Design, Modeling and Analysis of a PEM Fuel Cell Excavator with Supercapacitor/Battery Hybrid Power Source

Abstract

The objective of this study was to design and model the PEM fuel cell excavator with supercapacitor/battery hybrid power source to increase efficiency as well as eliminate greenhouse gas emission. With this configuration, the system can get rid of the internal combustion engine, which has a low efficiency and high emission. For the analysis and simulation, the governing equations of the PEM system, the supercapacitor and battery were derived. These simulations were performed in MATLAB/Simulink environment. The hydraulic modeling of the excavator was also presented, and its model implemented in AMESim and studied. The whole system model was built in a co-simulation environment, which is a combination of MATLAB/Simulink and AMESim software. The simulation results were presented to show the performance of the system.

Nomenclature

H₂ : Hydrogen

O₂ : Oxygen

H₂O : Water

e^- : Electron

FCS: Fuel cell stack

1. Introduction

Construction excavators play an important role in construction site. Due to the environmental pollution and the lack of fossil fuel, many researches have been focusing on saving energy and reducing emission with respect to construction excavators^1-4). The internal combustion engine (ICE) excavator has shown low energy efficiency, limited working torque and speed range, noise and a lot of emissions. Thus, ICE type excavator has been recently replaced by the hybrid type^5-14). Hydraulic hybrids excavators are energy-effective with good power performance and fuel economy^8-14). However, the excavators are still using an engine which is not ‘green’ power sources and cannot get rid of the carbon emission. Fuel cell (FC) power sources have shown great performance and become a successful application when applied to fuel cell vehicles^15-17). Yi et al. suggested that we can replace the traditional diesel/gas ICE by fuel cells system in construction excavator¹⁸⁾. The advantages of Proton-exchange membrane (PEM) fuel cell are high energy conversion efficiency, different size available, low chemical pollution, quiet operation, low running costs, and lower weight and volume than conventional batteries for electric powered vehicles. The efficiency of fuel cell hybrid excavators is also high, and it produces zero emission. Thus, fuel cell power source has gained great interest in the potential application of fuel cells to construction equipment^18-21).

Two different configurations have been proposed by Yi¹⁸⁾ using fuel cell-battery and Li^19-21) using fuel cell-supercapacitor. These researches used the simulation model to obtain the performance of the proposed system. However, these studies only used a simplified model of the fuel cell system and did not provide a sufficient model of the excavator. This reduces the reliability of the research results.

This paper proposes a configuration of a PEM fuel cell excavator with supercapacitor/battery hybrid power source. A fully dynamic model of the fuel cell system which deeply concerns the mechanism of the system is studied and analyzed. Supercapacitor (SC) and battery (BAT) mathematical model are also presented. These simulations are performed in MATLAB/Simulink environment. A hydraulic model of an excavator is presented, and its model is implemented in AMESim and studied. A model of the whole system is built in a co-simulation environment, which is a combination simulation of AMESim software and MATLAB/Simulink software. System working performance is also presented and discussed.

The rest of the paper is organized as follows. The proposed system is shown and discussed in Section 2. The system modeling which includes fuel cell, supercapacitor, battery model coupled with excavator hydraulic power model is presented in Section 3. Simulation results and analyses of the system performance are shown in Section 4. Conclusions are presented in Section 5.

2. System structure and principle

The proposed system structure of PEM fuel cell excavator is shown in Fig. 1. The system is divided into two parts: power sources and hydraulic excavator. The main power source PEMFC stack includes hydrogen tank, normal valve, motor, compressor, fuel cell stack, inverter and cooling system as shown in Fig. 2; supercapacitor and battery are used as the auxiliary energy storage devices. The FC stack cannot provide instant responses to sudden variations in the load demand of the excavator. It is the reason that the supercapacitor is used. A battery is installed to store the regenerative power produced during return action of excavator actuators or swing brake motion. Fuel cell uses hydrogen fuel and oxygen from the air to produce electricity. This energy is transferred and managed by the converter which plays the role as the brain of the system. The hydraulic system of PEM fuel cell excavator essentially involves an electric motor, a hydraulic pump, directional valves, and cylinders. The hydraulic power is supplied by the hydraulic pump driven by the electric motor. The movement of actuators is controlled by the directional valves which are received the control signal from the operator.

Fig. 1 System structure of PEM fuel cell excavator

Fig. 2 shows the working principle of PEM fuel cell. Hydrogen fuel is supplied from the hydrogen tank to the anode, while the oxygen from the air goes to the cathode of the fuel cell stack. At the anode, a platinum catalyst causes the hydrogen to split into positive hydrogen ions and negatively charged electrons. The Polymer Electrolyte Membrane (PEM) allows only the positively charged ions to pass through it to the cathode. The negatively charged electrons must travel along an external circuit to the cathode, create an electrical current. At the cathode, the electrons and positively charged hydrogen ions combine with oxygen to form water, which is used for a cooling system.

