air flow is different. Since the fuel cell system needs to rely on high-speed high-temperature gas to carry the water out, the higher the load current, the more significant the impact of the air metering ratio.

Therefore, to maintain the long-term stable operation of the fuel cell system, appropriate operating conditions need to be selected. The following principles should be considered when choosing these conditions:

The fuel cell system should be in a normal state under this condition.
In the actual operation process, there are certain fluctuations in the working temperature and air metering ratio. The fluctuation range of the working temperature is about $\pm 2 ° C$ , and the fluctuation range of the air metering ratio is about $\pm 0.1$ , so the selected conditions should make the points within the fluctuation range reach a normal state.
A larger air metering ratio and a lower working temperature will cause additional consumption of the auxiliary system, so we must try to choose working conditions with a low air metering ratio and a high working temperature.

As shown in Figure 8, 120 A/67

° C

/2.15; 210 A/68

° C

/2.15; and 300 A/70

° C

/2.05 are selected as the appropriate operating conditions under each load current. Next, we compare the rate of change in the water content inside the fuel cell system under different load currents.

From Table 3, it can be seen that as the load current increases, the rate of change in the water content inside the fuel cell system increases to some extent, but the increase is not large. This may be because the higher the load current of the fuel cell, the more water flow is generated, so the water accumulated inside correspondingly increases. In addition, it was found that when the load current is 210 A, the range is larger compared to that at 120 A and 300 A. Correspondingly, the fuel cell system cannot operate stably under the conditions of 210 A/55

° C

/1.6 and 210 A/55

° C

/1.8. This further reflects the connection between the rate of change in the internal water content of the fuel cell system and the water content fault.

However, the above calculation method can only calculate the absolute value of the water content inside the fuel cell system. The output performance of the fuel cell in actual operation is related to the working temperature, intake pressure, and air metering ratio. To find the most suitable working conditions under each load current, it is necessary to establish a fuel cell stack model and study the correlation between the difference between the actual output and theoretical output of the fuel cell stack under different conditions and the absolute value of the water content inside the fuel cell system.

4. Conclusions

This study investigates the water content state of a high-power fuel cell system and constructs a water balance model. To authenticate this model, a condensation tail-gas water collection device was designed around the original high-power fuel cell system. Subsequently, control variables involving three factors, namely, working temperature, air metering ratio, and load current, were applied during the experiments to measure the flow rate of water emanating from both the air side and hydrogen side of the fuel cell system under stable status. The experimental outcomes were as follows:

Under larger air metering ratios, elevated coolant inlet temperatures, and higher load currents, the water content in the exhaust gas on the air side is higher; conversely, under smaller air metering ratios, lower coolant inlet temperatures, and higher load currents, the water content in the exhaust gas on the hydrogen side is higher.
Under the same load current, as the working temperature and air metering ratio escalate, the rate of change in the water content inside the fuel cell system progressively decreases. However, the degree of influence of working temperature and air metering ratio on the rate of change in the water content inside the fuel cell system slightly varies. When the load current is 120 A or 210 A, the influence of working temperature is more pronounced, whereas when the load current is 300 A, the influence of the air metering ratio is more evident.
With the amplification of load current, the rate of change in the water content inside the fuel cell system somewhat increases, but the increase is not substantial. Simultaneously, the range of the rate of change in the internal water content at 210 A is greater than that at 120 A and 300 A, and the corresponding fuel cell system cannot operate stably under the conditions of 210 A/55 $° C$ /1.6 and 210 A/55 $° C$ /1.8. This further substantiates the correlation between the rate of change in the internal water content of the fuel cell system and the water content fault.

In conclusion, the water balance model developed in this study has demonstrated its efficacy in accurately predicting the water content within high-power fuel cell systems. The experimental data obtained from this research serve as a valuable reference for the precise detection of water content in such systems. Specifically, the monitoring of tail-gas water volume can be identified as a reliable method for assessing the water content status within a fuel cell system. The findings of this research not only contribute to the theoretical understanding of water content detection in high-power fuel cell systems, but also offer practical insights that can be leveraged for operational and maintenance strategies for these systems. Furthermore, the methodologies and conclusions drawn from this research can be extended to other similar systems, thereby enhancing the broader applicability of our findings. The integration of these insights into the design and optimization of high-power fuel cell systems is expected to improve their overall performance and reliability, ultimately contributing to the sustainable development of clean-energy technologies.

