Efficient waste heat utilization in high-temperature proton exchange membrane fuel cell bus through integration of lithium bromide absorption refrigeration

Abstract

Compression-type air-conditioning heat pump systems used in high-temperature proton exchange membrane fuel cell (HT-PEMFC) buses significantly increase the vehicle's hydrogen consumption. This study introduces a lithium bromide (LiBr) absorption refrigeration air-conditioning system into a fuel cell bus, aiming to convert the high-quality waste heat produced by the HT-PEMFC into cooling and heating capabilities for balancing the temperature within the vehicle cabin and recover waste heat. Modeling and co-simulation of the HT-PEMFC, LiBr absorption refrigeration system, vehicle thermal model, and compression-type air-conditioning heat pump system were conducted using MATLAB/Simulink. The simulation results indicate that, compared with the traditional compression-type air-conditioning heat pump system, the LiBr absorption refrigeration system can save 6.13–18.17 % of hydrogen and improve the electrical energy and exergy efficiencies by 3.58–10.74 % and 3.74–11.22 %, respectively, under different driving scenarios. Using the LiBr absorption refrigeration system significantly enhances the vehicle's overall fuel utilization efficiency and driving range.

1. Introduction

Recently, the greenhouse effect caused by carbon emissions from fossil fuels and air pollution has garnered widespread attention. Many countries have established various goals for low-carbon development to reduce carbon emissions [1,2]. High-temperature proton exchange membrane fuel cells (HT-PEMFCs) are considered one of the best energy devices for electric vehicles and the aviation industry owing to their rapid start-up time, high power density, environmental friendliness, and simple structure [3,4].

HT-PEMFCs utilize a high-temperature-resistant phosphoric acid-doped polybenzimidazole membrane to operate at temperatures between 120 °C and 200 °C [5]. A higher operating temperature enhances the reaction kinetics, leading to higher efficiency of the fuel cell stack [6]. Furthermore, it restricts the formation of liquid water and reaction of platinum catalyst with CO [7,8], resulting in simpler thermal management [9] and excellent CO tolerance (<1 %) [10]. Balyat et al. [11] studied the working temperature, inlet pressure, relative humidity, and membrane thickness of HT-PEMFCs and found that as the operating temperature increased from 448 K to 453 K and 473 K, the fuel cell stack efficiency at the maximum power point increased by 6.7 % and 39.71 %, respectively. With increasing current density, the energy efficiency of the fuel cell stack decreased from 63.75 % to 25.56 %, indicating that substantial heat was generated during the HT-PEMFC operation. Research has shown that fully exploiting this heat can significantly improve the hydrogen utilization efficiency [12]. Various methods are available for recycling heat [13], such as vapor absorption systems [14,15], vapor ejector cycles [16], vapor adsorption systems [17], and metal hydride systems [18]. Among them, the absorption cycle has the highest efficiency and is considered the optimal method for heat recovery. Javani et al. [19] analyzed an ejector cooling cycle and lithium bromide (LiBr)/H2O absorption cooling cycle. For a waste heat power of 15.4 kW, the cooling capacities produced by the two cycles were 7.23 kW and 7.93 kW, with coefficients of performance (COPs) of 0.48 and 0.53, respectively. The results indicate that the LiBr/H2O absorption refrigeration (LBAR) system is more efficient in utilizing waste heat. Liang et al. [20] innovatively proposed integrating an HT-PEMFC with a compression-assisted absorption heat pump. They reported that a reasonable increase in compression ratio could enhance the entropy efficiency and performance coefficient. Guo et al. [21] introduced a comprehensive waste heat recovery system model encompassing an HT-PEMFC, a regenerator, and an absorption cycle. In this system, the absorption cycle serves as a heat pump for heating and refrigerator for cooling, resulting in remarkable power density increases of 33.41 % and 19.34 % in the heating and cooling modes, respectively. Arsalis et al. [22] integrated a 100 kW HT-PEMFC with absorption cooling equipment, efficiently absorbing 107 kW of waste heat through an H₂O/LiBr double-effect absorption system and an NH₃/H2O single-effect absorption system, yielding cooling capacities of 128 kW and 64.5 kW, respectively. Ma et al. [23] proposed a double-effect absorption heating/cooling cogeneration cycle system, achieving decoupling of power production and heating/cooling by allocating the steam ratio between the turbine and evaporator. In the cooling mode, the system achieved a modulation range of 17.78–137.55 kW, resulting in an overall efficiency improvement of 5.9–25.2 % compared with a single HT-PEMFC system. Wu et al. [24] integrated an HT-PEMFC with a hybrid-energy heat pump, allowing seamless switching between a single-effect absorption heat pump and an absorption-compression hybrid heat pump. Impressively, the system provided cooling temperatures ranging from −10 to 10 °C and heating temperatures from 40 °C to 60 °C in both modes, accompanied by noteworthy power density increases of 18.5 % and 54.8 %, respectively. Ma et al. [25] introduced a PEMFC-based combined cooling, heating, and power system to enhance the efficiency through cascade utilization of waste heat. Employing electrochemical and thermodynamic models, their research demonstrated significant improvements in system performance under various operational settings. The study highlighted increases in equivalent power density from 59.4 kW to 211.5 kW as the operating current density of the PEMFC rose from 0.2 A/cm² to 1.0 A/cm². In contrast, the exergy efficiency decreased from 0.689 to 0.491. The results underscore the system's capability to improve energy recovery, substantially reduce fossil fuel consumption by up to 22.6 %, and lower carbon emissions, offering robust evidence for the advantages of integrating cooling, heating, and power systems in the transition to low-carbon energy sources.

For fuel cell vehicles, ensuring passenger comfort is of utmost importance. Currently, electrically driven compression-type air-conditioning heat pump (CACHP) systems are widely adopted in fuel cell vehicles. These systems utilize the thermodynamic properties of the working fluid to enable cooling and heating of electric vehicles using an air compressor. However, CACHP systems consume significant additional power [26]. Pino et al. [27] indicated that using CACHP systems increases the hydrogen consumption in fuel cell vehicles by 12 %, significantly reducing the vehicle's driving range. To minimize the additional hydrogen consumption of the fuel cell vehicle's air-conditioning system, many scholars have studied the possibility of using an absorption refrigeration system (ARS) to replace the onboard compression heat pump air-conditioning system. This approach makes full use of the waste heat generated during fuel cell operation to provide a comfortable cabin temperature for passengers. Helm et al. [28] investigated the thermodynamic performance of fuel cell vehicles with a LiBr/H₂O absorption–compression hybrid refrigeration system. The results show that heat can be fully utilized when the generator's hot water temperature reaches 80 °C. However, this hybrid system still requires some vehicle power to drive the compressor. George et al. [29] investigated the potential of using low-grade waste heat from the exhaust of hybrid electric vehicles to power a LiBr/H2O absorption cooling system for cabin air conditioning. By converting waste heat into useful cooling energy, this system achieved a COP of 0.721, demonstrating an innovative approach for improving fuel efficiency and vehicle performance. Li et al. [30] combined an ARS with a fuel cell using a novel working fluid, LiBr-[BMIM]Br/C₂H₅OH, which lowered the generator's operating temperature. The overall efficiency of the fuel cell-ARS coupled system reached 85 %. Wu et al. [31] proposed a microchannel membrane-based absorption cooling system and applied it to fuel cell vehicles, achieving an efficiency improvement of 11.4–14.8 %. The cooling-to-electrical ratio of this integrated system ranges from 2.02 to 2.73, with a cooling power density of 129.4–345.9 kW/m3 and cooling power per unit mass of 0.0439–0.1132 kW/kg. However, the above research only analyzed the integration of fuel cells and ARSs without fully considering the dynamic nature of the vehicle's cooling and heating requirements under different operating conditions.

Owing to their long operating hours and rapid refueling capabilities, hydrogen fuel cell buses have considerable potential as alternatives to internal combustion and pure electric buses. Long-distance buses have large volumes and high passenger capacities, requiring significant power for their air-conditioning systems because of the spacious passenger cabins. This substantially impacts the fuel economy of fuel cell buses [32]. At the same time, the fuel cell systems of buses usually have high working power, leading to a large amount of energy being lost as heat. Current research mainly focuses on the control strategy for heating, ventilation, air-conditioning, and cooling systems [32,33] and integrated thermal management system of the entire vehicle [34,35]. However, there has been relatively limited research on utilizing waste heat from fuel cell stacks for absorption cooling while considering the cabin thermodynamic load and impact of vehicle dynamic characteristics. Therefore, this study evaluates the fuel economy of a LBAR system and compares it with that of a CACHP system under different driving cycles. It aims to provide a scientific reference for improving the overall efficiency of long-distance hydrogen fuel cell buses.

Section 1 reviews the current status of waste heat utilization of HT-PEMFC and the previous attempts to apply this cogeneration system to the automotive field. Section 2 will establish a whole vehicle dynamics model, detailed model of HT-PEMFC, LBAR system, vehicle cabin thermodynamic model, and CACHP system. In Section 3, the simulation settings and corresponding simulation cases are introduced. Section 4 will discuss and analyze the simulation results in detail. Finally, in Section 5, the research content will be comprehensively summarized, and future possible research directions will be given.

2. Modeling methodology

The arrangement of the fuel cell bus system devices are illustrated in Fig. 1. The vehicle is equipped with two power sources: HT-PEMFC and battery. Both power sources are connected to the high-voltage bus through DC/DC converters. The vehicle's powertrain system integrates the driving motor, which is connected to the high-voltage bus via a DC/AC inverter. The LBAR is interconnected with the cooling system of the HT-PEMFC through pipelines. This refrigeration system captures the heat generated during the fuel cell operation. It transforms it into cooling/heating capacity to meet the thermal load requirements of the vehicle cabin, thereby regulating the cabin temperature.

Fig. 1.

Arrangement of fuel cell bus system devices.

This section focuses on the model of the vehicle dynamics, HT-PEMFC system, LBAR system, thermodynamic model of the cabin, and model of CACHP system.