Fig. 2 Fuel Cell Stack system

3. System modeling

3.1 Supercapacitor mode

The model of supercapacitor in this paper is shown as Fig. 3. A MATLAB simulation model is showed as Fig. 4^22)..

Fig. 3 Supercapacitor simplified model

The equation for circuit on Fig. 3 can be described as the following equation²²⁾:

\(U_{s c}=N_{s_{-} s c}\left(v_{1}+R_{1} \frac{I_{s c}}{N_{p_{-} s c}}\right)\)       (1)

Where:

U_sc and I_sc are the voltage and current of the pack supercapacitor

v_sc and i_sc are the voltage and current of elementary supercapacitor

The voltage of secondary capacity C₂:

\(v_{2}=\frac{1}{C_{2}} \int \frac{1}{R_{2}}\left(v_{1}-v_{2}\right) d t\)       (2)

The instantaneous charge of C₂:

\(Q_{2}=\int i_{2} d t\)       (3)

The current of main capacitor:

\(i_{1}=i_{s c}-i_{2}\)       (4)

We can describe i₁ into the charge of Q₁:

\(i_{1}=C_{1} \frac{d v_{1}}{d t}=\frac{d Q_{1}}{d t}=\left(C_{0}+C_{v} v_{1}\right) \frac{d v_{1}}{d t}\)       (5)

The formula for Q₁ and v₁:

\(Q_{1}=C_{0} v_{1}+\frac{1}{2} C_{v} v_{1}^{2}\)       (6)

Fig. 4 MATLAB simulation model of Supercapacitors pack

3.2 Fuel cell model

- Electrochemical model The electrochemical reactions at the anode and cathode are showed as below^23-25):

Anode:

          \(H_{2} \leftrightarrow 2 H^{+}+2 e^{-}\)       (7)

^Cathode:

\(\frac{1}{2} O_{2}+2 H^{+}+2 e^{-} \leftrightarrow H_{2} O\)       (8)

Overall:

\(H_{2}+\frac{1}{2} O_{2} \leftrightarrow H_{2} O+H e a t\)       (9)

The output voltage of a single fuel cell can be defined by the following equation:

\(V_{\text {cell}}=E_{\text {Nernst}}-V_{a c t}-V_{\text {ohmic}}-V_{\text {conc}}\)       (10)

Where:

E_Nernst is thermodynamic potential

V_act is activation overvoltage

V_ohmic is the ohmic overvoltage

V_conc is the concentration overvoltage

The total voltage is created by combining the number of cell N as below:

\(V_{\text {stack}}=N V_{\text {cell}}\)       (11)

- Thermodynamic Potential

The equation for thermodynamic potential is displayed as following: 

\(E_{\text {Nermst }}=E^{O}+\frac{R T}{n F} \ln \left[p_{H_{2}}^{\prime}\left(p_{O_{2}}^{\prime}\right)^{0.5}\right]\)       (12)

Where:
E^O is the reference potential at unity activity

\(p_{H_{2}}^{\prime}, p_{O_{2}}^{\prime}\)represent the hydrogen and oxygen pressure, respectively

T is the cell temperature (K)

R is the universal gas constant (8.314 Jmol-1K-1)

F is Faraday constant

We can express ENernst as below:

\(\begin{aligned} E_{\text {Nermst }} &=1.229-8.5 \times 10^{-4}(T-298.15) \\ &+\frac{R T}{2 F} \ln \left[p_{H_{2}}^{\prime}\left(p_{o_{2}}^{\prime}\right)^{0.5}\right] \end{aligned}\)         (13)

- The activation overvoltage

The activation overvoltage can be described as equation following:

\(\eta_{a c t}=\xi_{1}+\xi_{2} T+\xi_{3} T\left[\ln \left(c_{o_{2}}\right)\right]+\xi_{4} T[\ln (i)]\)       (14)

We have four coefficients:

\(\begin{array}{l} \xi_{1}=-0.948 \\ \xi_{2}=0.00286+0.0002 \ln (A)+4.3 \times 10^{-5} \ln \left(c_{H_{2}}\right) \\ \xi_{3}=7.6 \times 10^{-5} \\ \xi_{3}=-1.93 \times 10^{-4} \end{array}\)           (15)

The following equations can be used for the reaction concentrations at the electrodes:

\(c_{O_{2}}=p_{o_{2}}^{\prime} \times 1.97 \times 10^{-7} \exp \left(\frac{498}{T}\right)\)       (16)

\(c_{H_{2}}^{\prime}=p_{H_{2}}^{\prime} \times 9.174 \times 10^{-7} \exp \left(\frac{-77}{T}\right)\)       (17)

The derivation of a positive term is:

  _{\(V_{a c t}=-\eta_{a c t}\)}       (18)

\(R_{a c t}=\frac{V_{a c t}}{i}\)       (19)