Author Contributions

Conceptualization: Y.Y. and W.L.; mehtodology: Y.Y. and T.M.; validation: W.L. and N.Y.; investigation: N.Y. and Y.Z.; writing—original draft preparation: Y.Z.; writing—review and editing: Y.Y.; supervision: T.M. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Data Availability Statement

The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author(s).

Conflicts of Interest

The authors declare no conflicts of interest.

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Figure 1. Power system diagram.

Figure 3. Comparison of flow rate of water flowing out of hydrogen side at different operating temperatures ((a) 120 A; (b) 210 A; (c) 300 A; vertical axis shows water flow; horizontal axis shows temperature; data from top to bottom show flow rates of 1.8/2.0/2.2/2.4).

Figure 4. Comparison of flow rate of water flowing out of air side at different operating temperatures ((a) 120 A; (b) 210 A; (c) 300 A; vertical axis shows water flow; horizontal axis shows temperature; data from top to bottom show flow rates of 1.8/2.0/2.2/2.4).

Figure 5. Comparison of flow rate of water flowing out of air side under different air metering ratios ((a) 120 A; (b) 210 A; (c) 300 A; vertical axis shows water flow; horizontal axis shows air flow rate; data from top to bottom show temperatures of 63/65/68/70/73 °C).

Figure 6. Comparison of water flow rate flowing out of hydrogen side under different air metering ratios ((a) 120 A; (b) 210 A; (c) 300 A; vertical axis shows water flow; horizontal axis shows air flow rate; data from top to bottom show temperatures of 63/65/68/70/73 °C).

Figure 7. Comparison chart of internal water content of fuel cell system under different conditions ((a) 120 A; (b) 210 A; (c) 300 A).

Figure 8. Selection of fuel cell OS operating environment (working environment surrounded by dots; (a) 120 A; (b) 210 A; (c) 300 A).

Table 1. Water state experimental parameter table.

Load Current (A)/ Currency Density (A·cm⁻²)	Working Temperature (°C)	Air Metering Ratio
120/0.4	55, 60, 65, 70, 73	2, 2.2, 2.4, 2.6, 2.8
210/0.7	55, 60, 65, 70, 73	1.8, 2, 2.2, 2.4
300/1.0	63, 65, 68, 70, 73	1.8, 2, 2.2, 2.4

Table 2. Regression analysis under different load currents.

Load Current (A)	Temperature Ratio Regression Coefficient	Air Metering Ratio Regression Coefficient
120	−0.8469	−0.4145
210	−0.9341	−0.4347
300	−0.4637	−0.7618

Table 3. Statistical table of change rate of internal water content of different load currents.

Load Current (A)	Maximum	Minimum	Range	Average	Variance
120	0.342	−0.177	0.519	0.086	0.019
210	0.909	0.009	0.900	0.562	0.067
300	0.615	0.103	0.512	0.402	0.028

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Zhong, Y.; Yang, Y.; Yao, N.; Ma, T.; Lin, W. Water Status Detection Method Based on Water Balance Model for High-Power Fuel Cell Systems. Energies 2024, 17, 5410. https://doi.org/10.3390/en17215410

AMA Style

Zhong Y, Yang Y, Yao N, Ma T, Lin W. Water Status Detection Method Based on Water Balance Model for High-Power Fuel Cell Systems. Energies. 2024; 17(21):5410. https://doi.org/10.3390/en17215410

Chicago/Turabian Style

Zhong, Yiyu, Yanbo Yang, Naiyuan Yao, Tiancai Ma, and Weikang Lin. 2024. "Water Status Detection Method Based on Water Balance Model for High-Power Fuel Cell Systems" Energies 17, no. 21: 5410. https://doi.org/10.3390/en17215410

APA Style

Zhong, Y., Yang, Y., Yao, N., Ma, T., & Lin, W. (2024). Water Status Detection Method Based on Water Balance Model for High-Power Fuel Cell Systems. Energies, 17(21), 5410. https://doi.org/10.3390/en17215410

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