Open AccessArticle

Simulation of a Novel Integrated Multi-Stack Fuel Cell System Based on a Double-Layer Multi-Objective Optimal Allocation Approach

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

School of Intelligent Manufacturing, Shanghai Zhongqiao Vocational and Technical University, Shanghai 201514, China

Shanghai TXJS Engineering Technology Co., Ltd., Shanghai 201804, China

Authors to whom correspondence should be addressed.

Appl. Sci. 2024, 14(7), 2961; https://doi.org/10.3390/app14072961

Submission received: 28 February 2024 / Revised: 21 March 2024 / Accepted: 28 March 2024 / Published: 31 March 2024

(This article belongs to the Topic Thermal-Related Design, Application, and Optimization of Fuel Cells and Batteries)

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Browse Figures

Figure 1
CWTVC condition. "> Figure 2
Flowchart of the optimal allocation approach. "> Figure 3
MFCS structure. "> Figure 4
PEM fuel cell hydrogen cycle diagram. "> Figure 5
Radiator MAP diagram. "> Figure 6
MFCS model validation. "> Figure 7
Dynamic response of MFCS parameters: (a) Current; (b) Voltage; (c) Mass flow; (d) Inlet pressure. "> Figure 8
Impact of common rail buffer volume on air supply subsystem: (a) Maximum pressure drop; (b) Maximum power; (c) Energy consumption. "> Figure 8 Cont.
Impact of common rail buffer volume on air supply subsystem: (a) Maximum pressure drop; (b) Maximum power; (c) Energy consumption. "> Figure 9
The air pressure in the common rail buffer under the CWTVC condition. "> Figure 10
The pressure in the hydrogen inlet common rail under the CWTVC condition. "> Figure 11
The anode inlet pressure under the CWTVC condition: (a) 20 kW; (b) 70 kW; (c) 120 kW. "> Figure 12
The variation of nitrogen concentration in anode channels under the CWTVC condition: (a) 20 kW; (b) 70 kW; (c) 120 kW. "> Figure 13
Effects of thermal subsystems on stack temperature: (a) Relationship between coolant temperature and steady state temperature of stacks; (b,c) The stabilization time and stabilization temperature for stacks at coolant temperatures of 333 K and 338 K; (d) Relationship between the mass flow rate of coolant and the stabilization temperature. "> Figure 14
Correlation effects of different stacks in the integrated thermal subsystem: (a) 20 kW; (b) 70 kW; (c) 120 kW. "> Figure 14 Cont.
Correlation effects of different stacks in the integrated thermal subsystem: (a) 20 kW; (b) 70 kW; (c) 120 kW. "> Figure 15
Temperature variation comparisons of the integrated and distributed thermal subsystems under the CWTVC condition: (a) 20 kW; (b) 70 kW; (c) 120 kW. "> Figure 15 Cont.
Temperature variation comparisons of the integrated and distributed thermal subsystems under the CWTVC condition: (a) 20 kW; (b) 70 kW; (c) 120 kW. ">

Versions Notes

Abstract

Featured Application

The multi-stack fuel cell system proposed in this paper can be applied to high-power generation, transport, and other engineering fields.

Abstract

A multi-stack fuel cell system (MFCS) is a promising solution for high-power PEM fuel cell applications. This paper proposes an optimized stack allocation approach for power allocation, considering economy and dynamics to establish integrated subsystems with added functional components. The results show that an MFCS with target powers of 20 kW, 70 kW, and 120 kW satisfies lifetime and efficiency factors. The common rail buffer at the air supply subsystem inlet stabilizes pressure, buffers, and diverts. By adjusting the volume of the common rail buffer, it is possible to reduce the maximum instantaneous power and consumption of the air compressor. The integrated hydrogen supply subsystem improves hydrogen utilization and reduces parasitic power consumption. However, the integrated thermal subsystem does not have the advantages of integrated gas supply subsystems, and its thermal management performance is worse than that of a distributed thermal subsystem. This MFCS provides a solution for high-power non-average distribution PEM fuel cell systems.

Keywords:

PEM fuel cell; multi-stack; optimal allocation; integrated design; common rail buffer

1. Introduction

Fuel cells, with the advantages of high energy conversion efficiency, low noise, clean air, and low carbon, have been gradually applied to transportation, aerospace, and distributed generation [1,2]. Fuel cell research and development are fully consistent with the strategic approach to renewable and sustainable energy development. Proton exchange membrane (PEM) fuel cells are the most promising fuel cells because of their low operating temperature and portability [3].

