A review of water management in proton exchange membrane fuel cell systems

Abstract

Water management has been an unavoidable problem for proton exchange membrane fuel cells (PEMFCs), and effective water management measures can improve the performance and extend the lifespan of the PEMFC. The water management state of the PEMFC system is influenced by various operating conditions, and these operating conditions are adjusted using external devices. To understand how to achieve an optimal water management state in the PEMFC system, this review summarizes the main influencing factors in water management, including temperature, humidity and pressure. Then, a generalized overview of the key devices for controlling the above factors in water management is provided, including gas supply devices and humidifiers. Afterwards, the control methods of the above devices are summarized, including conventional control methods and neural network control methods. At last, the whole paper is summarized and appropriate recommendations are given for the study of water management, the direction of optimization of the device and the improvement of control methods in the future.

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1 Introduction

In recent years, with the change in the international situation and the arrival of the world energy crisis, getting rid of the dependence on fossil fuels and stepping up the transformation of clean energy has become a reality faced by all countries in the world.^1,2 Currently, many countries have proposed zero-emission strategies and clean energy roadmaps to achieve carbon neutrality by the middle of the century.³ With growing energy demand, fossil fuels' negative environmental impact and energy market price fluctuations urgently need to be addressed worldwide. Hydrogen, as a sustainable clean energy alternative to fossil fuels, can alleviate energy consumption and cope with the coming energy crisis. More and more countries are committed to the development of technology for hydrogen fuel cells.^4,5 The hydrogen fuel cell is a device that consumes hydrogen and oxygen in an electrochemical reaction to generate electric power. It produces only water and emits no harmful gases or greenhouse gases. Therefore, it is developing rapidly in the fields of power generation, transportation and housing.^6–8

As shown in Fig. 1, there are many types of fuel cells. According to different electrolytes, fuel cells are divided into proton exchange membrane fuel cells (PEMFCs), solid oxide fuel cells (SOFCs), alkaline fuel cells (AFCs), phosphoric acid fuel cells (PAFCs) and molten carbonate fuel cells (MCFCs).⁹ Among them, PEMFCs show strong attraction due to their advantages of low noise, no pollution, low temperature (usually 60–80 °C), no mechanical movement structure, high reliability and efficient utilization of hydrogen energy.^10,11 Nowadays, PEMFCs have been widely used in energy storage equipment, portable power supply, fuel cell vehicles, aviation and other fields.¹² According to the current situation and policy guidance, PEMFCs will play a key role in the development of new energy vehicles, especially in the heavy-duty vehicle industry.¹³

Fig. 1 Types of commonly used fuel cells.

However, PEMFC's shortcomings in reliability and durability have limited its large-scale commercialization.¹⁴ The phenomena of electrochemistry, mass transfer and heat generation usually occur during PEMFC operation. The most common problem is related to water balance.¹⁵ The PEMFC needs water to operate properly. However, excessive or insufficient water can cause the performance of the PEMFC to deteriorate. The phenomenon of water flooding will happen when the water in the cell's stack increases to a certain level.¹⁶ It will cause cavities and micropores in the gas diffusion layer (GDL) to become plugged and also cause the gas flow paths to be covered with water.^17–19 In contrast, if the water in the cell's stack decreases to a certain level, the phenomenon of dehydration will happen and dry out the membrane. Both of these phenomena reduce the conversion's efficiency of the PEMFC in the short term and cause irreversible defects in the cell in the long term, leading to premature degradation of its function.²⁰

Although there are many studies on water management in PEMFCs, few scholars have conducted a systematic summary and discussion specifically on water management. In the literature that can be found, the review of water management is mostly based on water management diagnostic mechanisms,^21–23 PEMFC structure and materials,^24–27 the different mechanisms of water transport in PEMFCs and methods to improve water management.²⁸ Therefore, it is necessary to explore and analyze the water management system comprehensively, especially the key factors affecting water management.

This paper focuses on water management in the PEMFC, providing impetus for the healthy and rapid development of PEMFCs to promote the development of the hydrogen energy industry. In Section 2, the key factors affecting water balance are introduced, including temperature, humidity, and pressure drop. Section 3 summarizes the key control devices that affect water management in the PEMFC, which can be implemented by changing the operating parameters in Section 2. Section 4 summarizes the control methods for the PEMFC water management system, including control methods based on traditional control improvements and the now popular neural network-based control methods. Finally, the highlights of research related to PEMFC water management are summarized and suggestions for future research are given.

2 Water management in PEMFCs

Water management in the PEMFC can be divided into two categories: internal and external water management. Internal water management methods for the PEMFC include the selection of the GDL material and thickness,^29–31 gas flow channel's geometry^32–35 and the PEM.^26,36,37 The external water management of the PEMFC is based on the pressure, temperature and humidity of the gas. This can be controlled during PEMFC's operation.^38–41 Therefore, this section summarizes external water management for PEMFCs.

2.1 Principle of PEMFC operation

In a PEMFC, fuel is electrochemically converted to electrical energy through the oxygen reduction reaction (ORR) and the hydrogen oxidation reaction (HOR).⁴² As shown in Fig. 2a, the PEMFC structure consists of gaskets, end plates, current collectors, bipolar plates (BPs), gas diffusion layers (GDLs), and a proton exchange membrane (PEM). The main function of a current collector is to conduct and bridge the flow of electrons between the active material and the external cell's terminals.⁴⁵ End plates provide a channel for the reactant gases and coolant fluid to maintain an effective seal and provide sufficient and uniform contact pressure between the different components.^46,47 Bipolar plates collect and conduct the current from cell to cell and they separate the gases, and the flow channels in the plates deliver the reacting gases to fuel cell electrodes.^48,49

Fig. 2 (a) Components of a PEMFC,⁴³ and (b) principle of a PEMFC.⁴⁴

PEMFC's working principle is shown in Fig. 2b. At the anode, hydrogen passes through the GDL and undergoes the oxidation reaction, generating hydrogen ions and releasing electrons at the same time. The anode reaction formula is 2H₂ → 4H⁺ + 4e⁻.⁵⁰ Electrons are forced to move from the anode to the cathode through an external circuit, and hydrogen ions move through the PEM to the side of the cathode containing the acidic electrolyte.⁵¹ The anode reaction formula is O₂ + 4H⁺ + 4e⁻ → 2H₂O. Adding the two equations for the anode and cathode can be expressed as: O₂ + 2H₂ → 2H₂O.³² Since water is the only product of the electrochemical reaction in the PEMFC, the water balance and hydration level play a key role in the efficiency and performance of the PEMFC.⁵²

2.2 Effect of temperature on water management

2.2.1 Effect of temperature. Excessive temperatures tend to decrease PEMFC's performance, and low temperature tends to lead to membrane flooding.⁵³ Therefore, water management of PEMFCs through control of rational temperature has always been researched. The relationship between the saturation pressure of water and the fuel cell temperature has been derived in the literature²³ based on Clapeyron's relationship, as shown in eqn (1) below:where P_sat is the saturation pressure of water (Pa), P₀ is the pressure at the known temperature T₀ (Pa), M_H2O is the molar mass of water (kg mol⁻¹), h_fg is the latent heat of vaporization of water (kJ kg⁻¹), R is the gas constant (J mol⁻¹ K⁻¹), T is the temperature (K), and T₀ is the known temperature (K). From eqn (1), it can be seen that if the fuel cell temperature is too high, the saturated vapor pressure will increase, and the water content of the PEM will decrease, resulting in worse performance of the fuel cell.^54,55 On the other hand, if the temperature is too low, the electrochemical reaction rate of the fuel cell will decrease, the saturated vapor pressure will decrease as well, and the water in the cathode will predominantly be in a liquid form.^54,56,57