2.1. Vehicle model

In this study, the bus vehicle model is based on a fuel cell bus, whose specific parameters are presented in Table 1. Based on the dynamics of the vehicle system, the driving force $F_t$ of the vehicle during motion is influenced by rolling friction resistance $F_f$, air resistance $F_w$, gradient resistance $F_g$, and acceleration resistance $F_a$ [33]:

$$F_t=F_f+F_w+F_g+F_a=mgf\cos \left(\alpha \right)+\frac{C_{d}A{v}^2}{21.15}+mg\sin \left(\alpha \right)+\delta m\frac{dv}{dt}$$ (1)

where $m$ is the mass of the vehicle, $g$ is the gravitational acceleration, $f$ is the rolling resistance coefficient, $\alpha$ is the gradient of the slope, $C_d$ is the air drag coefficient, $A$ is the maximum windward area, $v$ is the vehicle speed, $\delta$ is the rotational mass coefficient, and $dv/dt$ is the vehicle acceleration.

Table 1.

Specific parameters of the fuel cell bus.

Parameters	Value	Unit
Length × width × height	11970 × 2550 × 3635	mm
Curb mass ($m_{curb}$)	13,050	kg
Gravitational acceleration ($g$)	9.8	m·s−2
Full load mass ($m_{full}$)	18,000	kg
Maximum windward area ($A$)	8.16	m2
Air drag coefficient ($C_d$)	0.55	N/A
Rolling resistance coefficient ($f$)	0.0085	N/A
Maximum speed ($v_{\mathit{max}}$)	100	km·h−1
Maximum number of passengers ($N_{\mathit{max}}$)	56	N/A
Gradient of the slope ($\alpha$)	0	rad
Rotational mass coefficient ($\delta$)	1.05	N/A
DC/DC efficiency (${\eta }_{DC/DC}$)	0.9	N/A
DC/AC efficiency (${\eta }_{DC/AC}$)	0.9	N/A
Motor efficiency (${\eta }_{motor}$)	0.95	N/A
Drivetrain efficiency (${\eta }_{tran}$)	0.9	N/A

The power required for the vehicle to travel is calculated using the following equation:

$$P_{Req}=\frac{F_{t}v}{{\eta }_{DC/DC}\cdot {\eta }_{DC/AC}\cdot {\eta }_{motor}\cdot {\eta }_{tran}}$$ (2)

where ${\eta }_{DC/DC}$, ${\eta }_{DC/AC}$, ${\eta }_{motor}$, and ${\eta }_{tran}$ represent the efficiencies of the DC/DC, DC/AC, motor, and transmission systems, respectively. The assumed values are listed in Table 1.

2.2. HT-PEMFC model

HT-PEMFCs convert hydrogen into electrical energy via electrochemical reactions. Their operating principle involves the following chemical reactions [36]:

$$\text{Anode}:{\mathrm{H}}_2\to 2{\mathrm{H}}^{+}+2{\mathrm{e}}^{-}$$ (3)

$$\text{Cathode}:0.5{\mathrm{O}}_2+2{\mathrm{H}}^{+}+2{\mathrm{e}}^{-}\to {\mathrm{H}}_2\mathrm{O}$$ (4)

$$\text{Overall}:{\mathrm{H}}_2\left(g\right)+0.5{\mathrm{O}}_2\left(g\right)\to {\mathrm{H}}_2\mathrm{O}\left(g\right)+\text{electricity}+\text{heat}$$ (5)

Several parameters, including cathode and anode inlet pressures, operating temperatures, O₂ and H₂ concentrations, relative humidity, and mass flow rate, influence the efficiency of HT-PEMFCs. To simplify the complexity of the HT-PEMFC model, this study makes the following reasonable assumptions [21].

• ⁃The cells operate in a steady state, and the operational states of individual cells are assumed to be identical. The sum of the power outputs from individual cells is considered as the output power of the fuel cell stack.
• ⁃The working temperature and pressure of the fuel cell stack are treated as constants.
• ⁃Performance losses owing to uneven working temperatures caused by irrational flow channel design, uneven gas distribution, and other related factors are neglected.
• ⁃Performance losses resulting from potential issues such as water flooding and gas diffusion resistance during the fuel cell reaction process are disregarded.
• ⁃Performance losses arising from catalyst deactivation and CO poisoning are also neglected.

The cell voltage $V_{cell}$ is determined by the thermodynamic equilibrium potential and polarization losses during operation [37]:

$$V_{cell}=E_{Nernst}-{\eta }_{act}-{\eta }_{ohm}-{\eta }_{con}$$ (6)

where ${\eta }_{act}$, ${\eta }_{ohm}$, and ${\eta }_{con}$ are the activation polarization loss, ohmic polarization loss, and concentration polarization loss, respectively. The thermodynamic equilibrium potential is calculated based on the stack operating temperature $T_{cell}$ using the following equation [38,39]:

$$E_{Nernst}=1.1669-0.24\times {10}^{-3}\left(T_{cell}-373.15\right)$$ (7)

The activation polarization loss ${\eta }_{act}$ is generated by the hydrogen oxidation reaction at the anode and oxygen reduction reaction at the cathode. It is calculated using equations (8), (9), (10) [24].

$${\eta }_{act}={\eta }_{act,a}+{\eta }_{act,c}$$ (8)

The activation losses in the anode ${\eta }_{act,a}$ and cathode ${\eta }_{act,c}$ are given by

$${\eta }_{act,a}=\frac{R_u{T}_{cell}}{n_{e}F\alpha }\ln \left(\frac{i+i_{leak}}{i_{0,a}}\right)$$ (9)

$${\eta }_{act,c}=\frac{R_u{T}_{cell}}{n_{e}F\alpha }\ln \left(\frac{i+i_{leak}}{i_{0,c}}\right)$$ (10)

where $R_u$ is the universal gas constant, $n_e$ is the number of electrons during the reaction, $F$ is the Faraday constant, $\mathrm{\alpha }$ is the charge transfer coefficient, $i$ is the operating current density of the fuel cell, $i_{leak}$ is the leakage current density, $i_{0,a}$ and $i_{0,c}$ are the exchange current densities in the anode and cathode, respectively, which are obtained from the following equations [24]:

$$i_{0,a}=i_{0,a}^{ref}\exp \left[\frac{16900}{R_u}\left(\frac{1}{433.15}-\frac{1}{T_{cell}}\right)\right]$$ (11)

$$i_{0,c}=i_{0,c}^{ref}\exp \left[\frac{72400}{R_u}\left(\frac{1}{423.15}-\frac{1}{T_{cell}}\right)\right]$$ (12)

where $i_{0,a}^{ref}$ and $i_{0,c}^{ref}$ are the exchange current density references at the anode and cathode, respectively.

The ohmic loss ${\eta }_{ohm}$ is calculated as follows [24]:

$${\eta }_{ohm}=i\left(R_{H^{+}}+R_{e^{-}}\right)$$ (13)

where $R_{H^{+}}$ and $R_{e^{-}}$ are the area-specific resistances due to proton and electron transport, respectively. The proton transport resistance $R_{H^{+}}$, which depends on the proton exchange membrane and catalyst layer properties, is expressed as follows [24]:

$$R_{H^{+}}=\frac{{\delta }_{PEM}}{{\kappa }_{PEM}}$$ (14)

where ${\delta }_{PEM}$ is the thickness of the proton exchange membrane, and ${\kappa }_{PEM}$ is the proton conductivity of the membrane, which is determined by the doping level $X$, relative humidity $RH$, and operating temperature $T_{cell}$ of the membrane as expressed by equations (15), (16), (17), (18) [24]:

$${\kappa }_{PEM}=\frac{AB}{T_{cell}}\exp \left(\frac{-P_{act}}{R_u{T}_{cell}}\right)$$ (15)

$$A=168X^3-6324X^2+65750X+8460$$ (16)

$$B=\{\begin{array}{c}\begin{array}{cc}1+\left(0.01704T_{cell}-4.767\right)\cdot RH& 373.15\mathrm{K}\le T_{cell}\le 413.15\mathrm{K}\end{array}\\ \begin{array}{cc}1+\left(0.1432T_{cell}-56.89\right)\cdot RH& 413.15\mathrm{K}\le T_{cell}\le 453.15\mathrm{K}\end{array}\\ \begin{array}{cc}1+\left(0.7T_{cell}-309.2\right)\cdot RH& 453.15\mathrm{K}\le T_{cell}\le 473.15\mathrm{K}\end{array}\end{array}$$ (17)

$$P_{act}=-619.6X+21750$$ (18)

where $A$ and $B$ are coefficients, and $P_{act}$ is the activation energy.

Assuming that the average electron transport path in the catalyst layer is half of the catalyst layer thickness, the electron transport resistance is determined using Ohm's law as follows:

$$R_{e^{-}}=\frac{{\delta }_{CL}}{{\mu }_{CL}}+2\cdot \frac{{\delta }_{GDL}}{{\mu }_{GDL}}+\frac{{\delta }_{BPP}}{{\mu }_{BPP}}$$ (19)

where ${\delta }_{CL}$ and ${\delta }_{GDL}$ are the thicknesses of the anode/cathode catalyst layer (CL) and gas diffusion layer (GDL), respectively; ${\delta }_{BPP}$ is the thickness of the bipolar plate (BPP); and ${\mu }_{CL}$, ${\mu }_{GDL}$, and ${\mu }_{BPP}$ are the electronic conductivities of the CL, GDL, and BPP, respectively.

The concentration polarization ${\eta }_{con}$ can be expressed by the following equation [24]:

$${\eta }_{con}=\left(1+\frac{1}{\alpha }\right)\frac{R_u{T}_{cell}}{n_{e}F}\ln \left(\frac{i_{\mathit{lim}}}{i_{\mathit{lim}}-i}\right)$$ (20)

where $i_{\mathit{lim}}$ represents the limiting current density.