Currently, PEM fuel cells are available in a variety of structural forms to meet the output power requirement, including low-power single-stack fuel cell systems (SFCSs) and high-power multi-stack fuel cell systems (MFCSs) [4,5,6,7]. The rated power of large-scale power equipment typically ranges from several hundred kilowatts to several megawatts. However, current SFCS technology is not advanced enough to support such a high-power demand [8,9]. Therefore, in facing this demand, the decision to create a high-power MFCS using technologically mature stacks from the market or to develop a new high-power SFCS is a crucial issue that needs to be addressed. This decision is primarily related to the efficiency, availability, durability, and cost of PEM fuel cell power systems [10]. The development of high-power single-stack fuel cell systems leads to an increase in minimum output power as the power rating increases. In this case, there is no advantage of SFCS power coverage compared to MFCS. Duan et al. [11] investigated the dynamic and transient characteristics of a DC/DC-free sub-healthy fuel cell multi-stack system and found the fuel cell system current and voltage characteristics of series and parallel structures.

MFCSs, consisting of multiple fuel cells, are mainly available in integrated and distributed configurations. Candusso et al. [12] proposed the concept of multi-stack association in fuel cell systems, after which MFCSs have evolved considerably in the intervening decades. Since then, Hawke et al. [13] proposed the concept of a modular fuel cell system. The combination of modular fuel cell systems into MFCSs is clearly an effective solution for dealing with the power output of large-scale devices. Jahromi et al. [14] developed a power management strategy and designed a triple-stack configuration applied in a vehicle; this PEM fuel cell system could prolong the lifetime and cut the stack cost. Gadducci et al. [15] proposed a 240 kW MFCS with 30 kW per stack based on an average split-stack scheme in a ship-like environment, and they identified a management procedure for performance optimization. Zhang et al. [16] built a dual-stack fuel cell system and proposed an improved overall efficiency maximization strategy based on this MFCS; the results show that this system and control strategy can improve system efficiency and economy. Li et al. [17] proposed a fault-tolerant control strategy for energy allocation and considered the global switching sequence calculation in an MFCS, resulting in lower hydrogen consumption and a longer service life. Wang et al. [7] proposed a co-optimized power allocation strategy based on the maximum efficiency range, which aims to improve the efficiency and economy of multi-stack fuel cell systems at different altitudes. Ghaderi et al. [18] used a cooperative independent Q-learning algorithm for energy management of vehicles with multi-stack fuel cell systems, defined a comprehensive reward function including hydrogen consumption and degradation, and demonstrated its superior performance relative to other online strategies. Shi et al. [19] used a multi-agent reinforcement learning method for energy management of multi-stack fuel cell hybrid vehicles and transplanted the method to an actual controller for online operation.

In summary, MFCSs offer the practicality of a longer service life, energy efficiency, and economy in high-power application scenarios. However, the above advantages are not only due to the deployment of the energy management strategy of the MFCS but are also reflected in the optimization of the system architecture. Integrated multi-stack fuel cell subsystems with better distribution and fewer components have less parasitic power. These are key issues that must be considered for subsystem framework design and stack rated power selection in the development of an MFCS, and the above literature has apparently not focused on this point. This paper focuses on the optimization of an MFCS, subsystem structure, and PEM fuel cell rated power based on the optimal stack allocation approach and integrated configuration system simulation. First, the rated power of each fuel cell stack is determined based on the optimal stack division method; then, the functional components added to each subsystem in the MFCS are introduced; and, finally, the MFCS structure is optimally designed and simulated.

2. Approach for Optimal Allocation of MFCS

The approach for optimal allocation of the MFCS consists of the following steps: (1) selecting the upper-level target of the power system, (2) selecting the operating conditions and allocating the MFCS demand power according to the first-level energy management strategy, (3) determining the PEM fuel cell characteristic parameters, and (4) selecting the optimization objective and method for allocating the rated power of each stack.

2.1. Target Selection

In this paper, the selected target is a heavy commercial vehicle application in a high-power application scenario. Its power system adopts a power output mode combining a PEM fuel cell system and an auxiliary power battery. The dynamics parameters are shown in Table 1.

Based on historical vehicle driving data, the power demand and changes in different application scenarios and working conditions are very different. This paper takes the China-World Transient Vehicle Cycle (CWTVC) conditions as the prerequisite for optimal MFCS stack allocation, as shown in Figure 1.

The optimal allocation of stacks for MFCS requires the relevant parameters of the PEM fuel cell, and in this paper, the parameters of the 70 kW PEM fuel cell system in the Tongji-Refire Joint Laboratory are used to optimize the split stacks. The objects’ response times in the PEM fuel cell system according to the experimental testbench data are shown in Table 2, which are also used in the MFCS simulation.

2.2. Approach for Optimal Allocation

The selected target maximum demand power depends on the drive motor, which can be calculated to be 400 kW according to the vehicle balance equation. The MFCS power supply ratio and conversion efficiency are set to be 0.5 and 0.95, respectively. Based on this, the MFCS power rating can be calculated to be 210 kW.