Many scholars have studied the effects of temperature on water management, as shown in Table 1. Anderson et al.⁵⁸ compared different operating temperatures of fuel cells and concluded that an increase in the operating temperature would greatly increase the water concentration gradient between the anode and cathode, causing water produced at the cathode to diffuse more quickly to the anode. Yin et al.⁵⁹ used an ejector as a recirculation device and found that both the temperature and humidity of the secondary stream affect the performance of the fuel cell. They guessed that at higher humidity and temperature of secondary stream, there is more water vapor and less hydrogen in the recirculated gas. Al-Zeyoudiet al.⁶⁰ evaluated the effect of monthly ambient conditions on the water management of fuel cells and found that hot and humid conditions favored adequate PEM hydration, whereas hot and dry conditions led to PEM dehydration. Tang et al.⁶¹ investigated the effect of operating temperature on the membrane's resistance and showed that the performance of the fuel cell improves as the cell's temperature increases. This is mainly due to the activation of the catalyst with increasing temperature. At the same time, they also concluded that high temperature leads to high water vapor content and it is difficult for the membrane to hydrate with water vapor. These experiments all used electrochemical impedance spectroscopy⁶³ or polarization curves to diagnose the state of water management. But neither of these two methods can establish the specific effects of temperature on water management or provide a visualization of the water management process in the PEMFC.

Table 1 Research on the effect of temperature on water management

Highlight	Method	Key findings	References
Using a dry hydrogen stream to remove product water from the cathode	Experiment	Water removal from the anode is optimal when the operating temperature is 75 °C and the relative humidity of air is 25%	58
Creating the renormalization group k–ε turbulent model for the three-dimensional numerical model of an ejector	Numerical	With higher temperatures resulting in more water vapor recirculation and less hydrogen recirculation	59
	Simulation
Open-cathode PEMFC stack under ambient conditions: a case study of the United Arab Emirates	Numerical	Hot and humid ambient conditions are beneficial for maintaining the fast reaction kinetics and keeping the membrane at an adequate hydration level	60
	Simulation
The printed circuit board technique was utilized to study the effects of operating temperature on membrane resistance	Experiment	The water vapor content contained in the reactant gas at 90 °C was more than that at 70 °C. It was difficult for the membrane as it underwent a hydration reaction with water vapor	61
An investigation of parameter effects on the performance of high-temperature PEMFCs	Numerical	The appropriate operating temperature could be about 160–180 °C	62
	Simulation

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At present, it is generally accepted that when the operating temperature of the cell's stack is regulated to be the same as the inlet temperature, its performance will increase with an increase in inlet temperature.⁵⁴ Water management in fuel cells is also related to the temperature of the gas humidifier.⁶⁴ Increasing the temperature of the humidifier can increase the rate of water vapor transfer.⁶¹ However, if the temperature of the humidifier is too high, the amount of water vapor in the humidifier is not enough to compensate for the humidity which tends to cause the membrane to dry out.⁶⁴

Some scholars have begun to use popular neural networks to assess the impact of each operating condition in PEMFCs on water management. In 2009, Lobato et al.⁶⁵ evaluated the effect of operating temperature by using three types of feed-forward neural networks. They found that there is a nonlinear relationship between temperature and the cathode resistance of inlet gas. Although the relationship has not been explained, it is certain that the internal resistance of the cell is able to reflect the water content of the membrane. In 2018, Laribi et al.⁶⁶ optimized an internal resistance model for PEMFCs by using artificial neural networks (ANNs), which can be employed to diagnose the effect of air temperature on fuel cell water management. The proposed approach enabled them to identify the five physical parameters of the impedance that exhibited high sensitivity in the PEMFC diagnostic, as shown in Fig. 3a–f. Strangely, they found that the water content of cathode increases as the oxidizer temperature decreases. Wan et al.⁶⁷ further proposed the gray wolf optimization-based reverse learning particle swarm optimization (HGPSO) algorithm on the basis of Laribi. As shown in Fig. 3g–i, they superimposed the interlayer weights ω of the different input factors corresponding to the neurons in the fitted model to obtain the magnitude of the effect of these factors on the water management of the fuel cell. The above studies on the application of neural networks to PEMFCs are based on modeling the internal resistance of PEMFCs, using neural networks for prediction and evaluation. However, the model does not accurately reflect the water management status of the PEMFC and has to be adjusted accordingly under different operating conditions. This is because the modeling is based on empirical or semi-empirical formulae.

Fig. 3 Evolution of the model parameters according to different times and operating temperatures: (a) the membrane ohmic resistance, (b) the double layer capacitance of the electrode/electrolyte interfaces, (c) the polarization resistance, (d) diffusion ohmic resistance, (e) diffusion time constant, and (f) RH.⁶⁶ Magnitude of the input factor impact: (g) 0.2 A cm⁻², (h) 0.5 A cm⁻², and (i) 1.0 A cm⁻².⁶⁷

Some scholars have also analyzed the effect of flow field channels with different geometries on temperature distribution. Freire et al.⁶⁸ investigated the effect of inlet gas temperature on PEMC performance by using serpentine flow field channels with different (rectangular and trapezoidal) cross-sectional shapes. They found that the serpentine channel with a trapezoidal cross-section has a higher water removal capability when the inlet temperature is higher than the cell's temperature.

2.2.2 Summary. The above studies have made quite a few contributions to the effect of temperature on water management, including operating temperature, inlet's temperature, ambient temperature and temperature's distribution. Many conclusions indicate that high operating temperatures and high humidity conditions are favorable for enhancing the performance of PEMFCs.⁶⁹ However, most of the operating temperatures they studied ranged from 30° to 90°. There are few papers investigating the effect of low operating temperatures on PEMFCs. And these studies do not really quantify the relationship between temperature and water management. These optimal temperatures suggested in the experiments can also only be achieved under specific conditions. In fact, temperature affects the water concentration gradient, as well as the water vapor content, the catalyst's activity and the membrane conductivity.²⁸ Future studies are necessary to further reveal the transport and transformation mechanisms of water in PEMFCs, which are associated with the internal resistance. In addition, it must find ways to enhance the water removal ability at low temperatures and the water retention ability at high temperatures.

2.3 Effects of humidity on water management

2.3.1 Effects of humidity. The gradient between the anode water concentration and the cathode water concentration is determined by the thickness of the membrane, the water content of the membrane and the humidity of the reaction gas.⁷⁰ In general, an automotive PEMFC system only needs to humidify the air at the cathode's entrance.⁷¹ This is because the humidity of the hydrogen gas has an almost negligible effect on the PEMFC performance.⁷² Some early literature studies have established semi-empirical equations for membrane water content versus humidity,^55,73–76 as shown in eqn (2) to (4), where RH is relative humidity, P_v is partial pressure of water vapor, r_m is resistivity of the membrane, I is the current of the PEMFC, A is cell active area, L is the thickness of the membrane, R_int is the internal resistance of the PEMFC, and λ_m is the water content of the membrane. So far, much of the literature has been based on improving or calculating eqn (2) to (4).

Morever, Yousfi-Steiner et al.²³ pointed out that the decrease in anode gas humidity would have a positive effect on membrane drying and prevent the formation of liquid water in the cell. However, more scholars still choose to conduct research by simulation or experiment. Hou et al.⁷⁷ simulated the gas–liquid two-phase flow in PEMFCs. The results showed that the water removal process in the cathode channel is easier than that in the anode under the same operating conditions, and increasing the hydrogen humidity and flow rate is favorable for anode water removal. Wang et al.⁷⁸ used polar analysis to determine that the most important factor affecting the performance of PEMFCs is the air stoichiometry ratio, followed by the RH of air. Esmaili et al.⁷⁹ simulated the segmented model of PEMFCs and found that increasing the stoichiometry of the inlet gas can effectively control water generation, while appropriately decreasing the inlet gas humidity is beneficial for preventing water flooding. However, they don't distinguish whether cathodic or anodic humidity has a greater effect. In addition, Neyerlin et al.⁸⁰ found through experiments that in the case of reducing cathode humidity, the plasmonic membrane caused an increase in the conductivity of the membrane and a decrease in the rate of the ORR due to dehydration.