By combining the above equations, the voltage of a single cell $V_{cell}$ can be obtained. Therefore, based on the series connection of the cells, the total voltage $V_{stack}$ and output power $P_{stack}$ of the high-temperature fuel cell stack can be expressed as follows [40,41]:

$$V_{stack}=N_{cell}\cdot V_{cell}$$ (21)

$$P_{stack}=N_{cell}\cdot V_{cell}\cdot i\cdot A_{MEA}$$ (22)

where $N_{cell}$ is the number of individual cells in the high-temperature fuel cell stack, and $A_{MEA}$ represents the active area of the membrane electrode assembly (MEA).

The energy efficiency of HT-PEMFC ${\eta }_{FC}$ is determined by the stack output power and power requirements of pump $P_{pump}$ and compressor $P_{comp}$, as shown in the following equations [40]:

$${\eta }_{FC}=\frac{P_{stack}-P_{pump}-P_{comp}}{n_{H_2}\cdot LH{V}_{H_2}}$$ (23)

$$P_{pump}=\frac{{\dot{m}}_{liq}\cdot \left(P_1-P_0\right)}{{\eta }_{pump}\cdot {\rho }_{liq}}$$ (24)

$$P_{comp}=\frac{{\dot{m}}_{gas}\cdot C_p\cdot T_0}{{\eta }_{comp}}\left[{\left(\frac{P_1}{P_0}\right)}^{\frac{k-1}{k}}-1\right]$$ (25)

where $n_{H_2}$ is the molar flow rate of hydrogen; $LH{V}_{H_2}$ is the lower heat value of hydrogen; $\dot{m}$ is the mass flow rate; $C_p$ is the specific heat capacity; $T_0$ and $P_0$ are the temperature and pressure before compression, respectively; $P_1$ is the pressure of gas or liquid after compression; $k$ is the ratio of the specific heat capacity (for diatomic gases $k$ = 1.4); ${\rho }_{liq}$ is the density of liquid; ${\eta }_{pump}$ and ${\eta }_{comp}$ are the efficiencies of pump and compressor.

During the operation of the fuel cell, the polarization losses generate a considerable amount of heat. The total heat generated is expressed as equation (26) [39], and most of it will be absorbed by the coolant and removed away from the stack:

$${\dot{Q}}_{stack}=\left(E_{Nernst}-T_{cell}\frac{d{E}_{Nernst}}{d{T}_{cell}}-V_{cell}\right)\cdot i\cdot A_{MEA}\cdot N$$ (26)

The specific model parameters are listed in Table 2 [24,39,40].

Table 2.

Specific parameters of the HT-PEMFC model.

Parameter	Value	Unit
Operating temperature ($T_{cell}$)	448	K
Faraday constant ($F$)	96485	C·mol−1
Active area of MEA ($A_{MEA}$)	0.08	m2
Number of cells ($N_{cell}$)	700	N/A
Universal gas constant ($R_u$)	8.314	J·mol−1·K−1
Number of electrons ($n_e$)	2	N/A
Charge transfer coefficient ($\mathrm{\alpha }$)	0.5	N/A
Leak current density ($i_{leak}$)	50	A·m−2
Exchange current density reference in anode ($i_{0,a}^{ref}$)	7.2 × 102	A·m−2
Exchange current density reference in cathode ($i_{0,c}^{ref}$)	1.315 × 10−4	A·m−2
Doping level ($X$)	15	N/A
Relative humidity ($RH$)	0.38	N/A
Thickness of anode/cathode CLs (${\delta }_{CL}$)	3.5 × 10−4	m
Thickness of anode/cathode GDLs (${\delta }_{GDL}$)	1.5 × 10−5	m
Thickness of BPP (${\delta }_{BPP}$)	1.9 × 10−3	m
Electronic conductivity of CL (${\mu }_{CL}$)	300	S·m−1
Electronic conductivity of GDL (${\mu }_{GDL}$)	1250	S·m−1
Electronic conductivity of BPP (${\mu }_{BPP}$)	14000	S·m−1
Limiting current density ($i_{\mathit{lim}}$)	20000	A·m−2
Initial temperature ($T_0$)	273.15	K
Initial pressure ($P_0$)	1	atm
Compressor efficiency (${\eta }_{comp}$)	95	%
Pump efficiency (${\eta }_{pump}$)	85	%

2.3. LBAR model

The LBAR can be divided into single-stage and multi-stage types. Single-stage LBAR is typically suitable for low-grade heat sources below 120 °C and operates in environments with relatively low overall power. Although single-stage refrigerator has a slightly lower coefficient of performance (COP) than multi-stage refrigerator, its advantages, such as small system volume and long service life, make it a good choice for practical vehicle applications. Therefore, this study selects single-stage LBAR system as the research object to meet the practical application requirements.

As shown in Fig. 2, the single-stage LBAR mainly comprises a generator, a condenser, an evaporator, an absorber, a heat exchanger, a solution pump, and an expansion valve.

Fig. 2.

LiBr absorption refrigeration system.

The working principle of the lithium bromide absorption refrigerator can be simplified into the following steps.

• 1)The coolant of the HT-PEMFC absorbs the heat generated by the electrochemical reaction in the stack, causing its temperature to rise. This high-temperature coolant flows into the generator, exchanges heat with the lithium bromide weak solution, cools down, and then flows back to the high-temperature fuel cell system, completing a cooling cycle.
• 2)In the generator, the weak solution (point 6) absorbs the heat from the high-temperature coolant, causing some of the water in the solution to evaporate into high-pressure vapor (point 7) and flow into the condenser.
• 3)In the condenser, the high-pressure vapor (point 7) exchanges heat with the cooling water, condenses into saturated water (point 8), and releases heat that is absorbed by the cooling water.
• 4)The condensed high-pressure saturated water (point 9) enters the evaporator from the condenser through the expansion valve and evaporates into low-pressure steam (point 10) due to the pressure drop. This evaporation process absorbs heat from the refrigerant of the vehicle air conditioning system and decreases the refrigerant temperature.
• 5)The low-pressure steam (point 10) enters the absorber from the evaporator and is absorbed by the lithium bromide strong solution (point 3) in the absorber. The absorption process releases heat, which is removed by the cooling water.
• 6)After the strong lithium bromide solution absorbs the steam, it becomes a weak solution (point 4). It flows into the generator through the solution pump and heat exchanger for the next cycle. The strong solution transfers heat to the weak solution, achieving preheating in the heat exchanger.

For convenience, the numbers in the subscripts of the variables in the subsequent analysis indicate the working points. For example, ${\dot{m}}_1$, $h_1$, and $T_1$ represent the solution mass flow rate, enthalpy, and temperature at working point 1, respectively. Before modeling and analysis, simplifying assumptions are made to appropriately reduce the complexity of the system. These assumptions are as follows:

• ⁃The refrigeration system operates in a steady state, or its dynamic adjustment time is negligible.
• ⁃Owing to the short length of the pipes between components, the heat leakage and pressure drop resulting from the flow of solution and vapor between different components are neglected [41].

• ⁃The temperature and condensation variations in the LiBr solution in the solution pump are ignored; therefore, $h_5=h_4$.

• ⁃The solutions at the expansion and solution valves are considered isenthalpic [42], which means that $h_9=h_8$ and $h_3=h_2$.
• ⁃The gas pressures inside the generator and condenser are equal, and both operate at a higher pressure $p_h$. The gas pressures inside the absorber and evaporator are equal, and both operate at a lower pressure $p_l$ [41].

The five main components of the LBAR can be categorized into two types based on their heat and mass transfer relationships. The condenser, evaporator, and heat exchanger involve only heat transfer processes; therefore, they focus is on energy conservation. The processes in the generator and absorber are coupled, involving heat transfer, evaporation, and absorption [43]. Therefore, during modeling and analysis, energy conservation and mass conservation relationships should be considered.

2.3.1. Condenser, evaporator, and heat exchanger

The mass flow rate of steam (point 7) from the generator is ${\dot{m}}_7$, with enthalpy $h_7$. After releasing heat ${\dot{Q}}_c$ to the cooling water, it condenses into water and flows out of the condenser with a rate ${\dot{m}}_8$ and enthalpy $h_8$ at working point 8. Therefore, the energy conservation equation in the condenser is [43]:

$${\dot{m}}_7{h}_7={\dot{m}}_8{h}_8+{\dot{Q}}_c$$ (27)

The saturated water (point 9) entering the evaporator through the expansion valve undergoes evaporation owing the pressure drop. In the evaporator, it absorbs heat ${\dot{Q}}_e$ from the refrigerant from the cabin. The produced vapor (point 10) enters the absorber through the pipeline. The energy conservation equation in the evaporator is a follows [43]:

$${\dot{m}}_9{h}_9+{\dot{Q}}_e={\dot{m}}_{10}{h}_{10}$$ (28)

In the generator, the strong solution has a higher temperature, and the absorption characteristics of the LiBr solution for water depend on the concentration and temperature. The lower the temperature, the stronger the absorption capacity. A heat exchanger is added between the generator and absorber to heat the weak solution with the strong solution, making full use of the heat. The energy conservation equation in the heat exchanger is [43].

$${\dot{m}}_1{h}_1+{\dot{m}}_5{h}_5={\dot{m}}_2{h}_2+{\dot{m}}_6{h}_6$$ (29)

2.3.2. Generator and absorber

In the generator, the weak solution (point 6) absorbs the heat ${\dot{Q}}_g$ from the HT-PEMFC, evaporates into pure steam (point 7), and becomes a strong solution (point 1). The mass and energy conservation equations in the generator are as follows [43]:

$${\dot{m}}_6={\dot{m}}_1+{\dot{m}}_7$$ (30)

$${\dot{m}}_6{h}_6+{\dot{Q}}_g={\dot{m}}_1{h}_1+{\dot{m}}_7{h}_7$$ (31)

The strong solution (point 3) flows from the generator through the heat exchanger into the absorber. Subsequently, it absorbs pure steam (point 10) from the evaporator and releases heat ${\dot{Q}}_a$ to the coolant. The produced weak solution (point 4) is pumped back to the generator. The mass and energy conservation equations for the absorber are given by Ref. [43]:

$${\dot{m}}_3+{\dot{m}}_{10}={\dot{m}}_4$$ (32)

$${\dot{m}}_3{h}_3+{\dot{m}}_{10}{h}_{10}={\dot{m}}_4{h}_4+{\dot{Q}}_a$$ (33)

2.3.3. System constraints

The steam generated and absorbed in the generator and absorber is pure water vapor; therefore, the mass of LiBr in the solution remains constant [43].

$${\dot{m}}_{str}{x}_{str}={\dot{m}}_{weak}{x}_{weak}$$ (34)

The mass flow rates of the strong and weak LiBr solutions are denoted as ${\dot{m}}_{str}={\dot{m}}_1={\dot{m}}_2={\dot{m}}_3$ and ${\dot{m}}_{weak}={\dot{m}}_4={\dot{m}}_5={\dot{m}}_6$, respectively. The concentrations of the strong and weak LiBr solutions are represented by $x_{str}=x_1=x_2=x_3$ and $x_{weak}=x_4=x_5=x_6$, respectively.