To allocate all stack power in the MFCS, it is necessary to determine the influencing factors and constraints, which can be converted into an optimization problem to solve. The influencing factors and constraints considered in this paper include the number of stacks, the range of power ratings for each stack, the efficiency and lifetime of the stacks, and the power allocation strategy. The solution required for optimal allocation is an optimization model with a two-level objective function, which can be formulated as

\begin{array}{l} J_{o}^{\max} = \sum_{i = 1}^{end} \frac{t_{i}}{t_{end}} (α η_{MFCS} ({\bar{P}}_{fc_i}) + β {RUL}_{MFCS} ({\bar{P}}_{fc_i})) \\ s . t . \{\begin{cases} η_{MFCS} ({\bar{P}}_{fc_i}) = \frac{{\bar{P}}_{fc_i}}{\sum_{i = 1}^{n} \frac{P_{fc_i}}{η (P_{fc_i})}} \\ {RUL}_{MFCS} ({\bar{P}}_{fc_i}) = \min RUL (P_{fc_i}) \\ α + β = 1 \\ P_{fc_i}^{\min} \leq P_{fc_i} \leq P_{fc_i}^{\max} \\ \sum_{i = 1}^{n} P_{fc_i} = P_{MFCS_d} \\ Δ P_{low} \leq \sum_{i = 1}^{n} P_{fc_i}^{\max} - P_{MFCS_d}^{\max} \leq Δ P_{high} \end{cases} \end{array},

(1)

where

J_{o}^{\max}

denotes the optimal solution objective;

{\bar{P}}_{fc_i}

denotes the real-time output power of the ith stack; α and β denote the weights of the MFCS efficiency and RUL, respectively; η_MFCS and RUL_MFCS denote the efficiency and remaining useful life of the MFCS, respectively;

P_{fc_i}

denotes the demanded power of the ith stack;

P_{fc_i}^{\min}

denotes the minimum rated power;

P_{fc_i}^{\max}

denotes the maximum rated power; ΔP_high and ΔP_low denote the upper and lower bounds of the MFCS rated power, respectively; and

P_{MFCS_d}^{\max}

is the rated power of the MFCS.

For the optimal allocation scheme shown in Figure 2, a two-layer objective function is solved. The outer-layer optimization model adopts a genetic algorithm (GA) to solve the optimal stacking scheme based on the power demand determined by the MFCS on the basis of the first-level energy management strategy. The inner-layer optimization model uses sequential quadratic programming (SQP) algorithm to determine the optimal solution for the power demand allocated to each PEM fuel cell.

According to the above process, the number of PEM fuel cells is taken as 2 to 4, and the number of stack combinations is 100. When the number of PEM fuel cells is 2, there is no optimal solution; when the number of PEM fuel cells is 3, the optimal stack solution is 20/70/120 kW; and when the number of stacks is 4, the optimal stack solution is 10/10/70/120 kW. Compared with the optimal stack solution for 3 stacks, the target value of the stack solution for 4 stacks is not greatly improved, but the cost increases. Therefore, this research selects the 20/70/120 kW stack solution.

3. MFCS Model

Different structures of the MFCS have different impacts on the output performance and energy consumption of the system. In Section 2, the MFCS basic framework is established based on the optimal allocation stack method. In this section, the MFCS model is established, including the model of the PEM fuel cell stack, air supply subsystem, hydrogen supply subsystem, and thermal subsystem. The MFCS model structure is shown in Figure 3. The MFCS adopts a feed-forward + PID control strategy. The following assumptions are made in the modelling of the MFCS: (1) Gases are regarded as ideal gases and stable flows. (2) The gas pressure in the flow channel is uniformly distributed in the radial direction. (3) Each single PEM fuel cell maintains consistency. (4) The pressure in the common rail is equal everywhere, and the volume of the common rail remains constant during operation. (5) There is no leakage of fluid anywhere.

3.1. PEM Fuel Cell Stack

PEM fuel cell models of 20 kW, 70 kW, and 120 kW are obtained by fitting based on data from a 70 kW fuel cell system. The effective area of a single cell is 280 cm², and the number of cells is 130, 440, and 750, respectively. The PEM fuel cell outputs electrical energy, which can be simplified to an equivalent circuit model consisting of multiple resistors and capacitors connected in series or in parallel. The output voltage of a single cell can be expressed as

\begin{array}{l} V_{cell} = E_{cell} - V_{act} - V_{ohm} - V_{conc} \\ s . t . \{\begin{matrix} E_{cell} = 1.229 - 8.5 \times 10^{- 4} (T_{st} - 298) + \\ 4.308 \times 10^{- 5} T_{st} (\ln \frac{p_{H_{2}}}{1.013} + \frac{1}{2} \ln \frac{p_{O_{2}}}{1.013}) \\ V_{act} = V_{0} + V_{a} (1 - e^{- C_{1} \cdot i}) \\ V_{ohm} = I R_{ohm} \\ V_{conc} = m \exp C_{2} i \end{matrix} \end{array},