In addition to the above, humidity affects the performance of the MEA in the fuel cell, as shown in Fig. 4. This indirectly affects the water management. In particular, CL degradation by humidity is significant. The catalyst materials for the anode and cathode are usually platinum (Pt) or nano-sized Pt alloy particles.⁸³ Carbon paper or cloth is used to build the basic mechanical structure of the electrode. Pt catalyst particles are coated on the carbon surface. The carbon structure forms irregular Pt/C catalyst clusters with Pt, which are adsorbed on the surface of the PEM.^44,84 Degradation of Pt catalysts is essentially an oxidation reaction of the carbon carrier under the influence of humidity, oxygen and temperature. This not only implies structural loss and changes in the distribution of Pt on the carbon carrier but also reduces electrochemically active surface area of the electrode.⁸⁵

Fig. 4 Multi-serpentine segmented cell design: segment distributions at the (a) anode and (b) cathode side, with (c) color codes for current density value ranges; the G arrow represents the position of the cell in the gravitational field.⁸¹ Carbon photoemission spectra of catalyst layers reveal distinct ionomer defluorination under fully humidified conditions, in particular on the anode (d) and close to the gas inlet (segment I5) of the cathode (e).⁸¹ (f) Comparison of polarization curves under fully humified conditions,⁸² and (g) the brief structure of the MEA.

Sanchez et al.⁸¹ compared the degradation of the PEM by fully humidified and non-humidified inlet gases. The results showed that the degradation of the membrane under low humidity conditions has a very strong effect on the cathode and a negligible effect on the anode. The reason for this is the presence of a microporous layer (MPL) in the GDL. The deposition of silicon in the MPL, combined with the oxidative dissolution of Pt on the surface of the cathode catalyst, leads to an increase in the resistance to gas transport and a decrease in the membrane activity. Kim et al.⁸⁶ and Li et al.⁸² explored the effect of the humidity of the air on the internal operating mechanisms of the PEMFC during the cycle. The results all showed that when the humidity of air is high, significant oxidation, dissolution, segregation and migration of Pt were observed on most of the cathode catalyst layers and there was also corrosion of the carbon carrier. These changes resulted in a significant loss of Pt for electrochemical reactions and the active surface area of the cathode catalyst. As a result, water management performance of the fuel cell was reduced. Taymaz et al.⁸⁷ used numerical simulation and found that increasing the RH at the anode side not only prevents membrane dehydration, but also significantly reduces proton transport resistance and accelerates electrochemical reactions. Zhang et al.⁸⁸ showed that humidity highly affects the distribution of condensates in the CL and Pt activity. The surface area for electrochemical reactions in the cell also increases progressively with higher condensates. It is noteworthy that their pore-scale modeling helps improve the fundamental understanding of the oxygen reactive transport process in CLs. In particular, the coupling effects of operating conditions and CL structural parameters can be comprehensively investigated by using the pore-scale model. Nishimura et al.⁸⁹ used numerical calculations and found that increasing humidity of the inlet can significantly affect the mass transfer capacity of the PEM. But their models are too ideal and not experimentally validated.

2.3.2 Summary. The above research has mainly explored the effect of humidity on water management. Proper humidity prevents membrane drought and allows for adequate hydration of the membrane to enhance proton conductivity and reaction rates. This reduces the internal resistance of the membrane and increases the conversion efficiency.^28,90 In PEMFCs, it is common to humidify the inlet gas at the cathode, but in recent years, there has been a growing number of papers indicating that suitable hydrogen humidification helps in anode water removal. In addition, humidity also affects the degradation of the CL and GDL, especially high humidity indirectly affects water management in the cell, but few scholars have studied it, so there is a huge gap in this field. Future research should deeply study the effect of humidity on water management, especially the relationship between humidity and degradation of the CL and GDL, and provide a deeper understanding of optimal water management.

2.4 Effect of pressure on water management

2.4.1 Effect of pressure. If there is any water accumulation in the cell, increasing pressure will cause the reactant to force the water to flow.²⁸ And the higher the back pressure, the weaker the ability of the gas to carry water out of the PEMFC.⁹⁰ The main benefit of pressurization is to maintain sufficient water in the membrane.⁹¹ But, increased pressure can also lead to a buildup of liquid water in the cell, although higher operating pressures can also have a positive impact on efficiency of cell.^91,92 In eqn (5), P_ab is the absolute outlet pressure and ω denotes the magnitude of the ability of the gas to carry water out of the PEMFC.⁹⁰ At a certain temperature, P_sat is a constant. The higher the back pressure, the smaller the ω. In other words, the weaker the gas drainage, the higher the water content in the PEMFC is likely to be.

As claimed by Hussaini et al.,⁹³ in the case of flooding in the flow path, the pressure drop may be two to five times higher and it can lead to higher parasitic losses. Therefore, a certain pressure drop is required to discharge the accumulated water. The lower the pressure drop, the lower the pumping power.⁹⁴ Ma et al.⁹⁵ fabricated transparent parallel PEMFCs and investigated the effect of water accumulation on pressure drop at the inlet and outlet. The results showed that the pressure drop increased with the increase in water content in the channel and decreased rapidly with the discharge of the water segment plug. However, their study was a qualitative evaluation of water content and did not quantify the effect of water accumulation on pressure drop. Both Chen et al.⁹⁶ and Reshetenko et al.⁹⁷ analyzed and quantified the effects of key operating parameters on the PEMFC, obtaining conclusions consistent with those by Ma⁹⁵et al. Furthermore, Cai et al.⁹⁸ found experimentally that high back pressure leads to an increase in water content and it is mainly due to a decrease in the water management capability of the GDL, rather than deterioration of the membrane and catalyst. They also concluded that when the fuel cell operates at high back pressure, the water in the channel is not easily carried away by exhaust gas. As a result, the GDL is prone to flooding. It exacerbates corrosion of carbon and loss of PTFE (polytetrafluoroethylene), leading to a reduction in the GDL's capacity for water management. On the other hand, they used a semi-empirical polarization curve model to fit the polarization curves, which can't accurately reflect the performance of PEMFCs and internal electrochemical processes.

What's more, scholars have summarized the experimental statistics of water management in PEMFCs. And a linear fitting equation for the two-phase pressure drop and water coverage is given⁹⁹ as eqn (6):

where WCR denotes the average water coverage, which is used to quantify water accumulation in the cathode-side runners, Φ denotes the average two-phase pressure drop coefficient, ΔP_V represents the instantaneous two-phase voltage drop obtained at the cell's operating voltage, ΔP_OCV is then the instantaneous two-phase voltage drop at the open circuit voltage, Φ_t denotes the instantaneous two-phase voltage drop coefficient, t_ss is the quasi-steady state time, and t_f is the end time. The instantaneous WCR value is unstable at the beginning of the test until a quasi-steady state is reached.