For the generator and absorber, the pressure equilibrium relationships are as follows [43]:

$$p_s\left(T_1,x_1\right)=p_s\left(T_6,x_6\right)=p_w\left(T_7\right)$$ (35)

$$p_s\left(T_3,x_3\right)=p_s\left(T_4,x_4\right)=p_w\left(T_{10}\right)$$ (36)

where $p_s\left(T,x\right)$ and $p_w\left(T\right)$ are the saturated vapor pressures of the LiBr solution and pure water, respectively. The calculation details for the physical properties of water vapor and LiBr solution can be found in Refs. [44,45].

The above equations establish the working models of the five components of the LBAR system, forming the overall model of the refrigeration system through the relationships between each component. Considering that the main purpose of this study is to utilize the waste heat from the high-temperature fuel cell to meet the cooling and heating requirements of vehicle cabin, the focus is placed on the relationship between the cooling capacity ${\dot{Q}}_{cool}$, heating capacity ${\dot{Q}}_{heat}$, and heat carried by the cooling water of the fuel cell stack ${\dot{Q}}_g$.

The cooling capacity ${\dot{Q}}_{cool}$ of the refrigeration system is the heat released from the refrigerant water. Therefore, it can be derived from equation (28):

$${\dot{Q}}_{cool}={\dot{Q}}_e={\dot{m}}_{10}{h}_{10}-{\dot{m}}_9{h}_9$$ (37)

The heating capacity ${\dot{Q}}_{heat}$ is the sum of the heat carried away by the cooling water in the condenser and evaporator, which can be derived from equations (27), (33):

$${\dot{Q}}_{heat}={\dot{Q}}_a+{\dot{Q}}_c={\dot{m}}_3{h}_3+{\dot{m}}_{10}{h}_{10}-{\dot{m}}_4{h}_4+{\dot{m}}_8{h}_8-{\dot{m}}_7{h}_7$$ (38)

Therefore, the cooling and heating COP of the absorption refrigerator can be expressed as

$$CO{P}_{cool}=\frac{{\dot{Q}}_{cool}}{{\dot{Q}}_g}$$ (39)

$$CO{P}_{heat}=\frac{{\dot{Q}}_{heat}}{{\dot{Q}}_g}$$ (40)

The state parameters at various working points of the refrigeration system are listed in Table 3 [43].

Table 3.

State parameters at working points.

Points	State	Temperature	Pressure	Concentration	Specific enthalpy	Mass flow rate
1	Strong solution	$T_1$	$p_h$	$x_1=x_{str}$	$h_1$	${\dot{m}}_1={\dot{m}}_{str}$
2	Strong solution	$T_2$	$p_h$	$x_2=x_{str}$	$h_2$	${\dot{m}}_2={\dot{m}}_{str}$
3	Strong solution	$T_3=T_2$	$p_l$	$x_3=x_{str}$	$h_3=h_2$	${\dot{m}}_3={\dot{m}}_{str}$
4	Weak solution	$T_4$	$p_l$	$x_4=x_{weak}$	$h_4$	${\dot{m}}_4={\dot{m}}_{weak}$
5	Weak solution	$T_5=T_4$	$p_h$	$x_5=x_{weak}$	$h_5=h_4$	${\dot{m}}_5={\dot{m}}_{weak}$
6	Weak solution	$T_6$	$p_h$	$x_6=x_{weak}$	$h_6$	${\dot{m}}_6={\dot{m}}_{weak}$
7	Steam	$T_7$	$p_h$	/	$h_7$	${\dot{m}}_7$
8	Water	$T_8$	$p_h$	/	$h_8$	${\dot{m}}_8={\dot{m}}_7$
9	Steam-water mixture	$T_9=T_8$	$p_l$	/	$h_9=h_8$	${\dot{m}}_9={\dot{m}}_8$
10	Steam	$T_{10}$	$p_l$	/	$h_{10}$	${\dot{m}}_{10}={\dot{m}}_9$

2.4. Cabin thermodynamic model

As shown in Fig. 3, for the fuel cell buses, the thermal load in the cabin mainly originates from four sources, as shown in the following equation [46,47]:

$${\dot{Q}}_{cab}={\dot{Q}}_{amb}+{\dot{Q}}_{rad}+{\dot{Q}}_{ven}+{\dot{Q}}_{met}$$ (41)

where ${\dot{Q}}_{cab}$ represents the total thermal load of the entire cabin; ${\dot{Q}}_{amb}$ is the thermal load caused by the temperature difference between the external environment and the cabin; ${\dot{Q}}_{rad}$ is the solar radiation heat; ${\dot{Q}}_{ven}$ is the heat brought in or taken away by the cabin ventilation system, and ${\dot{Q}}_{met}$ represents the metabolic heat dissipated by the driver and passengers.

Fig. 3.

Bus cabin thermal load.

The environmental thermal load is generated by convective heat exchange between the vehicle body, windows, and external ambient air [46]:

$${\dot{Q}}_{amb}={\dot{Q}}_{body}+{\dot{Q}}_{glass}$$ (42)

The bus body can be divided into five parts: roof, floor, sides, front, and rear. These five parts contribute to the convective heat transfer within the vehicle body. The convective heat transfer through the windows is similar to that through the body and can be decomposed into the front windshield, rear glass, and side glass.

$${\dot{Q}}_{body}={\dot{Q}}_{roof}+{\dot{Q}}_{floor}+{\dot{Q}}_{front,b}+{\dot{Q}}_{side,b}+{\dot{Q}}_{rear,b}$$ (43)

$${\dot{Q}}_{glass}={\dot{Q}}_{front,g}+{\dot{Q}}_{rear,g}+{\dot{Q}}_{side,g}$$ (44)

The convective heat transfer is calculated as follows [33]:

$${\dot{Q}}_j=K_j\cdot A_j\cdot \left(T_{amb}-T_{cab}\right)$$ (45)

where $K_j$ is the convective heat transfer coefficient; $A_j$ is the heat transfer area; $T_{amb}$ and $T_{cab}$ represent the ambient temperature outside the vehicle and the temperature inside the cabin, respectively. It is assumed that the ambient temperature outside the vehicle and the temperature inside the cabin are uniform. The subscript $j$ the convective heat for different parts.

The convective heat transfer coefficient $K_j$ is calculated using [33]:

$$K_j=\frac{1}{\frac{1}{k_{amb}}+\sum \frac{{\delta }_{b,i}}{{\lambda }_{b,i}}+\frac{1}{k_{cab}}}$$ (46)

where $k_{amb}$ is the interface convective heat transfer coefficient between the exterior surface of the bus and the environment; $k_{cab}$ is the convective heat transfer coefficient between the interior surface of the bus body and the cabin, and $\sum {\mathrm{\delta }}_{b,i}/{\mathrm{\lambda }}_{b,i}$ represents the sum of thickness and thermal conductivity ratio of various layers of the bus body. Since the airflow rate inside the cabin is very low, $k_{cab}$ can be approximated as a constant value of 29 W/(m²∙K) [33]. Meanwhile, $k_{amb}$ is related to the airflow rate over the exterior surface of the vehicle and is estimated as follows:

$$k_{amb}=1.613\cdot \left(4+12\sqrt{v}\right)$$ (47)

where $v$ is the vehicle velocity.

The heat load ${\dot{Q}}_{rad}$ is the heat transmitted into the cabin through the bus window glass and body owing to solar radiation. Its value is related to the solar radiation intensity $R_{sun}$, as shown in the following equation [33]:

$${\dot{Q}}_{rad}=1000\cdot \left[{\eta }_{solar,g}{R}_{sun}{A}_{sun,g}+K_{roof}{A}_{roof}\left(\frac{{\sigma }_{rad}{R}_{sun}}{k_{amb}}\right)\right]$$ (48)

where ${\eta }_{solar,g}$ is the solar radiation penetration coefficient of the window glass; $A_{sun,g}$ is the effective area of the window under sunlight; $K_{roof}$ and $A_{roof}$ represent the convective heat transfer coefficient and effective area of the bus roof under sunlight, respectively; ${\mathrm{\sigma }}_{rad}$ is the solar radiation absorption coefficient of the bus body, and $R_{sun}$ is the solar radiation intensity.

During the driving process, the CO₂ concentration in the cabin increases owing to passenger breathing, and active ventilation is required to exchange air between the cabin and the external environment [48]. The heat brought in or taken away by ventilation is the ventilation heat load ${\dot{Q}}_{ven}$, which is given by Ref. [49]:

$${\dot{Q}}_{ven}={\rho }_{air}N{\dot{V}}_{ven}\Delta H$$ (49)

where ${\rho }_{air}$ is the air density; $N$ is the total number of occupants (including the driver); ${\dot{V}}_{ven}$ is the ventilation volume of the cabin (25 m³/h per occupant according to Chinese standard JT/T325-2018), and $\Delta H$ is the enthalpy difference between the external air and cabin air, which can be obtained from air enthalpy tables.