(2)

where V_cell denotes the single-cell output voltage; E_cell denotes the single-cell reversible potential, which is a temperature-dependent function; T_st denotes the PEM fuel cell temperature;

p_{H_{2}}

and

p_{O_{2}}

denote the pressure of hydrogen on the anode channel and oxygen on the cathode channel, respectively; V_act denotes the activation voltage drop; V₀ and V_a are related to the fuel cell stack temperature and the cathode oxygen pressure, respectively; i denotes the current density; V_ohm denotes the ohmic voltage drop; R_ohm denotes the resistance of the PEM fuel cell; V_conc denotes the concentration voltage drop; m denotes an empirical parameter that is negatively correlated with stack temperature; and C₁ and C₂ are data-based fitting constants.

There is transmembrane transport of liquid and nitrogen within the PEM fuel cell. Transmembrane transport of liquid is classified as proton electrical drag, concentration diffusion, and pressure diffusion. Transmembrane transport of nitrogen is caused by concentration diffusion.

The mass flow rate of liquid water transmembrane transport in a single PEM fuel cell can be expressed as

\begin{array}{l} {\dot{m}}_{liquid} = (N_{liq, diff} - N_{liq, drag}) \times M_{liq} \times A_{mem} \\ s . t . \{\begin{cases} N_{liq, diff} = D_{liq} \frac{c_{v, ca} - c_{v, an}}{l_{mem}} \\ N_{liq, drag} = n_{d} \frac{i}{F} \end{cases} \end{array},

(3)

where N_liq,diff denotes the liquid molar flow rate of the concentration diffusion; D_liq denotes the liquid diffusion coefficient; c_v,ca and c_v,an denote the liquid water concentration on the PEM surface of the cathode and anode, respectively; l_mem denotes the PEM thickness; N_liq,drag denotes the liquid molar flow rate of the proton electrical drag; n_d denotes the proton electric drag coefficient; F denotes a Faraday constant; M_liq denotes the molar mass of H₂O; and A_mem denotes the effective PEM area. The liquid pressure diffusion is of a very small order of magnitude, and this phenomenon is ignored when calculating transmembrane transport of liquid.

According to Fick’s law, the mass flow rate of nitrogen that is transported across the membrane into the anode flow channel can be expressed as

{\dot{m}}_{N_{2}, mem} = M_{N_{2}} k_{N_{2}} \times \frac{Δ p_{N_{2}} \times A_{mem} \times l_{mem}}{R T_{st}},

(4)

where

M_{N_{2}}

denotes the nitrogen molar mass,

k_{N_{2}}

denotes the nitrogen diffusion coefficient,

Δ p_{N_{2}}

denotes the nitrogen pressure difference between the cathode and anode, and R denotes the gas constant.

3.2. Air Supply Subsystem

The MFCS air supply subsystem is made up of an air filter, air compressor, hand valve, intercooler, common rail buffer, proportional valve, humidifier, and backpressure valve, with the functions of air supply and discharge, as shown in Figure 3.

For the MFCS, the air compressor is different from an SFCS and needs to satisfy the demands of three stacks at the same time. In previous studies [20], the advantages and disadvantages of several types of air compressors for SFCSs and MFCSs were compared, and a reciprocating piston air compressor was selected in this paper. The function of the intercooler is to cool the high-temperature air that has been compressed by the air compressor so that it is within a reasonable temperature range for the electrochemical reaction.

The common rail buffer is inspired by the common rail technology for the engines of fuel vehicles [21] and is designed for the MFCS air supply subsystem under the integrated optimized stacking method to provide the case of one device supplying multiple fuel cell stacks, which can use one set of pressurized air supply equipment and an intercooler to complete the supply of air to the cathode side of multiple fuel cell stacks. In addition to solving the problem of air supply for one set of multiple fuel cell stacks, the common rail buffer is designed to store a certain amount of air to supplement the air supply in case of an air supply shortage from the air compressor or to serve as a buffer in case of a large variable load.

For high-power PEM fuel cell systems, the cathode exhaust gas usually contains a large amount of water vapor, which can be recycled for thermal mass recovery and humidification of the cathode into the stack air. A humidifier model is established considering the characteristics of the high-power output of the MFCS, and a gas–gas humidifier is selected as the air humidification equipment.