Due to the pressure drop being so closely related to water management, it can easily be obtained through sensor monitoring. Therefore, much of the diagnosis for water management is based on changes in pressure drop.^9,20,100 The pressure drop combined with the voltage signal can detect drying faults, as shown in Fig. 5a–f. The current density was also used as one of the diagnostic variables considering the stack load variations, as shown in Fig. 5g–j. Then Hussaini et al.⁹³ carried out experiments to observe the flooding of the cathode channel and the conclusion is that the two-phase pressure drop coefficient was uniquely related to the water content in the channel. Based on the conclusion, Banerjee et al.¹⁰¹ determined the relationship between the cathode pressure drop multiplier and the cell voltage under different operating conditions. But the results just demonstrated that the pressure drop multiplier for the cathode is a diagnostic tool for predicting flooding and dehydration. Ko et al.⁹¹ investigated the effect of operating pressure on the water distribution. They found that the PEMFC showed higher performance when the cathode side was pressurized than when the anode side was pressurized. Their study also showed that the main contribution to performance enhancement was different for different operating pressures. When there is insufficient water in the PEMFC, the effect of water transport dominates, and when there is sufficient water in the PEMFC, the effect of increased gas partial pressure dominates.

Fig. 5 Voltage and cathode pressure drop variation curves during flooding and drying experiments: (a)–(f).¹⁰³ Flooding experiments: (a)–(c), and drying experiments: (d)–(f). Polarization curves with 3 different pressurization conditions at (g) relative humidity 25% and 0.2 bar, (h) relative humidity 25% and 0.4 bar, (i) relative humidity 100% and 0.2 bar and (j) relative humidity 100% and 0.4 bar.⁹¹

2.4.2 Summary. The aforementioned studies intuitively revealed the effect of pressure on water management; especially at low humidity, increasing the pressure can increase the water content of the membrane. However, they did not really elucidate the operation mechanism between pressure and water content inside the fuel cell. Most of the experiments conducted were limited to experimental fuel cells or small power fuel cell stacks. Therefore, future research should focus on the relationship between the pressure of a large fuel cell and the water content inside the cell by a combination of visual experimentation and neural networks. This is because its huge nonlinear computational power alleviates the dependence on the complex physical properties of the fuel cell.

3 Key devices in water management

The above factors can be adjusted using some devices to achieve optimal working conditions for water management. The gas supply device and humidifier are important mechanical equipment in the PEMFC system. In the early days, it was argued that water management systems were simply humidification systems,³⁸ because some scholars understand water management as the circulation of water required by the humidifier. In fact, there is no single water management system, because problems with any of the subsystems in the PEMFC system can affect the water management of the PEMFC. Therefore, this section focuses on common pumps in gas delivery units and common humidifiers in humidification units (Fig. 6).

Fig. 6 System of a PEMFC.⁴³

3.1 Gas supply device

The pump is one of the core devices in the PEMFC system, not only because it can effectively improve utilization of hydrogen as a hydrogen recirculation pump, but it can also effectively purge liquid water from the anode channel and humidify the hydrogen.^102,104 In the hydrogen recirculating mode, excess water can be discharged from the anode outlet as long as a certain percentage of excess hydrogen (typically a stoichiometric ratio of 1.2) is supplied to the anode of the fuel cell.^105,106 Most discharged liquid water can be collected using a gas–water separator. Finally, unreacted hydrogen with a RH of 80% or more is sent through recirculation to a pipeline for hydrogen supply. It is then mixed with fresh hydrogen and supplied again to the anode.^40,107 There are three types of gas supply devices currently used in fuel cell systems: injectors, hydrogen circulating pumps and electrochemical hydrogen pumps (EHPs). And the mechanical pumps in the gas delivery unit can also be used as water pumps in the cooling cycle.

3.1.1 Mechanical pump (MP). MPs are controlled by motor drives and are some of the most widely used gas delivery devices in fuel cell systems, especially in the field of hydrogen-fueled vehicles.¹⁰⁸ Nowadays, scroll pumps, claw pumps, roots pumps and ejectors are commonly used as circulation devices in PEMFC systems, as shown in Fig. 7.^109,113,114

Fig. 7 (a) Claw pump,¹¹⁵ (b) roots pump,¹¹⁰ (c) scroll pump,¹¹⁵ and (d) ejector.¹¹¹

(1) Claw pumps have the advantages of high reliability, simple and compact construction, and oil-free operation. They are already being used in PEMFC vehicles.¹¹³ It is worth noting that the volumetric efficiency of the claw pump is optimized at high pressure ratios due to its built-in compression characteristics. And it also maintains its simple structure and high reliability.¹¹² A large number of studies and experiments have been carried out on claw pumps, most of which are validated by using three-dimensional numerical calculations on improved profiles.^116–121 In particular, Gu et al.^122,123 obtained the most significant influences on volumetric efficiency and shaft power by ANOVA and Taguchi's method. They used them as inputs to an artificial neural network, which was trained to predict the performance of the claw pump by using a simulated dataset. But their training data are only 38 cases, so their precision of prediction and evaluation are not high.

(2) The roots pump offers the advantages of high reliability and low cost. Although it allows for reverse rotation, its efficiency is lower compared to claw pumps due to the lack of built-in compression.¹⁰⁸ However, built-in compression is not important in hydrogen delivery systems because the pressure difference between the fuel cell anode inlet and outlet is relatively small. Hence, the roots pump is a good choice as a hydrogen recirculation device for fuel cell systems. The studies on roots pumps are similar to those of claw pumps. But most of them focus on the improvement of profile^124–127 and analysis of transient flow.^128,129 These include an exploration of the major influences on the performance of roots pumps, such as inter-rotor clearance, radial clearance between the rotor and casing, the lift ratio and speed.

(3) Scroll pumps have the advantages of a wide adjustable flow range, high efficiency, low noise and low vibration.^130,131 Compared to claw pumps and roots pumps, scroll pumps are small and light and have lower power consumption. Because of this, scroll pumps can be used not only as hydrogen recirculation devices in hydrogen fuel cell vehicles¹³² but also as heat pumps in electric vehicles.¹³³ Thus, many scholars aim to improve their operational performance, including the geometry and sealing of scroll pumps.^134–137 It is worth noting that due to the special structure of the scroll pump, it is difficult to obtain the internal flow characteristics of the pump by using experimental methods.¹³⁸ Hence, most studies have used numerical calculations to investigate the internal flow field of a scroll pump.^139–142

However, claw pumps and roots pumps have the disadvantages of high power consumption, large noise and general efficiency. Scroll pumps have the disadvantages of a large outlet pressure fluctuation range, high manufacturing cost and troublesome maintenance. Besides, claw pumps and roots pumps are prone to wear between the rotors, resulting in hydrogen leakage and reduced efficiency. Scroll pumps are prone to head-to-face wear due to the seal between the two vortices. As the manufacturing process improves, precision machining technology should be used in the future to improve manufacturing accuracy. The MP can also be used in conjunction with ejectors to minimize additional power consumption due to wear and tear. At the same time, optimization for mechanical pumps should not be limited to the traditional Taguchi method or response surface method. In the future, more intelligent algorithms coupled with neural networks can be introduced for optimization design.

3.1.2 Ejector. An ejector generally consists of a nozzle, a suction chamber, a mixing chamber and a diffuser, as shown in Fig. 7d. The ejector has two inlet ports and one exhaust port. One of the inlets is the main flow, while the other is the secondary flow. The two streams are mixed in the ejector and discharged at some intermediate pressure called back pressure. Thus, the ejector has a pump effect in which the vacuum required to generate suction is generated by accelerating the main flow through a converging–diffusing nozzle.¹¹¹

The working principle of the ejector in the fuel cell is to utilize the Venturi effect, so the ejector has the advantages of no power consumption, low manufacturing cost, low noise, no leakage, and high efficiency.¹¹¹ Nevertheless, due to the sensitivity of the ejector to geometry and operating conditions, even small deviations from ideal conditions can have a significant negative impact on the efficiency of the ejector. A wide range of stack output power alone may lead to large changes in the hydrogen flow rate of the hydrogen supply system and affect the operational performance of the ejector.^143,144 Thus, many scholars have devoted themselves to studying fluid flow characteristics,^59,145 structural design and its optimization^146–149 to improve ejector performance.