Metabolic activities in the human body continuously generate heat, which is dissipated into the cabin air through the body's skin, known as the metabolic heat load ${\dot{Q}}_{met}$, which is calculated as follows [49]:

$${\dot{Q}}_{met}=N\cdot M\cdot A_{Du}$$ (50)

where $M$ is the metabolic heat generation rate (55 W/m² for passengers and 85 W/m² for the driver according to ISO8996), and $A_{Du}$ is the Dubois area, estimated based on the height and weight of passengers [48]. $A_{Du}$ is calculated using the average weight $m_{avg}$ and height of a Chinese male $h_{avg}$, which are 66.2 kg and 1.671 m, respectively.

$$A_{Du}=0.202\cdot {m_{avg}}^{0.425}\cdot {h_{avg}}^{0.725}$$ (51)

To simplify the model and calculations, the air temperature inside the cabin is assumed to be uniform. The cabin air temperature equation is given by Ref. [49]:

$${\rho }_{air}{V}_{cab}{c}_{p,air}\frac{d{T}_{cab}}{dt}={\dot{Q}}_{cab}+{\dot{Q}}_{AC}$$ (52)

where ${\rho }_{air}$ is the air density, $V_{cab}$ is the bus cabin volume, $c_{p,air}$ is the specific heat capacity of air, ${\dot{Q}}_{cab}$ is the total thermal load in the cabin, and ${\dot{Q}}_{AC}$ is the air condition cooling/heating capacity. The calculation parameters for the above equations are listed in Table 4 [49].

Table 4.

Parameters of cabin thermal model.

Parameters	Value	Unit
Convective heat transfer coefficient (${\mathrm{\lambda }}_{b,i}$)	30 - 0.025–30 (steel – air - steel)	W·m−1·K−1
Thickness of various layers of bus body (${\mathrm{\delta }}_{b,i}$)	1–18 – 1 (steel – air - steel)	mm
Solar radiation intensity ($R_{sun}$)	800 for summer, 0 for winter	W·m−2
Solar radiation penetration coefficient (${\eta }_{solar,g}$)	0.9	N/A
Solar radiation absorption coefficient (${\mathrm{\sigma }}_{rad}$)	0.75	N/A
Effective area ratio of window on body side	0.5	N/A
Ventilation volume of the cabin (${\dot{V}}_{ven}$)	25 per passenger	m3
Metabolic heat production rate ($M$)	85 for driver, 55 for passenger	W·m−2
Dubois area for adult ($A_{Du}$)	1.741	m2
Cabin air density (${\rho }_{air}$)	1.293	kg·m−3
Cabin volume ($V_{cab}$)	55.5	m3
Cabin air specific heat capacity ($c_{p,air}$)	1.005	kJ·kg−1·K−1

2.5. CACHP system

In recent years, CACHP systems have been considered excellent energy-saving methods because they can meet climate control requirements while achieving energy efficiency and providing both cooling and heating functions [50]. To facilitate the cyclic process, this study selects R134a as the working medium for the CACHP system. R134a is widely used in automotive air conditioning systems because of its environmental friendliness and excellent thermodynamic performance [51].

As shown in Fig. 4(a), the six main components of the CACHP system are the compressor, inner heat exchanger, 4-way valve, heat exchanger, bidirectional expansion valve, and outer heat exchanger [52]. The operating cycle of the air-conditioning system is illustrated in Fig. 4(a). In the cooling mode, refrigerant R134a is compressed into a high-temperature, high-pressure gas in the compressor. Then, it enters the outer heat exchanger through the 4-way valve, undergoing isobaric condensation. After condensation, the saturated liquid exchanges heat with the saturated vapor generated by evaporation in the inner cabin heat exchanger. The subcooled liquid then adiabatically expands through the bidirectional expansion valve, entering the inner heat exchanger. Here, it undergoes the evaporation process, absorbing heat from the vehicle cabin before returning to the compressor to start the next cycle [53]. In the heating mode, the direction of the 4-way valve is changed, allowing the compressed gas to first release heat through the inner heat exchanger for condensation and then undergo heat exchange, expansion, evaporation, and other processes.

Fig. 4.

Compression-type air-conditioning heat pump system: (a) system schematic; (b) p-h diagram for R134a.

The refrigerant cycle can be represented by a p-h diagram, as displayed in Fig. 4(b). Process 1–2s represents the ideal isentropic compression, whereas the actual compression process is depicted by process 1–2n. Process 2n–4 denotes the condensation process, where the refrigerant state changes from superheated vapor (2n) to saturated vapor (3) and then to saturated liquid (4). Process 5–6 is the adiabatic expansion through the expansion valve. Process 6–7 represents the evaporation process in the evaporator, where the refrigerant absorbs heat. The saturated vapor enters the heat exchanger, undergoes the preheating, and finally enters the compressor to start the next cycle.

The cooling capacity under refrigeration conditions $q_e$ and the heating capacity $q_h$ in the heating mode are given by the following equations [53]:

$$q_e=h_6-h_7$$ (53)

$$q_h=h_{2n}-h_4$$ (54)

The unit compression work $q_c$ of the compressor is expressed as [53]:

$$q_c=h_{2n}-h_1$$ (55)

The cycle mass flow rates of the refrigerant in the cooling mode ${\dot{m}}_{ref,e}$ and in the heating mode ${\dot{m}}_{ref,h}$ are calculated using the following equations [53]:

$${\dot{m}}_{ref,e}=\frac{{\dot{Q}}_{ACC}}{q_e}$$ (56)

$${\dot{m}}_{ref,h}=\frac{{\dot{Q}}_{ACH}}{q_h}$$ (57)

where ${\dot{Q}}_{ACC}$ and ${\dot{Q}}_{ACH}$ represent the cooling and heating capacities, respectively, required for cabin temperature balancing.

The power of the compressor in the cooling $P_{comp,e}$, and heating mode $P_{comp,h}$ can be obtained as follows [54]:

$$P_{comp,e}=\frac{{\dot{m}}_{ref,e}\cdot q_c}{{\eta }_{isen}{\eta }_{mech}}$$ (58)

$$P_{comp,h}=\frac{{\dot{m}}_{ref,h}\cdot q_c}{{\eta }_{isen}{\eta }_{mech}}$$ (59)

where ${\eta }_{isen}$ is the isentropic compression efficiency of the compressor, set as 0.75 based on experimental results [55], and ${\eta }_{mech}$ is the mechanical efficiency of the compressor, assumed to be 0.9. The specific working points for the air-conditioning heat pump system used in this study are listed in Table 5, based on Sun et al. [51] and the physical properties of R134a.

Table 5.

Working points of the CACHP model.

Points	State	Temperature (K)	Pressure (MPa)	Specific enthalpy (kJ·kg−1)
1	Superheated steam	299.03	0.42	419.00
2n	Superheated steam	358.15	1.90	454.00
3	Saturated steam	338.38	1.90	414.50
4	Saturated liquid	338.38	1.90	310.00
5	Subcooled liquid	326.74	1.90	277.00
6	Two-phase	283.54	0.42	277.00
7	Saturated steam	283.54	0.42	385.00

2.6. Energy and exergy efficiency

The electrical efficiency ${\eta }_{elec}$ of the integrated system is calculated from the ratio between the required power and lower heating value of the fuel input, as follows:

$${\eta }_{elec}=\frac{P_{Req}}{n_{H_2}•LH{V}_{H_2}}\times 100\%$$ (60)

where $P_{Req}$ is the required power for driving the vehicle.

The cooling efficiency ${\eta }_{cool}$ and heating efficiency ${\eta }_{heat}$ can be calculated using the heat for producing chilled refrigerant ${\dot{Q}}_{cool}$ and the heat for producing the hot water ${\dot{Q}}_{heat}$, as follows:

$${\eta }_{cool}=\frac{{\dot{Q}}_{cool}}{n_{H_2}•LH{V}_{H_2}}\times 100\%$$ (61)

$${\eta }_{heat}=\frac{{\dot{Q}}_{heat}}{n_{H_2}•LH{V}_{H_2}}\times 100\%$$ (62)

Exergy analysis, which is grounded in the second law of thermodynamics, is typically employed for a more precise system investigation. Exergy represents the maximum theoretical useful work obtained from a system as it transitions to the standard state (25 °C, 1 atm). In this study, the input exergies $\dot{E}{x}_{in}$ for the combined system is calculated as follows [40]:

$$\dot{E}{x}_{in}=\sum _{in}{\dot{n}}_{i}e{x}_i-\sum _{out}{\dot{n}}_{i}e{x}_i$$ (63)

where $i$ represents the various streams at the inlet and outlet, while ${\dot{n}}_i$ and $e{x}_i$ denote the mole flow rate and exergy of each stream, respectively.

In this study, the kinetic and potential exergies are neglected. Therefore, the specific exergy of a stream can be calculated as follows [40]:

$$e{x}_i=e{x}_{ph,i}+e{x}_{ch,i}$$ (64)

The specific physical exergy ($e{x}_{ph,i}$) and specific chemical exergy ($e{x}_{ch,i}$) are defined in equations (65), (66), respectively [40].

$$e{x}_{ph,i}=\left(h_i-h_{i,0}\right)-T_0\left(s_i-s_{i,0}\right)$$ (65)

$$e{x}_{ch,i}=\sum y_j\cdot e{x}_{ch,j}+R_u{T}_0\sum y_j\cdot \mathit{ln}{y}_j$$ (66)

where $h_{i,0}$ and $s_{i,0}$ are the enthalpy and entropy of species $i$ at the standard state conditions, respectively; $y_j$ is the molar fraction of each substance in stream $i$; and $e{x}_{ch,j}$ is the standard chemical exergy of each substance, as listed in Table 6. For an ideal gas substance, the specific physical exergy ($e{x}_{ph,i}$) can also be obtained as [56]:

$$e{x}_{ph,i}=C_p{T}_0\left[\frac{T_i}{T_0}-1-\ln \left(\frac{T_i}{T_0}\right)+\ln {\left(\frac{P_i}{P_0}\right)}^{\frac{\gamma -1}{\gamma }}\right]$$ (67)

where $\gamma =C_p/C_v$ is the specific heat ratio; $C_p$ and $C_v$ are specific heat at constant pressure and volume respectively.