3.3. Hydrogen Supply Subsystem

As shown in Figure 3, the MFCS hydrogen supply subsystem consists of a hydrogen tank, hand valve, pressure-reducing valve components, ejector, proportional valve, common rail, and hydrogen circulation pump, with the functions of hydrogen supply and circulation. The common rail includes an inlet common rail and outlet common rail. The function of the inlet common rail is to ensure the stability of the different stack inlet pressures, which is referenced to the high-pressure common rail technology [22]. The function of the out common rail is to ensure the same circulating pressure because only one hydrogen-circulating pump is set up.

An active hydrogen circulation pump and passive ejector are used as hydrogen circulation equipment for hydrogen circulation. During the circulation of anode exhaust gas, the anode channel pressure is stabilized by a hydrogen discharge valve, while the transmembrane transport of nitrogen is considered to ensure the hydrogen concentration. For the MFCS hydrogen supply subsystem, the rate of hydrogen utilization is an interest point in hydrogen circulation. The PEM fuel cell hydrogen cycle diagram is shown in Figure 4. x₁, x₂, x₃, x₄, and x₅ denote the hydrogen discharged from the hydrogen tank, the hydrogen involved in electrochemical reactions, the hydrogen discharged from PEM fuel cells, the hydrogen recycled from the ejector and hydrogen-circulating pump, and the hydrogen discharged from the discharge valve, respectively.

\{\begin{cases} x_{1} + x_{4} = λ_{H_{2}} \cdot x_{2} \\ x_{3} = x_{1} + x_{4} - x_{2} \\ x_{4} = k_{H_{2}} \cdot x_{3} \\ x_{5} = x_{3} - x_{4} = (1 - k_{H_{2}}) \cdot x_{3} \end{cases},

(5)

where

λ_{H_{2}}

denotes the excess coefficient of hydrogen,

k_{H_{2}}

denotes the circulation factor for hydrogen, and x₂ can be calculated according to the load current and Faraday’s equation.

Then, the real-time hydrogen utilization is the ratio of the current electrochemically reacted hydrogen to the current inlet gas from the hydrogen tank, and it can be expressed as

η_{H_{2}} = \frac{x_{2}}{x_{1}} = \frac{1}{λ_{H_{2}} (1 - k_{H_{2}}) + k_{H_{2}}},

(6)

where

η_{H_{2}}

denotes the real-time hydrogen utilization. Of course, the utilization rate does not consider the parasitic power used during hydrogen circulation.

3.4. Thermal Subsystem

Components of the MFCS thermal subsystem include a coolant tank, coolant circulation pump, diverter valve, intercooler, mixer, deionizer, thermostat, radiator, and bypass valve; the purpose of the intercooler is to service the air supply subsystem. The thermal subsystem structure of the MFCS is shown in Figure 3, which ensures that the PEM fuel cell operates at a reasonable temperature. With a structure different from that of the SFCS thermal subsystem, the MFCS thermal subsystem established in this study is equipped with a diverter valve and a mixer so that the MFCS thermal subsystem achieves the thermal management of multiple stacks using a piece of the coolant supply and circulation system.

The purpose of the MFCS thermal subsystem is to discharge the excess heat generated during the electrochemical reaction through cooling circulation in order to ensure the constant operating temperature of the PEM fuel cell. The main reason for the change of the PEM fuel cell stack temperature is the change of heat in the stack, which can be expressed as

{\dot{Q}}_{st} = {\dot{Q}}_{total} - {\dot{Q}}_{conv_nat} - {\dot{Q}}_{rad} - {\dot{Q}}_{conv_force},

(7)

where

{\dot{Q}}_{st}

denotes heat change of the stack,

{\dot{Q}}_{total}

denotes total heat production of the stack,

{\dot{Q}}_{conv_nat}

denotes natural convective heat change,

{\dot{Q}}_{rad}

denotes radiant heat change, and

{\dot{Q}}_{conv_force}

denotes forced convective heat change.

The change in heat causes a change in the temperature of the PEM fuel cell stack,

\frac{d T_{st}}{d t} = \frac{{\dot{Q}}_{st}}{c_{st} m_{st}},

(8)

where c_st denotes the average specific heat capacity of the PEM fuel cell stack; m_st denotes the mass of the PEM fuel cell stacks (29, 100, and 172 kg for 20 kW, 70 kW, and 120 kW stacks, respectively).

Heat generated by the electrochemical reaction of the PEM fuel cell is carried out by forced convective heat change of the coolant. The radiator is required to dissipate the heat of the circulating coolant. For the modelling of the MFCS thermal subsystem, an air-cooled radiator is selected, and the MAP of the radiator’s calibration relationship under standard temperature conditions is shown in Figure 5.