Besides, more research studies have been done on the optimal design of ejectors by using intelligent algorithms than on mechanical pumps. Carrillo et al.¹⁵⁰ optimized the geometrical parameters of the ejector by using a multi-objective optimization algorithm, and the back pressure and entrainment ratio of the ejector were effectively improved. Both Maghsoodi et al.¹⁵¹ and Liu et al.¹⁵² used artificial neural networks and genetic algorithms to obtain optimal geometric parameters in order to ensure the relevance of each geometric parameter to the performance of the ejector. Ahmed et al.¹⁵³ used ANNs to study the effect of geometrical parameters of a steam ejector under three optimizers on the coefficient of performance of the ejector and pressure reduction ratio. Zhang et al.¹⁵⁴ optimized the geometric parameters of the water supply ejector by the particle swarm algorithm and the results showed that the ejector diameter had a significant effect on the flow state and the degree of cavitation.

3.1.3 Electrochemical hydrogen pump (EHP). The EHP has been used for hydrogen compression and purification reuse in a variety of industrial environments.¹⁵⁵ The principle of the EHP is very similar to that of the PEMFC,¹⁵⁶ as shown in Fig. 8b. A mixture of gases enters at the anode and breaks down hydrogen into protons and electrons in the presence of an external DC power supply, with only the protons passing through the proton exchange membrane. At the cathode the protons recombine with the electrons to form hydrogen. The continuous pumping increases the pressure on the cathode side of the closed system. Obviously, the advantages of the EHP over mechanical pumps are not only the reduction of additional power and increased system efficiency, but also the purification of the gas and the reduction of noise. However, the EHP has its drawbacks, namely inefficient hydrogen purification and water management at low temperatures (50–80 °C).¹⁵⁷

Fig. 8 Schematic diagram of the working principle of an EHP: (a) principle of the PEMFC, (b) principle of the EHP, and (c) applications of the EHP.

Based on the above characteristics, EHPs are considered promising alternatives to MPs and ejectors in fuel supply systems. Toghyani et al.^158,159 specifically compared the EHP, ejector and MP and found that the system efficiency of the EHP is slightly lower than that of the ejector. But its controllability is much better than that of the ejector, as shown in Table 2. Because of the similarity between the EHP and PEMFC, the factors that affect the PEMFC also affect the EHP, including water management, the CL and the GDL. Hao et al.¹⁶⁰ investigated the operating performance of an EHP with an internal humidifier in order to alleviate the membrane drying problem of the EHP. Arenas et al.¹⁶¹ investigated the effect of different catalysts on the EHP and PEMFC. They found that the effect of catalysts on the performance of the PEMFC was more pronounced. However, the limited number of simulations and mathematical models of the above research studies is not universal. At present, the related studies have not formed a widely recognized theoretical system in the published articles.¹⁶² In the future, with the development of hydrogen and fuel cell vehicles, EHP research will show great scientific potential for utilizing electrochemical compression and purification technologies.

Table 2 Comparison of three types of pumps

Current density	System efficiency	Noise level	Power required	Reference
Lower than 0.1 A cm^−2	EHP > ejector > MP	MP > ejector > EHP	MP > EHP > ejector	158 and 159
Higher than 0.1 A cm^−2	Ejector > EHP > MP

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3.1.4 Summary. At present, the commonly used air supply equipment on the market is still the MP and ejector. However, the performance of the MP and ejector is limited by the precision of the manufacturing process. Meanwhile, the MP can be optimized by introducing more intelligent algorithms, but no one did that. Compared with the MP and ejector, the EHP has low power consumption, low noise and high efficiency. However, due to the similarity between the EHP and PEMFC, the technical challenges encountered in the PEMFC are also applicable to the EHP.

3.2 Humidifier

The humidifier ensures the hydration of the polymer electrolyte and effectively facilitates the internal process of proton transfer. The proper level of humidity plays a vital role in the performance and service life of the cell. It is currently divided into external humidification and internal humidification according to the way water enters the system.

3.2.1 External humidifier. External humidification is a very common method of humidification, because humidity can be adequately controlled through external humidifiers. Common external humidifiers can be categorized into three types: bubble humidifiers,¹⁶³ nozzle spray humidifiers¹⁶⁴ and membrane humidifiers,¹⁶⁵ as shown in Fig. 9.

Fig. 9 Schematic diagram of (a) bubble humidifier, (b) nozzle spray humidifier, (c) two-dimensional structure of a membrane humidifier, and (d) three-dimensional structure of a membrane humidifier.

(1) Bubble humidifier. The bubble humidifier is a simple and widely used device for humidification in PEMFC systems. It has the advantages of easy operation and easy control. The working principle of the bubble humidifier is very simple: dry gas flows through a tube into the bottom of a container with hot water and is dispersed into many small bubbles, which then flow out of the water. In some cases, the bottom can be filled with some glass beads, which provide enough contact area to ensure that the gas can be sufficiently humidified. Other scholars have found that increasing the temperature of deionized water can enhance the RH of the gas and increasing the flow rate will have the opposite effect.¹⁶⁶ The optimal operating conditions for bubble humidifiers are such that the dew point temperature of the outlet flow is the same as the temperature of the water,¹⁶⁷ but in practice, the water's temperature is generally set to 10 K above the dew point temperature. Vasu et al.¹⁶⁸ achieved continuous humidification of hydrogen by real-time adjustment of water temperature, water level, and gas flow in the vessel, and controlled the humidity well between 93% and 96%. Therefore, a bubble humidifier is the best choice for the highly accurate and constant humidification level required for the basic research of fuel cell systems.

However, the disadvantages of bubble humidifiers are obvious: they are large, are not easily portable and have parasitic power. Also, they are only suitable for stationary scenarios in high-power situations, such as power plants, test chambers and chemical plants.^163,169 Gas may carry excess liquid water into the PEMFC to block the gas transfer path and cause flooding.¹⁷⁰ The gas is humidified by heated water, which causes a considerable pressure drop on the humidifier. As a result, an additional heater is required to raise the water temperature, which can lead to larger parasitic losses.¹⁷¹ Besides, the change in the dew point (change in temperature of the water in the bottle) takes a while, which makes the system difficult to commercialize.

(2) Nozzle spray humidifier. The nozzle spray humidifier is mainly composed of a spray chamber, a nozzle and a mist eliminator, as shown in Fig. 9b. The nozzle at the top of the spray chamber sprays a large amount of water mist, dry gas from the bottom of the spray chamber into the mist, and then through the demister to remove the water mist to achieve the purpose of humidification.¹⁷² But as the gas is humidified, the water is atomized and mixed with the gas to form an aerosol. Hence, water droplets in the aerosol must be evaporated to avoid causing flooding in the fuel cell. This can be done by heating the water before it enters the nozzle. This is because water has a rather high latent heat. The temperature required to heat the water prior to atomization is much higher than the desired dew point temperature. Furthermore, the humidity of the outlet gas can be controlled using the flow rate of the gas or the temperature of the liquid water.¹⁷³ Zhang et al.¹⁶⁷ then precisely controlled the amount of water injected into the nozzle using the flow rate of the gas. The results indicated that the humidifier could provide good humidified air for the PEM fuel cell stack at high gas flow rates. Sung et al.¹⁷⁴ developed an ultrasonic atomizing humidifier. The RH of the ultrasonic waves can be increased by raising the driving voltage. In short, the size of microdroplets can be controlled by adjusting the driving frequency. As the driving frequency increases, the average diameter of the droplets becomes smaller, which improves the humidification efficiency.

Although nozzle spray humidifiers provide effective and precise humidity control, the humidified gas inevitably carries liquid water into the PEMFC. This is similar to bubble humidifiers. In fact, the main shortcoming of nozzle spray humidifiers is still due to pumping losses and heating of the injected water or steam. This is because it consumes additional power and multiplies the size, weight and complexity of the equipment. For these reasons, nozzle spray humidifiers are not suitable for portable or compact applications, but only for basic research on fuel cells and large-scale plants.