Table 6.

Standard chemical exergy of substances [40].

Substances	Standard chemical exergy (J·mol−1)
H2	238,490
O2	3970
N2	720
H2O	3120

The electrical exergy efficiency ${\psi }_{elec}$, the cooling exergy efficiency ${\psi }_{cool}$ and the heating exergy efficiency ${\psi }_{heat}$ are defined as follows:

$${\psi }_{elec}=\frac{P_{Req}}{\dot{E}{x}_{in}}\times 100\%$$ (68)

$${\psi }_{cool}=\frac{{\dot{Q}}_{cool}\left(1-\frac{T_{cab}}{T_{evap}}\right)}{\dot{E}{x}_{in}}\times 100\%$$ (69)

$${\psi }_{heat}=\frac{{\dot{Q}}_{heat}\left(1-\frac{T_{cab}}{T_{HW}}\right)}{\dot{E}{x}_{in}}\times 100\%$$ (70)

where $1-T_{cab}/T_{evap}$ and $1-T_{cab}/T_{HW}$ are the Carnot coefficient of heat stream; $T_{cab}$ is the cabin temperature; $T_{evap}$ is the evaporator temperature; $T_{HW}$ is the hot water temperature.

3. Simulation setup

3.1. Simulation topology

Using the equations described in the previous section, this study simulated the vehicle dynamic model, cabin thermodynamic model, HT-PEMFC, LBAR system, and CACHP system using MATLAB/Simulink software. The modules are interconnected, as depicted in Fig. 5. The upper and lower parts represent vehicles equipped with LBAR and CACHP systems, respectively.

Fig. 5.

Simulation topology.

The drive unit module first calculates the vehicle speed and acceleration based on driving cycle data to determine the power required for the current driving conditions. The cabin thermal models of the two vehicles calculate the thermal load based on the current vehicle speed, external ambient temperature, and cabin temperature, and transfer the results to the energy management system.

The power management system collects information from other modules and outputs the required power for the HT-PEMFC and high-voltage (HV) battery based on the current power demand for driving, temperature regulation target, quantity of remaining hydrogen, and state of charge (SOC) of the battery.

The HT-PEMFC module calculates the output power and generated heat based on the required power from the power management system and transfers this information to the high-voltage busbar and LBAR system. The high-voltage busbar module is used to calculate the electrical power production and consumption of the vehicle during simulation.

The LBAR system calculates the corresponding cooling and heating capacities based on the heat generated by the fuel cell to regulate the cabin temperature. For vehicles equipped with the CACHP system, the control process is similar to that of the former. However, there are some differences in the control strategy and power source for the air-conditioning system. The LBAR system utilizes heat from the HT-PEMFC, whereas the CACHP system obtains the required power from the high-voltage busbar.

The constraints on the power of the fuel cell, power of the battery, power of the drive unit, and battery SOC in the powertrain system during simulation are listed in Table 7.

Table 7.

System constraints.

Variables	Min.	Max.	Min. rate	Max. rate
FC power	5 kW	160 kW	−40 kW s−1	40 kW s−1
Battery power	−50 kW	120 kW	−60 kW s−1	60 kW s−1
Motor power	0 kW	250 kW	/	/
Battery SOC	0.5	0.95	/	/

3.2. Model validation

A comparison between the results of the fuel cell model used in this study and those of the experiments by Sousa et al. [57] is illustrated in Fig. 6(a). The simulation model was set to operate under the same conditions as in the experiment by Sousa et al., with a working temperature of 423.15 K and an inlet relative humidity of 38 %. The results show good agreement between the simulation and experimental data at this operating temperature. Although some deviations exist in the current density range of 4000–10000, the overall performance of the model is satisfactory.

Fig. 6.

Validation of models: (a) polarization of HT-PEMFC; (b) validation of LiBr absorption refrigeration system; (c) effect of evaporating temperature on COP at a condensing temperature of 323.15K.

For the LBAR system, the working conditions at various operating points are influenced by the mass flow rates of the working media in each component and the inlet/outlet temperatures. Therefore, the same conditions as those used by Rubio-Maya et al. [58] were selected for validation. The verification parameters are listed in Table 8. The simulation results were compared with those obtained by Rubio-Maya et al., as displayed in Fig. 6(b). It can be observed that the proposed model has a high level of accuracy.

Table 8.

Specific parameters for LiBr absorption refrigeration model validation.

Parameters	Value	Unit
Weak solution concentration ($x_{weak}$)	53.07	%
Strong solution concentration ($x_{str}$)	59.96	%
Higher pressure ($p_h$)	7.35	kPa
Lower pressure ($p_l$)	1.12	kPa
Generator heat flow rate (${\dot{Q}}_g$)	259.29	kW
Temperature of coolant in generator inlet ($T_{g,in}$)	373.2	K
Temperature of coolant in absorber inlet ($T_{a,in}$)	300.2	K
Temperature of refrigerant in evaporator inlet ($T_{e,in}$)	293.2	K

The experimental results of Zhang et al. [59] were compared with the COP results of the compression-type air-conditioning model in this study. Fig. 6(c) shows that the simulation values and experimental data match well.

3.3. Ambient condition

According to the data from the Shanghai Meteorological Bureau, as shown in Fig. 7, the highest and lowest temperatures in the year 2023 were 37.5 °C and −6.5 °C, respectively. To better validate the results, this study set the refrigeration conditions to the hottest period during summer. The atmospheric and initial temperatures inside the vehicle were set to 40 °C. Research findings indicate that a comfortable temperature inside the vehicle during summer cooling is 27.5 °C [60]. For the heating condition, the temperature was set to the coldest period during winter, with the atmospheric and initial temperatures inside the vehicle set to −10 °C. A comfortable temperature inside the vehicle during winter heating is considered to be 17.5 °C [61].

Fig. 7.

Ambient temperature in Shanghai during 2023.

3.4. Test driving cycles

In this experiment, two test driving cycles were used: the New European Driving Cycle (NEDC) and China Heavy-duty Commercial Vehicle Test Cycle (CHTC-C). The NEDC consists of four repeated urban driving cycles and an additional urban driving cycle, with a total duration of 1180s. The CHTC-C is used for heavy-duty vehicle fuel consumption and emission testing within the China Automotive Test Cycle, which is more in line with the driving conditions in China than the original C-WTVC. The characteristics of the two test cycles are depicted in Fig. 8, and their features are listed in Table 9.

Fig. 8.

Driving cycles profile: NEDC and CHTC-C.

Table 9.

Comparison of NEDC and CHTC-C.

	Unit	NEDC	CHTC-C
Time	s	1180	1800
Distance	km	11.03	19.62
Maximum speed	km·h−1	120	95.7
Maximum acceleration	m·s−2	1.04	1.25
Maximum deceleration	m·s−2	−1.39	−1.28
Average speed	km·h−1	33.86	39.24
Average acceleration	m·s−2	0.53	0.43
Average deceleration	m·s−2	−0.56	−0.49

3.5. Power management strategy

As illustrated in Fig. 9, the output power of fuel cell $P_{FC}$ and battery $P_{Batt}$ for a bus equipped with an LBAR system can be determined by the power management system, which adopts state machine control. To better allocate the output power of the HT-PEMFC and battery, the required vehicle driving power $P_{Req}$ is divided into three power zones: low-power demand (LPD), medium-power demand (MPD), and high-power demand (HPD) zones. This division is based on the specific fuel cell power $P_{ARReq}$ required by the heating/cooling capacity demand of the LBAR system and threshold power $P_{thres}$, which is equal to the smaller of the maximum power of the fuel cell and battery, $\min \left\{P_{FCmax},P_{Battmax}\right\}$. Within each power zone, corresponding state transition conditions were set based on the battery SOC, dividing it into two modes: battery first (BF) and fuel cell first (FF) output modes.

Fig. 9.

State machine of power management system.

In the LPD zone and FF output mode, the output power of the fuel cell is equal to the required output power $P_{ARReq}$ of the LBAR system, and any insufficient or excess power is provided by the battery or used to charge the battery. When the battery SOC reaches 95 %, it switches to the BF mode. In this mode, the fuel cell supplies power for driving the vehicle while the battery drives a small auxiliary compressor to supplement insufficient cooling or heating capacity. $P_{Comp}$ is the power for the small auxiliary compression air-conditioning system.

In the MPD zone and FF output mode, the fuel cell provides power for driving the vehicle while also charging the battery with charging power $P_{Charge}$. When the battery SOC exceeds 90 %, it switches to the BF output mode. The HT-PEMFC maintains power at the level required by the LBAR system, with any insufficient driving power provided by the battery.

In the HPD zone, when the lithium battery has a high SOC, it outputs power at maximum capacity $P_{Battmax}$, with any remaining power provided by the fuel cell. When the SOC of the HV battery is low, the fuel cell outputs power at maximum capacity $P_{FCmax}$, with any remaining power provided by the battery.

For a vehicle equipped with a CACHP system, the power management strategy is similar to the aforementioned strategy, replacing the power $P_{ARReq}$ required by the LBAR system with a specific power threshold. The purpose is to keep the fuel cell output stable at that power level as much as possible, reducing fluctuations in fuel cell output and improving stack life. When this power is insufficient for driving the vehicle, the battery supplements the shortfall. When this power exceeds the driving power, the excess energy is used to charge the battery.

3.6. Simulation cases

To thoroughly investigate the differences between the two air-conditioning systems under different test cycles, cycle counts, environmental conditions, and passenger loads, comprehensive test cases were formulated, as presented in Table 10. For each test case, the simulation time step was set to 0.2 s, the initial battery SOC was set to 60 %, and vehicles equipped with the two air-conditioning systems were simulated simultaneously. A comparative analysis was conducted on hydrogen consumption, battery SOC, and power system output.