Changes of ambient temperature during actual MFCS operation would affect the heat dissipation, so real-time correction of heat dissipation is required. The actual heat dissipation by the radiator can be expressed as follows:

{\dot{Q}}_{rad}^{'} = {\dot{Q}}_{rad} (\frac{T_{coolant_out} - T_{amb}}{60}),

(9)

where

{\dot{Q}}_{rad}^{'}

denotes the actual heat dissipation,

T_{coolant_out}

denotes the coolant temperature at the outlet from the mixer, and

T_{amb}

denotes the ambient temperature.

4. Results and Discussion

As shown in Figure 6, the polarization curve of the PEM fuel cell in the MFCS model established in this paper is in good accordance with the experimental data from the established 70 kW fuel cell test bench. The simulation results are verified with experimental data to ensure the accuracy of the established MFCS model.

Figure 7 shows the parameter variation of the MFCS under the step current. The MFCS exhibits a good dynamic response, as reflected by the response of the voltage of the stack, air mass flow, and pressure.

In contrast to the air supply subsystem of the SFCS, there is a common rail buffer in the MFCS. As shown in Figure 8, the volume of the common rail buffer affects the MFCS performance in terms of the maximum pressure drop, maximum power, and total power consumption. The relationship between the maximum pressure drop (Max PD) and the volume of the common rail buffer is shown in Figure 8a, where the maximum pressure drop decreases rapidly with the volume from 50 L to 200 L and then slows down. Figure 8b shows the relationship between the maximum power of the air compressor and the volume of the common rail buffer. It can be seen that as the volume of the common rail buffer increases, the maximum required power of the air compressor decreases gradually. However, when the volume of the common rail buffer reaches 200 L, the maximum power of the air compressor remains constant. As shown in Figure 8c, the power consumption of the air supply subsystem under the CWTVC condition gradually decreases as the volume of the common rail buffer increases. When the volume increases from 50 L to 150 L, the power consumption decreases significantly. Then, when the volume increases from 150 L to 600 L, the power consumption still decreases slowly. After that, the power consumption almost does not change with the increase in the common rail buffer volume. In the air supply subsystem, the common rail buffer plays the role of storing and stabilizing the air pressure; when the pressure and flow rate fluctuations are large, the buffer can absorb and stabilize these fluctuations. Within a certain volume range, the buffer tank is able to better stabilize the air pressure fluctuations in the subsystem, with a significant gain effect. However, as the volume increases further, although the buffer tank is better able to absorb and stabilize air pressure fluctuations, the gain effect is reduced. Therefore, the reduction in maximum pressure drop and power consumption slows down. Obviously, a common rail buffer tank volume of 200 L is a good choice for a 210 kW MFCS.

After determining the volume of the common rail buffer, it is important to observe the internal pressure under the CWTVC condition to ensure that the pressure is always greater than the air inlet pressure of the three stacks. The variation of pressure in the common rail buffer under the CWTVC condition is shown in Figure 9. The pressure of the common rail buffer adopts a constant pressure control strategy with a set pressure of 2.75 bar. An air pressure of 2.64 bar at 1283 s is the minimum instantaneous pressure in the common rail buffer under the CWTVC condition, which satisfies the maximum of cathode inlet pressure.

Since the hydrogen subsystem delivers hydrogen that is in the process of depressurization from the high-pressure hydrogen storage tank to the PEM fuel cell, the pressure setting of the hydrogen inlet common rail can be set without considering the energy consumption. The pressure in the hydrogen inlet common rail under CWTVC conditions is shown in Figure 10. The role of the hydrogen inlet common rail is to provide a certain buffer space and time for the hydrogen entering into the stack so that the release of hydrogen from the high-pressure hydrogen storage tank does not have to completely follow the system demand.

In Figure 11, the anode inlet pressures of 20, 70, and 120 kW stacks are compared between the integrated hydrogen circulation structure with an inlet common rail and the distributed hydrogen circulation structure under the CWTVC condition. As shown in Figure 11a–c, the pressure overshoot of the distributed hydrogen supply subsystems gradually increases with the increase in the stack power when the load changes, while the pressure of the integrated hydrogen supply subsystem can keep up with the variation of demand pressure. In addition, distributed hydrogen supply subsystems require three hydrogen recirculation pumps for exhaust gas circulation, whereas integrated hydrogen supply subsystems require only one hydrogen recirculation pump for this function. Under the CWTVC condition, distributed hydrogen subsystems consume 2030 kJ to complete gas circulation, whereas the integrated hydrogen subsystem consumes only 1715 kJ.