(3) Membrane humidifier. Membrane humidifiers are composed of a dry gas channel, a wet gas channel or a liquid water channel, as shown in Fig. 9c. The two channels are usually separated by a polymer membrane (typically the Nafion membrane).¹⁷⁵ The working principle of a membrane humidifier is simple: due to the gradient of relative humidity on the membrane, water vapor crosses the membrane from the water channel or the moisture channel into the dry gas channel for the purpose of humidification. There is no cross-flow between the dry gas and moisture channels. And membrane humidifiers do not have the same temperature and pressure drop requirements as those of the two humidifiers mentioned above. As a result, membrane humidifiers are considered to be the best choice for humidity control in the PEMFC.¹⁷⁶ Membrane humidifiers are divided into gas-to-gas and liquid-to-gas according to the different ways of humidification. At present, the membrane humidifier commonly used in fuel cell vehicles is the gas-to-gas membrane humidifier.¹⁷⁷ Hashemi et al.¹⁷⁸ found from 3D numerical computations that an increase in the inlet temperature of the dry and wet channels and an augmentation of the mass flow rate of the wet channel would facilitate the humidification process. Solsone et al.¹⁷⁹ proposed a low-temperature PEMFC model of the cathode humidifier and designed a nonlinear control strategy based on second-order sliding mode.

Table 3 provides a comparison of different types of membrane. Compared to bubble humidifiers and spray nozzle humidifiers, membrane humidifiers not only offer precise, easy and direct dew point control, but also have the benefit of small size and compactness.^180,181 The key point is that using a membrane humidifier in gas recirculation mode saves additional power consumption. In this strategy, the fuel cell cathode inlet is connected to the humidifier dry side outlet and the fuel cell cathode outlet is connected to the humidifier wet side inlet. The strategy utilizes the water vapor produced by the fuel cell to humidify the dry gas.^182,183 However, membrane humidifiers have limited precise control over humidification levels.¹⁸⁴ Also, when a liquid–air membrane humidifier is operated for a long period of time, the membrane may become plugged with impurities in the liquid water.¹⁷⁴

Table 3 Comparison of different types of membrane

Types	Advantages	Disadvantages
Bubble humidifier	Easy to operate and control	Not suitable for vehicles and high flow rates
	Good humidification effect	High parasitic power
		Dew point changes slowly
Nozzle spray humidifier	Easy to operate and control	Extra power
	Good humidification effect	Pumping losses
	Allows high flow rates	Complexity of structure
		Not good for portability
Membrane humidifier	Easy and straightforward humidity control and dew point control	Precise control is limited
	Compact structure and good for portability	Not suitable for long-term operation
	No parasitic power and extra power

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3.2.2 Internal humidification. The internal humidification or the self-humidification method refers to the proper retention of water generated in the cathode CL to humidify the membrane. This method removes the humidifier from the fuel cell system and is more conducive to commercialization.¹⁸⁵ Compared with external humidification, internal humidification makes the whole fuel cell system simpler, lighter and more economical. For this reason, internal humidification has been widely regarded as another effective approach.¹⁸⁶ In 2014, Toyota launched “Mirai”, the world's first commercial fuel cell vehicle without external humidification.¹⁸⁷ Mirai humidifies the system by reducing the thickness of the membrane, evaporating the water and utilizing circulation patterns.¹⁸⁸ As a matter of fact, internal humidification of fuel cells is mainly achieved by two methods, physical or chemical. The physical method is to change the physical structure or optimize the operating conditions. The chemical method is to change the material composition of the membrane or electrode.¹⁸⁹ In the field of fuel cell vehicles, the main purpose of self-humidification is achieved by using physical methods, especially the exhaust gas recirculation mode of the cathode.

In terms of flow field structure, Martins Belchor et al.¹⁹⁰ designed a parallel serpentine baffle flow field that reduces water's loss in the channel. This design allows the fuel cell to operate at higher temperatures with lower water content. Chen et al.¹⁹¹ researched the distribution of gas concentration, velocity distribution, liquid water distribution and current density distribution in conventional parallel and step flow fields. These studies were validated experiments and the results demonstrated that the stepped flow field not only improved the uniformity of gas concentration and current density distribution, but also accelerated the discharge of liquid water. Lian et al.¹⁹² presented a novel porous flow field which is based on a metal fiber. The fiber retains moisture and enhances the ability of moisture diffusion from the cathode to the anode for self-humidification. However, the method of changing the physical structure, though it does not require additional equipment or consume parasitic power, can only achieve proper water management under limited operating conditions. And it is not as effective as external humidification methods.¹⁹³

There is also a method of self-humidification that utilizes the exhaust gas recirculation. This type of humidification also belongs to the category of physical methods. Compared to external humidification, the cathode gas exhaust recirculation (CGER) pattern not only reduces the size of the system, but also responds quickly to the dynamics of the vehicle, as shown in Table 4. This is because CGER utilizes the water vapor produced by the fuel cell to humidify the air at the cathode side. It has the merit of changing the amount of water in the cathode outlet of the stack to regulate the relative humidity at the inlet of the stack.¹⁸³ The working process of CGER is simple. It is only necessary to mix the humid gas stream with fresh air before the inlet of the stack. The entire process requires only the adjustment of the pump's speed. During the operation of an external humidifier, the relative humidity at the reactor inlet is mainly determined by the operating pressure, temperature and stoichiometric ratio of the air. Therefore, CGER definitely reduces the number of control objects and the complexity of control.¹⁹⁴ Yang et al.¹⁰⁷ found that controlling the flow rate of the reactants in the CGER pattern can bring liquid water from the outlet to the inlet in the anode of the power reactor effectively humidifying the fresh dry gas and effectively removing the water from the cathode. Furthermore, Jiang et al.¹⁹⁷ Xu et al.,¹⁹⁸ and Zhang et al.¹⁹⁵ showed similar conclusions. The CGER could achieve the same RH level as that of the external humidifier. Nevertheless, the first two only performed Matlab simulations for verification. Zhang et al.¹⁹⁵ measured the effect of CGER on the water management characteristics of the PEMFC under different operating conditions. The experimental results of all three showed that CGER increased the RH at the cathode inlet and also improved the output performance of the electric stack. Meanwhile, the CGER mode also improves the water removal capacity at the outlet of the power reactor and significantly improves the consistency of the oxygen distribution along the flow path with less pump power, which is beneficial for the durability of the power reactor.

Table 4 Internal humidification

Types	Design	Specificities	Reference
Flow field structure		Retaining water in the channel	190
		Improvement of gas and water transmission	191
		Retaining the vapor content in the fuel cell and providing timely feedback to the anode	192
CGER		Removal of liquid water from the cathode. Reduced control complexity and achieving the same level of external humidification	194 and 195

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The effect of anode hydrogen recirculation on water management has also been studied. They all concluded that cathode recirculation is better for humidification.^106,196 Also, with the operation of the cathode self-circulation system, the maximum humidity of the gas mixture can nearly reach 85%.¹⁹⁹ This promotes evaporation of water vapor at high temperatures and suppresses the flooding of the MEA.¹⁹⁹ Nevertheless, there is a limit to the air flow rate and the hydrogen flow rate of the stack. The reason for this is that high gas flow rates cause high pressure differentials at the gas flow path. This may lead to irreversible damage to the membrane. Therefore, this improved humidification at high flow rates is limited by the structure of the hydrogen recirculation pump and the gas channel. And the power consumption of the CGER mode is much higher than that of anode recirculation. Considering the limitations of energy efficiency and the mechanical structure, anode recirculation is a good solution in the future.