Table 10.

Simulation cases.

Case no.	C/H condition	Driving cycle	No. of cycles	Ambient temperature	Number of passengers
CC1	Cooling	CHTC-C	1x	40 °C	1 driver, 56 passengers
CC2	Cooling	CHTC-C	5x	40 °C	1 driver, 56 passengers
CC3	Cooling	CHTC-C	1x	40 °C	1 driver, 0 passengers
CN1	Cooling	NEDC	1x	40 °C	1 driver, 56 passengers
CN2	Cooling	NEDC	5x	40 °C	1 driver, 56 passengers
CN3	Cooling	NEDC	1x	40 °C	1 driver, 0 passengers
HC1	Heating	CHTC-C	1x	−10 °C	1 driver, 0 passengers
HC2	Heating	CHTC-C	5x	−10 °C	1 driver, 0 passengers
HC3	Heating	CHTC-C	1x	−10 °C	1 driver, 56 passengers
HN1	Heating	NEDC	1x	−10 °C	1 driver, 0 passengers
HN2	Heating	NEDC	5x	−10 °C	1 driver, 0 passengers
HN3	Heating	NEDC	1x	−10 °C	1 driver, 56 passengers

4. Results and discussion

4.1. Simulation results

4.1.1. Cooling mode on CHTC-C driving condition

The test results for CC1 are displayed in Fig. 10, which compares the vehicle speed, fuel cell power, battery power, hydrogen consumption, battery SOC, electrical efficiency and working states in power management system for vehicles equipped with the LBAR and CACHP systems separately.

Fig. 10.

Comparison of LBAR and CACHP in CC1 Simulation: (a) vehicle speed in CHTC-C; (b) FC power $P_{FC}$; (c) battery power $P_{Batt}$; (d) H₂ consumption $m_{H_2}$; (e) battery SOC; (f) efficiency of HT-PEMFC ${\eta }_{FC}$; (g) working states in power management system.

Fig. 10(a) presents the vehicle speed during the simulation. In Fig. 10(b), it can be observed that vehicles equipped with the LBAR system maintain a relatively stable fuel cell output power. When the vehicle driving power demand is low, the fuel cell output is primarily determined by the cooling capacity demand, and any excess electricity generated is stored in the battery to ensure continuous cooling capacity. Vehicles equipped with the CACHP also adopt a similar strategy: charging the battery when the overall power demand is low and the battery SOC is low, and discharging the battery when the overall power demand is high. Fig. 10(c) shows the battery power output. When the power demand for the entire vehicle is low, the battery is in a charging state, preparing for the subsequent high-power operation to provide electrical energy.

Fig. 10(d) indicates that, during the first half of the test cycle, owing to the demand for cooling capacity, the fuel cell must be maintained at a higher power. Vehicles using the LBAR system have slightly higher hydrogen consumption, but the excess electricity generated is stored in the battery, resulting in a faster increase in battery SOC, as displayed in Fig. 10(e). As the vehicle enters the high-speed stage, the battery starts to assist in providing additional power output. Owing to the increased demand for cooling capacity at high speeds, vehicles using the CACHP experience a rapid increase in hydrogen consumption, surpassing those using the LBAR system. As depicted in Fig. 10(f), because vehicles equipped with the LBAR system have a higher fuel cell output power in the earlier stages, the electrical efficiency is relatively low. However, the generated waste heat could be reused, resulting in a smaller overall loss.

Fig. 10(g) presents the power management details during the simulation, and the values of the output power of the HT-PEMFC and battery are determined for both the vehicle's required power and battery SOC. At the beginning of the simulation, both vehicles operate in the LPD zone under the FF output mode (LPD-FF). As the vehicle's required power increases, the state shifts to the MPD zone while still maintaining the FF output mode (MPD-FF). When the simulation reaches 826 s, the battery SOC of the LBAR-equipped vehicle reaches 0.9; thus, the state shifts to the BF output mode in the MPD zone (MPD-BF). The state transition strategy is shown in Fig. 9.

4.1.2. Heating mode under NEDC driving condition

Fig. 11(a) displays the vehicle speed under NEDC driving conditions, while Fig. 11(b) and (c) illustrate the changes in HT-PEMFC output power and battery power during the simulation. Compared with the CHTC-C driving cycle, the NEDC cycle features more concentrated acceleration and deceleration periods, with the vehicle spending most of its time operating at a constant speed. In the HN1 case, where only the driver is present, the vehicle's reduced overall mass leads to lower power requirements.

Fig. 11.

Comparison of LBAR and CACHP in HN1 Simulation: (a) vehicle speed in NEDC; (b) FC power $P_{FC}$; (c) battery power $P_{Batt}$; (d) H₂ consumption $m_{H_2}$; (e) battery SOC; (f) efficiency of HT-PEMFC ${\eta }_{FC}$; (g) working states in power management system.

Under the energy management strategy proposed in this study, vehicles equipped with the CACHP system maintain a relatively constant fuel cell output. Excess energy is stored in the battery and discharged during high-speed driving.

Fig. 11(d)–(f) depict the hydrogen consumption, battery SOC, and fuel cell output efficiency during the simulation. The heat generated by the fuel cell can be utilized by the LBAR to produce hot water, which helps regulate the cabin temperature without consuming additional electricity. Consequently, vehicles equipped with the LBAR system demonstrate lower hydrogen consumption. Fig. 11(g) presents the state transition in the HN1 simulation. Under this condition, since the number of passengers is zero, the overall power requirement of the vehicle is relatively low. Therefore, the power system mainly operates in the LPD zone, with the primary output coming from the fuel cell (LDP-FF).

4.1.3. Results of simulation cases

Table 11 presents the simulation results of the different test cases, including the initial battery SOC, hydrogen consumption (kg and kg per 100 km), reduction in hydrogen consumption, electrical energy efficiency of integrated system ${\eta }_{elec}$ and electrical exergy efficiency ${\psi }_{elec}$.

Table 11.

Simulation results of test cases.

Case no.	Initial SOC	Final SOC $SO{C}_{act}$		Total Hydrogen consumption (kg)		Revised H2 consumption (kg/100 km)		Reduction in hydrogen consumption	Electrical energy efficiency		Electrical exergy efficiency
		LBAR	CACHP	LBAR	CACHP	LBAR	CACHP		LBAR	CACHP	LBAR	CACHP
CC1	0.6	0.787	0.759	1.358	1.535	5.641	6.731	16.20 %	61.23 %	51.31 %	63.96 %	53.60 %
CC2	0.6	0.776	0.811	5.905	7.037	5.774	6.879	16.06 %	59.82 %	50.21 %	62.49 %	52.45 %
CC3	0.6	0.693	0.651	1.063	1.084	4.781	5.171	7.54 %	57.32 %	52.99 %	59.87 %	55.36 %
CN1	0.6	0.792	0.674	0.988	0.994	6.627	8.098	18.17 %	59.10 %	48.36 %	61.74 %	50.52 %
CN2	0.6	0.833	0.715	4.113	4.601	6.854	8.017	14.51 %	57.02 %	48.75 %	59.56 %	50.92 %
CN3	0.6	0.773	0.739	0.818	0.811	5.309	5.655	6.13 %	58.45 %	54.87 %	61.06 %	57.32 %
HC1	0.6	0.769	0.905	1.172	1.422	4.822	5.169	6.70 %	56.82 %	53.02 %	59.36 %	55.38 %
HC2	0.6	0.759	0.632	5.056	5.659	4.933	5.719	13.74 %	56.23 %	48.14 %	58.74 %	50.28 %
HC3	0.6	0.904	0.759	1.604	1.552	6.101	6.818	10.53 %	56.61 %	50.65 %	59.14 %	52.91 %
HN1	0.6	0.721	0.719	0.770	0.838	5.516	6.151	10.32 %	56.26 %	50.45 %	58.77 %	52.70 %
HN2	0.6	0.725	0.738	3.369	3.791	5.772	6.503	11.23 %	54.78 %	48.34 %	57.23 %	50.50 %
HN3	0.6	0.708	0.676	0.934	0.993	7.151	8.078	11.47 %	54.76 %	48.48 %	57.21 %	50.65 %

Owing to the potential variation in battery SOC at the end of different numbers of test cycles, resulting in different battery SOC values for the two types of vehicles, discrepancies in the calculation of the reduction in hydrogen consumption may exist. Therefore, the electricity surplus or deficit in both vehicle batteries is converted into hydrogen consumption based on the average fuel cell efficiency ${\bar{\eta }}_{FC}$, considering the battery charging efficiency ${\eta }_{charge}$ and discharging efficiency ${\eta }_{discharge}$. The corrected equations for hydrogen consumption per 100 km and the reduction in hydrogen consumption are as follows (note that the values in the table are the corrected results):

$$\epsilon =\frac{m_{LBAR}-\Delta m_{LBAR}}{m_{CACHP}-\Delta m_{CACHP}}\times 100\%$$ (71)

where $m_{LBAR}$ and $m_{CACHP}$ represent the actual hydrogen consumption of the two vehicles, $\Delta m_{LBAR}$ and $\Delta m_{CACHP}$ denote the converted hydrogen quantity from the electricity surplus or deficit, as obtained by

$$\Delta m_j=\{\begin{array}{c}\frac{\left(SO{C}_{act}-0.6\right)\cdot Q_{batt}\cdot 3.6\times {10}^6}{{\bar{\eta }}_{FC}\cdot {\eta }_{charge}\cdot LH{V}_{H_2}},SO{C}_{act}>0.6\\ \frac{\left(SO{C}_{act}-0.6\right)\cdot Q_{batt}\cdot 3.6\times {10}^6\cdot {\eta }_{discharge}}{{\bar{\eta }}_{FC}\cdot LH{V}_{H_2}},SO{C}_{act}<0.6\end{array}$$ (72)

where $SO{C}_{act}$ is the actual SOC of the battery, $Q_{batt}$ is the total energy of the battery, which is equal to 20 kWh, and $LH{V}_{H_2}$ is the lower heating value of hydrogen. The average efficiency of the fuel cell ${\bar{\eta }}_{FC}$ is obtained from the ratio of the electricity provided by the fuel cell to the generated heat.

$${\bar{\eta }}_{FC}=\frac{\int P_{FC}dt}{\int P_{FC}dt+\int {\dot{Q}}_{stack}dt}$$ (73)

Based on the simulation results in Table 11, the following conclusions can be drawn.