In contrast to the air supply subsystem, the hydrogen supply subsystem needs to circulate the anode outlet gas, which requires attention to the hydrogen concentration in view of the transmembrane transport of nitrogen. The variation of nitrogen concentration in anode channels of the 20, 70, and 120 kW stacks is presented under the CWTVC condition in Figure 12. Under the same power allocation strategy, the nitrogen concentration of the distributed hydrogen supply subsystem quickly reaches the set value of 1%, after which the hydrogen discharge valve is frequently operated to discharge nitrogen, and the time for the nitrogen concentration to reach the set value is gradually delayed with the increase in the stack power level and different power allocations. However, the nitrogen concentration in the integrated hydrogen supply subsystem reaches the set value of 1% only in the 20 kW stack, mainly due to the circulation of hydrogen throughout the anode pipeline and the fresh inlet hydrogen from the hydrogen tanks, which dilutes the nitrogen concentration in the anode channels. This phenomenon leading to a lower concentration of nitrogen is not necessarily an advantage, as it contaminates the anode inlet pipeline, making the hydrogen utilization less efficient, which can be explained by the previously mentioned Equation (6).

For the integrated thermal subsystem, the coolant circulation affects the three stacks differently. The stable temperature of stacks at a load current of 100 A is shown in Figure 13. Figure 13a shows the relationship between inlet coolant temperature and PEM fuel cell steady-state temperature. Figure 13b,c show the stabilization time and stabilization temperature for three stacks at coolant temperatures of 333 K and 338 K, respectively. Figure 13d shows the relationship between the mass flow rate of coolant and the stabilization temperature of the three stacks. The reason for the conditions is the different masses of the three stacks and the different heat productions at the same current.

The integrated thermal subsystem could result in the heat production of stacks, affecting the temperature of the other stacks. In Figure 14, the variations in the temperature are compared for three stacks, where the load current is changed from 100 A to 150 A at 475 s for each of the three stacks under a radiator fan speed of 1500 rpm and a coolant circulation pump speed of 2000 rpm. As the stack power level increases, an abrupt change in the load of the stack results in a gradual increase in its temperature, as well as that of other stacks. Although they are all boosted by the same current, the high-power-rated stack produces more heat, and the heat varies more at the determined circulating pump speeds and the fan speed of the radiator.

In Figure 15, the stack temperature variations of the integrated and distributed thermal subsystems are compared under the CWTVC condition. With the increase in stack power level, the residual difference in stack temperature of integrated and distributed thermal management subsystems decreases. Comparing the integrated and distributed thermal subsystems, the residual of the stack temperature decreases with the increase in the stack power level. The reason is that the distributed thermal management subsystem becomes less effective in managing the temperature of a high-power fuel cell stack, resulting in an increase in the range of stack temperature fluctuations. Distributed subsystems have advantages over integrated subsystems in terms of thermal management performance, but distributed subsystems require more radiators and power circulation equipment for the coolant. On the other hand, in combination with the results presented in Figure 14, the integrated thermal subsystem possesses advantages in terms of cold start, since it is more closely coupled between the coolant circulation pipelines of different stacks.

5. Conclusions

In this work, the optimal allocation of power stacks to an MFCS is determined out based on the lifetime efficiency factor of the fuel cell. For the determined power stacks of the MFCS, integrated subsystem solutions are proposed, including a hydrogen subsystem, an air subsystem, and a thermal management subsystem. The proposed integrated subsystems are specified as follows:

(1): A common rail buffer is added to the integrated air supply subsystem, the function of which is to isolate the air compressor from the fuel cell air demand, providing a degree of buffering and pressure stabilization. It is of interest to note that the volume of the common rail buffer has an impact on the maximum power and energy consumption of the air compressor in the air supply subsystem, as well as the maximum pressure drop of the common rail buffer itself. From the results, it can be concluded that for the 210 kW MFCS, the volume of the common rail buffer chosen as 200 L is an optimal solution and that the choice of compressor power can be varied.
(2): In the hydrogen integration supply subsystem, an inlet common rail is added at the anode inlet to stabilize pressure, divert flows, and isolate demands, and an outlet common rail is added at the anode outlet to converge and circulate the gases. This realizes hydrogen supply and exhaust gas circulation for multiple stacks using one hydrogen supply and circulation system. In addition, the integrated hydrogen supply subsystem improves hydrogen utilization and reduces parasitic power.
(3): Compared to the distributed thermal subsystem, the integrated thermal subsystem has no advantage in thermal management performance—only in structure. The integrated thermal subsystem possesses advantages in terms of cold start, since this structure is more closely coupled between the coolant circulation pipelines of different stacks.

Author Contributions

Conceptualization, J.G. and S.Z.; methodology, J.G.; software, J.G. and Y.L.; validation, J.G. and Y.L.; formal analysis, J.G.; investigation, J.G. and Y.L.; resources, S.Z.; data curation, J.G.; writing—original draft preparation, J.G.; writing—review and editing, W.S. and S.Z.; visualization, J.G. and Y.L.; supervision, S.Z.; project administration, S.Z.; funding acquisition, W.S. and S.Z. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The data presented in this study are available upon request from the corresponding author.