3.2.3 Summary. In fact, whether in the laboratory or in the PEMFC for vehicles, the external humidifier is still the most popular humidifier. Because it can accurately control the humidity, it is also easy to control and operate. Although self-humidification has been applied in the PEMFC for vehicles, its humidity can only reach 85%. Among these humidification methods, the membrane humidifier is the most promising humidifier. The membrane humidifier has the characteristics of no power consumption, no noise and high humidity. How to improve the humidity level and controllability of the film humidifier is the focus of the current research. Also, the research content of the membrane humidifier mostly focuses on the material characteristics of the membrane.

4 Control of water management

The control of water management is usually achieved by controlling the above-mentioned devices so as to regulate the temperature, humidity and pressure. Appropriate control methods not only ensure that the PEMFC system achieves optimal performance, but also increase the durability and reliability of the PEMFC. This section focuses on control methods for water management, including traditional PID control and the contemporary popular neural network control. In particular, the control methods of neural networks are often used in combination with intelligent algorithms.

4.1 Traditional control methods

In fact, the practical application of water management is still dominated by traditional modern control methods. As far as we know, in 2006, Bao et al.²⁰⁰ proposed a control model for anode recirculation. The model is able to characterize the mixed effects of gas flow, pressure and humidity, as shown in Table 5 and Fig. 10a. On this basis, He et al.²⁰¹ proposed a novel model of a hydrogen supply system as shown in Fig. 10b. Many subsequent dynamic models of PEMFCs have been modified and adapted based on Bao's²⁰⁰ model. Damour et al.²⁰² presented a new nonlinear model-based control strategy and developed a flatness-based controller based on differential plane theory. They used the air mass flow rate as a control variable to regulate the membrane humidity and demonstrated satisfactory results. But there is a steady-state error in their control system and the error can be further reduced by introducing an integral term in the closed-loop control law. Ou et al.²⁰⁴ suggested a feed-forward fuzzy PID control and the results showed that good performance of the output voltage is ensured without affecting the cathode inlet humidity. Furthermore, Ou et al.¹¹ introduced a five-input, two-output fuzzy controller. The controller was used for real-time regulation of temperature and relative humidity in an open cathode fuel cell and was experimentally validated. However, the studies by Ou et al.¹¹ all involved static control of membrane humidity. Chen et al.⁷⁴ proposed a self-imposed disturbance control strategy to control the cathode humidity of PEMFCs. The results revealed that the self-immunity strategy can effectively shorten the response time, reduce overshoot and improve the energy efficiency by comparing with the traditional PID control and fuzzy PID control. Chen et al.²⁰⁵ introduced a fractional order PID control strategy to balance the water management. The results indicated that the fractional-order PID control is characterized by a short response time, a small overshoot of membrane humidity control, and high power generation efficiency compared with the traditional PID control method and fuzzy PID control method, as shown in Fig. 10c and d. In fact, in the above experiments, the humidity sensor was installed outside the cell. The voltage change ratio and input hydrogen humidity combined as a signal indicating the condition of the water content of the membrane. This method doesn't accurately represent the water content of the membrane. Fu et al.²⁰³ used the conventional PID method to control the external humidifier by monitoring the cathode water content. They maintained the optimal oxygen excess ratio by regulating the compressor voltage and compared with the conventional control methods, their control methods not only minimize the electrical power consumption of the humidifier but also avoid flooding in the PEMFC.

Table 5 Usual model for anode recirculation

Model	Description	Explanation
Hydrogen circulating pump		ω m is the angular velocity of the motor, γ is the speed ratio between the motor and the compressor, Jeq is the equivalent moment of inertia, feq is the equivalent friction coefficient, Tm is the motor torque, and Tcp is the compressor torque
Humidifier model		W humd,in and Whumd,out are the mass flow rates of a mixture at the inlet and outlet of humidifier and yhumd,in and yhumd,out are the mass fractions of the gas (air or hydrogen) in the mixture
Ejector model		W C is the compressed flow of the injector, Wan,in is the mass flow rate of the anode inflow, npump is the number of injection pumps, WP is the mass flow rate into the ejector, WH is the mass flow rate ejected by the ejector, yH2,an is the hydrogen mass fraction in the anode, and yH2,humd is the hydrogen mass fraction in the anode humidifier
Manifold model		p is the mixture pressure, Mm is the molecular weight of mixture, Wm,in and Wm,out are the inflow and outflow mass flow rates respectively, V is the manifold volume, R is the universal gas constant, and T is the temperature of gas
Valves for flow control	W fcv = ufcvWfcv,max	u fcv is the control input signal of the valve and Wfcv,max is the maximum mass flow rate through the flow control valve

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Fig. 10 Usual PEMFC system: (a) diagram of Bao's PEMFC's system structure, (b) diagram of He's PEMFC's system structure.²⁰¹ (c) Comparison of fractional-order PID, fuzzy PID, and conventional PID performances, and comparison of fractional-order PID, fuzzy PID, and conventional PID response times.²⁰⁵

4.2 Neural network control methods

In spite of the traditional modern control methods mentioned above, the method of control regarding neural networks has also been applied to the water management system of the PEMFC. Tan et al.²⁰⁶ used ANNs to fit the electric reactor model to the simulation data and the PSO algorithm was then used to obtain the optimal operating conditions as shown in Fig. 11. The efficiency of the optimized PEMFC system increased by 12.8%. Lebreton et al.¹⁰⁰ came up with a fault tolerant control strategy (FTCS) for water management and verified it experimentally. The control strategy coupled a water management fault detector of ANNs with a self-tuning PID controller. So the method is not only robust to noise measurements and model uncertainties, but also has the advantages of low computational cost and real-time performance. And yet, the efficiency of this control model is highly dependent on the selection of thresholds. In future work, threshold optimization based on operating conditions or FC degradation is a great research challenge. In addition, the use of empirical models limits the applicability of the proposed strategy. Zhang et al.³⁸ introduced the MPC method for controlling the concentration of the cathode in water and reducing the fluctuation of cathode humidity and optimizing it by using RNNs. Simulation results demonstrated that the method can be applied to real-time control of PEMFC water management. It can also avoid the fluctuation of the cathode water concentration. Yet, they used the cathode water injection method for humidification and this method is rarely used for humidification of fuel cells at present. Cho etal.²⁰⁷ established an ANN model based on the PEMFC in self-humidification mode and combined it with MPC. The system power is boosted by maintaining optimal stack temperature, cathode pressure and hydration of the membranes. Nevertheless, frequent changes in PEMFC operating conditions accelerate its degradation. They did not study the correlation between stack degradation and operating conditions. Therefore, their control system does not consider the performance changes caused by degradation. Lin-Kwong-Chon et al.²⁰⁸ built a data-driven neural controller that automatically adapts to the health of the system. The controller kept track of the water content of the membrane by controlling the stoichiometry, the pressure difference between the two sides of the membrane and the fuel cell temperature. Although the adaptive generic data-driven controller achieves the same performance as the PID control, the controller also needs to be validated by more tests. Li et al.²⁰⁹ selected 6 significant factors out of 11 by orthogonal experiments and performed simultaneous optimization of power density, system efficiency and distribution uniformity of oxygen in the cathode CL by using the NSGA-II algorithm. Notably, the optimization process of NSGA-II combined with the surrogate model requires less than 10 minutes to complete the multi-objective optimization. Compared with previous studies in the literature, this method can significantly reduce the optimization time.