• ●Under the CHTC-C and NEDC conditions, using an LBAR system can reduce hydrogen consumption by 6.13–18.17 % compared with vehicles using the CACHP system.
• ●Using the LBAR improves the electrical energy efficiency of the integrated system by 3.58–10.74 % under different driving cases, while the electrical exergy efficiency increases by 3.74–11.22 %.
• ●Under the cooling conditions of summer, the reduction in hydrogen consumption by the LBAR system slightly decreases during extended driving, whereas in the heating conditions of winter, the opposite trend is observed.
• ●Under both driving cycle conditions, the reduction in hydrogen consumption during summer cooling is greater than that during winter heating, indicating that the LBAR system is more advantageous for summer cooling.

Based on the above simulation results, this study further investigated the effects of driving cycle count and number of passengers on the two air-conditioning systems under different working conditions and modes. For easier presentation in the following sections, "C" and "H" are used to represent cooling and heating modes, respectively, while "C" and "N" denote the CHTC-C and NEDC driving conditions, respectively.

4.2. Effect of driving cycle counts

An initial SOC of 60 % was maintained, with cooling and heating ambient temperatures set at 40 °C and −10 °C, respectively, and all passenger seats occupied. Fifteen driving cycles were simulated, and the corrected results for hydrogen consumption reduction at the end of each cycle are shown in Fig. 12(a). The graph indicates that the reduction in hydrogen consumption under heating conditions is relatively low during the initial cycles. With an increase in the number of cycles, the reduction in H₂ consumption for the LBAR-equipped vehicle compared with the CACHP-equipped vehicle increases and gradually stabilizes. Under cooling conditions, this value is stable and exhibits minimal variations in different cycles. However, it is also indicated that during long-distance travel, LBAR has a more significant advantage over CACHP. The COPs, thermal energy efficiency ${\eta }_{ther}$, and thermal exergy efficiency ${\psi }_{ther}$ were categorized into two types, namely, heating efficiency and cooling efficiency, depending on the working mode. Fig. 12(b) reveals that an increase in the number of driving cycles has a minimal impact on the equivalent COP for both systems. The effect of driving cycles on the electrical energy efficiency of the vehicle is displayed in Fig. 12(c). The recovery of waste heat through the LBAR system significantly improves the vehicle's electrical energy efficiency. Under summer cooling conditions, the fuel cell output remains relatively stable to satisfy the cooling capacity, operating within the high-efficiency range of the HT-PEMFC. Consequently, the equivalent electrical energy efficiency is higher under summer cooling conditions than under winter heating conditions. Fig. 12(d) depicts the thermal energy efficiency of the vehicle. Because of the lower overall hydrogen consumption, the thermal energy efficiency of the LBAR-equipped vehicle is significantly higher than that of the CACHP-equipped vehicle.

Fig. 12.

Effects of cycle counts on vehicle performance parameters.

Fig. 12(e) shows the electrical exergy efficiency of the vehicle. Because the exergy coefficient for electrical energy is 1, it follows the same trend as the electrical energy efficiency. The effect of the driving cycles on the thermal exergy efficiency is illustrated in Fig. 12(f). The exergy of the heat stream is related to the temperature difference between the hot/chilled water and the environment. Once the cabin temperature stabilizes, the Carnot coefficient also tends to stabilize.

4.3. Effect of number of passengers

From the aforementioned tests, it can be observed that after five cycles, the reduction in hydrogen consumption stabilizes. Therefore, this research maintained the driving cycle count at five and studied the impact of different

numbers of passengers on the reduction in hydrogen consumption. The results are shown in Fig. 13(a). In the cooling mode, with an increase in the number of passengers, the reduction in hydrogen consumption increases, regardless of the cycle type (NEDC or CHTC-C). In the heating mode, the reduction in hydrogen consumption in the CHTC-C cycle decreases with an increase in the number of passengers. According to the thermodynamic model of the cabin, a larger number of passengers implies a higher fresh air ventilation volume and more metabolic heat. In the summer cooling mode, when the outside air temperature is higher than the cabin temperature, the increased ventilation volume and metabolic heat load increase the cooling capacity demand of the air-conditioning system. In the winter heating mode, the metabolic heat generated by passengers can also increase the cabin temperature, offsetting the cooling load caused by the low ambient air temperature. The trend of initially decreasing and then increasing in the NEDC cycle indicates that the increased cooling load, owing to the higher ventilation volume throughout the cycle, outweighs the effect of the increased metabolic heating load.

Fig. 13.

Effect of passenger numbers on vehicle performance parameters.

Fig. 13(b) presents the COPs for both the LBAR and CACHP systems. For the LBAR system, the heating COP increases slightly as the number of passengers rises, whereas the cooling COP decreases slightly. Fig. 13(c) shows the effect of the number of passengers on the electrical energy efficiency. In the cooling mode under CHTC-C driving cycle, the electrical energy efficiency of LBAR-equipped vehicle increases from 56.61 % to 59.53 % when the number of passengers increases, with an improvement of 4.13–9.26 % compared with CACHP-equipped vehicle. In the cooling mode, an increase in the number of passengers for the LBAR-equipped vehicle results in a higher HT-PEMFC output power. Initially, the fuel cell output efficiency improves but begins to decline after reaching its peak. In contrast, for the CACHP-equipped vehicle in the cooling mode, the rise in the number of passengers not only increases the power required for driving $P_{Req}$ but also leads to greater electricity consumption for cooling, causing a significant reduction in the overall electrical energy efficiency. In the heating mode, an increase in the number of passengers raises the power required for driving but simultaneously reduces the required heating capacity. As a result, the change in electrical energy efficiency is relatively minor. The effect of the number of passengers on the thermal energy efficiency is displayed in Fig. 13(d). The cooling energy efficiency rises with an increase in the number of passengers, whereas the heating energy efficiency decreases. Fig. 13(e) and (f) show that the variation trends in the electrical and thermal exergy efficiencies owing to changes in the number of passengers are relatively similar with energy efficiencies. In the cooling mode under CHTC-C driving cycle, the electrical exergy efficiency of LBAR-equipped vehicle increases from 59.14 % to 62.19 %, with an improvement of 4.32–9.67 % compared with CACHP-equipped vehicle.

In summary, in the cooling mode, as the number of passengers increases, the LBAR-equipped vehicle can save more hydrogen than the CACHP-equipped vehicle, thus improving the overall vehicle economy. In the heating mode, the extent of hydrogen savings depends strongly on the balance between the changes in HT-PEMFC output efficiency and variations in the required heating capacity of the vehicle owing to the increase in the number of passengers.

5. Conclusion

This study simulated the HT-PEMFC, LBAR system, vehicle cabin thermodynamic model, and CACHP system. The NEDC and CHTC-C were selected as the driving cycles. Simulations were conducted for long-distance buses equipped with two different air-conditioning systems under summer cooling and winter heating conditions to investigate their hydrogen consumption under various scenarios.

Through a comprehensive simulation analysis involving different driving cycles, cycle counts, operating modes, and passenger loads, the following conclusions were drawn.

• ⁃Vehicles equipped with the LBAR system can better utilize the heat generated during operation of the HT-PEMFC, thereby improving the overall energy utilization efficiency of the vehicle. Compared with CACHP-equipped vehicles, those equipped with the LBAR system can save 6.13–18.17 % of hydrogen.
• ⁃Using the LiBr ARS improves the electrical energy and exergy efficiencies of the integrated system by 3.58–10.74 % and 3.74–11.22 %, respectively, under different driving cases.
• ⁃Vehicles with the LBAR system demonstrate advantages during long-distance travel. However, as the cycle count increases, the reduction in hydrogen consumption tends to stabilize.
• ⁃As the number of passengers increases, the electrical energy and exergy efficiencies of the LBAR-equipped vehicle in the cooling mode under the CHTC-C driving cycle increase from 56.61 % to 59.53 % and from 59.14 % to 62.19 %, respectively. Compared with the CACHP-equipped vehicle, the electrical energy and exergy efficiencies improve by 4.13–9.26 % and 4.32–9.67 %, respectively.
• ⁃With increasing number of passengers, both the cooling energy and exergy efficiency of the two integrated systems increase, whereas the heating energy and exergy efficiency decrease.

In summary, the LBAR-equipped vehicle demonstrates superior overall performance compared with the CACHP-equipped vehicle, significantly enhancing fuel utilization and vehicle economy. However, some limitations should be addressed in future studies.

• ⁃The LBAR system relies on high-temperature cooling water generated by high-temperature fuel cells for operation. Therefore, it can function only when high-temperature fuel cells are in operation and lacks the ability for cold starts. To overcome this limitation, future research can introduce absorption thermal energy storage systems. Using this system, the excess waste heat generated by high-temperature fuel cells can be effectively stored, providing the necessary thermal energy for the air-conditioning system during cold starts or when the vehicle is parked.
• ⁃In this study, the employed state machine control method did not comprehensively consider the working efficiency between various components. In future research, more precise and excellent power management strategies should be explored.

CRediT authorship contribution statement

Ke Song: Writing – review & editing, Supervision, Project administration, Methodology, Funding acquisition, Conceptualization. Zhen Cai: Writing – original draft, Validation, Software, Methodology. Xing Huang: Validation, Data curation. Haoran Ma: Methodology, Investigation. Yanju Li: Validation, Software. Pengyu Huang: Investigation, Data curation. Boqiang Zhang: Writing – review & editing, Validation, Methodology.

Ethics statement

Not applicable.

Data availability statement

Data will be made available on request.

Declaration of competing 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.