Acknowledgments

This work was supported by Shanghai TXJS Engineering Technology Co., Ltd., Shanghai REFIRE Technology Co., Ltd. and AVL-List Gmbh.

Conflicts of Interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as potential conflicts of interest. There is no copyright issue associated with any of the figures.

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Figure 1. CWTVC condition.

Figure 2. Flowchart of the optimal allocation approach.

Figure 3. MFCS structure.

Figure 4. PEM fuel cell hydrogen cycle diagram.

Figure 5. Radiator MAP diagram.

Figure 6. MFCS model validation.

Figure 7. Dynamic response of MFCS parameters: (a) Current; (b) Voltage; (c) Mass flow; (d) Inlet pressure.

Figure 8. Impact of common rail buffer volume on air supply subsystem: (a) Maximum pressure drop; (b) Maximum power; (c) Energy consumption.

Figure 9. The air pressure in the common rail buffer under the CWTVC condition.

Figure 10. The pressure in the hydrogen inlet common rail under the CWTVC condition.

Figure 11. The anode inlet pressure under the CWTVC condition: (a) 20 kW; (b) 70 kW; (c) 120 kW.

Figure 12. The variation of nitrogen concentration in anode channels under the CWTVC condition: (a) 20 kW; (b) 70 kW; (c) 120 kW.

Figure 13. Effects of thermal subsystems on stack temperature: (a) Relationship between coolant temperature and steady state temperature of stacks; (b,c) The stabilization time and stabilization temperature for stacks at coolant temperatures of 333 K and 338 K; (d) Relationship between the mass flow rate of coolant and the stabilization temperature.

Figure 14. Correlation effects of different stacks in the integrated thermal subsystem: (a) 20 kW; (b) 70 kW; (c) 120 kW.

Figure 15. Temperature variation comparisons of the integrated and distributed thermal subsystems under the CWTVC condition: (a) 20 kW; (b) 70 kW; (c) 120 kW.

Table 1. Target dynamics parameters.

	Parameter	Value
Vehicle Parameters	Unladen mass (t)	13
	Full load mass (t)	30
	Rotating mass factor	1.1
	Travelling resistance coefficient	0.01
	Wheel rolling radius (m)	0.39
	Number of wheels	12
	Air resistance coefficient	0.75
	Windward area (m²)	7
	Deceleration ratio	3.8
Dynamics Indicators	Maximum speed (km/h)	100
	Maximum climbing gradient (%)	>30
	0–50 km/h acceleration time (s)	<15

Table 2. Target dynamics parameters.

Object	Response Time Scale
Electrochemical reaction	10^–19 s
Gas supply pipe	10^–1 s
Membrane water content	10⁰ s
Air compressor	10⁰ s
Coolant fluid	10⁰ s
Stack temperature	10² s

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Gao, J.; Zhou, S.; Lu, Y.; Shen, W. Simulation of a Novel Integrated Multi-Stack Fuel Cell System Based on a Double-Layer Multi-Objective Optimal Allocation Approach. Appl. Sci. 2024, 14, 2961. https://doi.org/10.3390/app14072961

AMA Style

Gao J, Zhou S, Lu Y, Shen W. Simulation of a Novel Integrated Multi-Stack Fuel Cell System Based on a Double-Layer Multi-Objective Optimal Allocation Approach. Applied Sciences. 2024; 14(7):2961. https://doi.org/10.3390/app14072961

Chicago/Turabian Style

Gao, Jianhua, Su Zhou, Yanda Lu, and Wei Shen. 2024. "Simulation of a Novel Integrated Multi-Stack Fuel Cell System Based on a Double-Layer Multi-Objective Optimal Allocation Approach" Applied Sciences 14, no. 7: 2961. https://doi.org/10.3390/app14072961

APA Style

Gao, J., Zhou, S., Lu, Y., & Shen, W. (2024). Simulation of a Novel Integrated Multi-Stack Fuel Cell System Based on a Double-Layer Multi-Objective Optimal Allocation Approach. Applied Sciences, 14(7), 2961. https://doi.org/10.3390/app14072961

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Simulation of a Novel Integrated Multi-Stack Fuel Cell System Based on a Double-Layer Multi-Objective Optimal Allocation Approach

Abstract

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Abstract

1. Introduction

2. Approach for Optimal Allocation of MFCS

2.1. Target Selection

2.2. Approach for Optimal Allocation

3. MFCS Model

3.1. PEM Fuel Cell Stack

3.2. Air Supply Subsystem

3.3. Hydrogen Supply Subsystem

3.4. Thermal Subsystem

4. Results and Discussion

5. Conclusions

Author Contributions

Funding

Institutional Review Board Statement

Informed Consent Statement

Data Availability Statement

Acknowledgments

Conflicts of Interest

References

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