Fig. 11 (a) The effect of temperature on the dimensionless power density, (b) the effect of temperature on system efficiency, (c) the effect of the oxygen excess ratio on the dimensionless power density, (d) the effect of the oxygen excess ratio on system efficiency, (e) the effect of cathode inlet humidity on the dimensionless power density, (f) the effect of cathode inlet humidity on system efficiency, (g) the effect of anode pressure on the dimensionless power density, (h) the effect of anode pressure on system efficiency, (i) the effect of cooling water temperature on the dimensionless power density, and (j) the effect of cooling water temperature on system efficiency.²⁰⁶

4.3 Summary

Both traditional control methods and neural network control methods are based on the dynamic model of the PEMFC system. These dynamic models involve many operating conditions that affect water management, including operating temperature, humidity, operating pressure, and other conditions. The control methods described above are designed to optimize these operating conditions to improve the water management of the PEMFC system, so that the system efficiency and power output of the PEMFC can be significantly improved. Hence the above studies on water management system control are all focused on achieving the optimal output power of the PEMFC, because the maximum power density point of the PEMFC system changes with the water management state.^210,211 When the PEMFC system reaches the optimal output power, it indicates that the PEMFC system also reaches a good water management state.

Traditional control methods are based on the improvement of PID. These methods do not significantly improve the performance of the PEMFC, but they can improve the stability very well. However, the traditional methods are not well suited for multi-input and multi-output control systems. Besides, traditional control methods are highly dependent on manual adjustment and lack flexibility.

Neural network-based controllers have made significant progress in PEMFCs. Many studies have proposed four main control variables based on adaptive control: mass flow of gas, pressure, temperature and humidity.²¹² Indeed, neural networks can compensate well for disturbances because they can perform water management diagnostics and provide corresponding predictions prior to formal control. This is one reason why many scholars have combined neural networks with modern control, especially for adaptive neural network control.

4.3.1 Summary of the whole paper. This paper provides a comprehensive and balanced review of water management based on the existing literature. Firstly, the effects of key factors on water management including temperature, humidity and pressure on water management are characterized. Secondly, key devices for water management including pumps and humidifiers are presented and clarified. Finally, control methods for water management are reviewed, including traditional control methods and neural network control methods. The conclusions and suggestions of this paper are as follows.

5 Conclusions

(1) Main factors: temperature, humidity and pressure. Temperature affects not only the water concentration gradient in the cell but also the progress of electrochemical reactions. The appropriately increasing operating temperature under low current conditions can improve PEMFC's performance. Humidity directly affects the hydration of the membrane and degradation of the CL and GDL. Increasing the humidity of hydrogen is beneficial for anode water removal, but the humidity of air has a larger impact on the performance of the PEMFC. Pressure affects the ability to manage water in the GDL and the hydraulic pushing effect. Pressurization improves the performance of the PEMFC, especially under low humidity conditions. Typically, the higher the back pressure, the lower the drainage capacity and the higher the water content of the membrane.

(2) Key devices: pumps and humidifiers. Pumps are not only used for anode circulation or cathode supply but also for water circulation and cooling and can serve as self-humidifiers. The pump is one of the indispensable devices in commercially available hydrogen fuel cell vehicles. It is often used in conjunction with an ejector to realize the functions of gas supply, circulation and self-humidification. Humidifiers can be divided into external and internal humidifiers. External humidification can accurately control the humidity range and has a good dynamic response. Its disadvantage is that the power is positively correlated with its size and generates additional power consumption. Although internal humidification doesn't generate additional power consumption, it also doesn't allow for precise humidity control. Even the pump's self-humidification of the air is only 85% effective at best.

(3) Control methods: traditional control and neural network control. The control of water management systems is still dominated by traditional modern control methods. Traditional control methods are stable and reliable, though they do not greatly improve the performance of the PEMFC. However, traditional control methods require manual adjustment to appropriate operating conditions. Therefore, many scholars have started to explore the optimal working conditions with the help of neural networks. Neural network control avoids manual regulation and is based on data analysis or experience to find the key factors affecting water management, which are subsequently improved and predicted by using intelligent algorithms. Eventually, the control is adjusted accordingly. But neural networks are highly dependent on how good the PEMFC model is, and if the model is not accurate enough, its results will not be good.

6 Suggestions

(1) For main factors, the relationship between either temperature, humidity or pressure and water management is unclear. Most existing formulae are semi-empirical or fitted formulae and are not generalizable and many experiments performed are also limited to experimental fuel cells or small power fuel cell stacks. Therefore, future research should focus more on large fuel cell stacks and automotive fuel cell stacks. Future experiments will need to use in situ visualization, neutron radiography, X-rays, and magnetic resonance imaging to further explore water distribution and transport inside the PEMFC. In addition, these main factors can be quantified with the help of artificial neural networks. This is because their enormous nonlinear computational power alleviates the dependence on the complex physical properties of the fuel cell.

(2) For key devices: at the moment, the commonly used devices are external humidifiers and MPs. We can use intelligent algorithms to optimize external humidifiers and MPs. Especially the optimization of the roots pump is still stuck in traditional optimization and no one used intelligent algorithms to optimize it. But people need to focus on the development of EHPs and membrane humidifiers in the future. Because the EHP and membrane humidifier are green, and there is no noise and extra power consumption.

(3) For control methods: firstly, it is necessary to improve the accuracy of PEMFC's water management working condition modeling, because the existing control is highly dependent on the model's ability to accurately reflect the PEMFC's operating conditions. Then, considering the powerful anti-interference performance and diagnostic mechanism of neural networks, the control of water management can be combined with diagnosis in the future. This control method is well-validated under simulation conditions, but lacks experimental validation.

Nomenclature

P sat	Saturation pressure of water
P 0	Pressure at the known temperature
M H2O	Molar mass of water
h fg	Latent heat of vaporization of water
R	Gas constant
T	Temperature
T 0	The known temperature
RH	Relative humidity
P v	Partial pressure of water vapor
r m	Resistivity of the membrane
I	Current of the PEMFC
A	Cell active area
L	Thickness of the membrane
R int	Internal resistance of the PEMFC
λ m	Water content of the membrane
P ab	Absolute outlet pressure
ω	Capacity of water removal
WCR	Average water coverage
Φ	Average pressure drop coefficient
ΔPV	The instantaneous two-phase voltage drop obtained at the cell's operating voltage
Φ t	The instantaneous two-phase voltage drop coefficient
t ss	The quasi-steady state time
t f	The end time

Abbreviations

PEMFC	Proton exchange membrane fuel cell
GDL	Gas diffusion layer
ORR	Oxygen reduction reaction
HOR	Hydrogen oxidation reaction
MEA	Membrane electrode assembly
ANN	Artificial neural network
CL	Catalyst layer
Pt	Platinum
C	Carbon
MPL	Microporous layer
Si	Silicon
EASA	Electrochemically active surface area
MP	Mechanical pump
EHP	Electrochemical hydrogen pump
CGER	Cathode gas exhaust recirculation
AFTC	Adaptive fault-tolerant control
FTCS	Fault tolerant control strategy
DC	Direct current
BPs	Bipolar plates

Data availability

No primary research results, software or code have been included and no new data were generated or analysed as part of this review.

Author contributions

Peihan Qi: conceptualization, methodology, formal analysis, investigation, writing – original draft. Zhenxing Wu: software, data curation, visualization, writing – original draft. Jiegang Mou: methodology, software. Denghao Wu: methodology, writing – original draft. Yunqing Gu: data curation, writing – original draft. Maosen Xu: software, writing – original draft. Zekai Li: conceptualization, resources, writing – review & editing, supervision, project administration, funding acquisition. Yang Luo: methodology, software.

Conflicts of interest

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

Acknowledgements

This study was supported by the Zhejiang Provincial Natural Science Foundation of China (No. LGG22E090001), Zhejiang Provincial Natural Science Foundation of China (No. LY22E050015), Scientific Research Fund of Zhejiang Provincial Education Department (No. Y202351240), and Fundamental Research Funds for the Provincial Universities of Zhejiang (No. 2023YW88).

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