\(\frac{d V_{a c t}}{d t}=\frac{i}{C_{d l}}-\frac{V_{a c t}}{R_{a c t} C_{d l}}\)       (20)

With C_dl is the double layer capacitance of a single cell

- The ohmic overvoltage

The ohmic overvoltage of the system is calculated as the following equation:

\(V_{\text {ohmic}}=i R_{\text {int}}\)       (21)

With R_int is the internal resistance of electrolyte membrane

Or we can describe the equation (21) by using r_M(Ωm) is the membrane resistivity and I_mem is the thick ness of membrane (cm):

\(R_{i n t}=\frac{r_{M} l_{m e m}}{A}\)       (22)

In this case, we can use:

\(r_{M}=\frac{181.6\left[1+0.03\left(\frac{i}{A}\right)+0.062\left(\frac{T}{303}\right)^{2}\left(\frac{i}{A}\right)^{2.5}\right]}{\left[\lambda-0.634-3\left(\frac{i}{A}\right)\right] \exp \left[4.18\left(\frac{T-303}{T}\right)\right]}\)       (23)

- The concentration overvoltage

The concentration overvoltage is calculated as:

\(V_{\text {conc}}=\frac{R T}{n F} \ln \left(\frac{(i / A)_{L}}{(i / A)_{L}-(i / A)}\right)\)       (24)

- The reactant flow model

The reactant flow model for anode is given by the following equation:

\(\frac{V_{a}}{R T} \frac{d p_{H_{2}}^{\prime}}{d t}=\dot{m}_{H_{2}, i n}-\dot{m}_{H_{2}, o u t}-\dot{m}_{H_{2}, \text { used }}\)       (25)

With \(V_{a}, \dot{m}_{H_{2}, i n}, \dot{m}_{H_{2}, \text {out}}\) are the anode volume, hydrogen inlet, and hydrogen outlet flow-rates through fuel cell stack. Or we can use a similar equation:

\(\frac{V_{a}}{R T} \frac{d p_{H_{2}}^{\prime}}{d t}=\dot{m}_{H_{2}, i n}-\dot{m}_{H_{2}, o u t}-\frac{N i}{2 F}\)       (26)

We can modify (30) by using k_a is the flow constant for the anode as below:

With:

  \(\dot{m}_{H_{2}, \text {out}}=k_{a}\left(p_{H_{2}}^{\prime}-p_{\text {tan } n k}\right)\)       (27)

Similar to cathode, we have:

 \(\frac{V_{c}}{R T} \frac{d p_{o_{2}}^{\prime}}{d t}=\dot{m}_{O_{2}, \text {in}}-\dot{m}_{O_{2}, \text {out}}-\dot{m}_{O_{2}, \text {used}}\)       (28)

With  \(V_{a}, \dot{m}_{O_{2}, i n}, \dot{m}_{O_{2}, o u t}\) are the anode volume, hydrogen inlet, and oxygen outlet flow-rates through fuel cell stack

 \(\frac{V_{c}}{R T} \frac{d p_{o_{2}}^{\prime}}{d t}=\dot{m}_{O_{2}, i n}-\dot{m}_{O_{2}, o u t}-\frac{N i}{4 F}\)       (29)

And:

  \(\dot{m}_{O_{2}, o u t}=k_{c}\left(p_{O_{2}}^{\prime}-p_{B P R}\right)\)       (30)

The total power input of the system:

\(P_{\text {tot}}=\dot{m}_{H_{2}, \text { used }} \Delta H=\frac{N i}{2 F} \Delta H\)       (31)

We have △H is the enthalpy of combustion for hydrogen

And the electrical output is:

\(P_{\text {elec}}=V_{\text {stack}} i\)       (32)

3.3 Battery model

The controlled voltage source is described by²⁶⁾:

\(E=E_{0}-K \frac{Q_{\max }}{Q_{\max }-i t}+A e^{(-B i t)}\)       (33)

The battery voltage:

\(V_{b a t t}=E-R i\)       (34)

The charge stored in battery:

\(Q=Q\left(t_{0}\right)-\int_{t_{0}}^{t} i d \tau\)       (35)

The battery power:

\(P_{\text {batt}}=V_{\text {batt}} i\)       (36)

The state of charge of the battery:

\(S O C=\frac{Q}{Q_{\max }}\)       (37)

3.4 Excavator hydraulic model

The outlet pressure and flow rate of the hydraulic pumps can be used to calculate the demand power of the hydraulic system P_p , as follows:

\(P_{p}=\frac{p_{i}(t) q_{i} n_{i}(t)}{60 \eta_{i}(t)}\)       (38)

Where p_i , q_i , n_i , and η_i denote the pressure, displacement, efficiency, and rotational speed of the hydraulic pump, respectively. The energy-balance equations are established for the electrical motors considering their operational efficiency. The demand power of the electric motor can be estimated as follows:

\(P_{M}=\frac{P_{p}}{\eta_{M}}\)       (39)

Where P_M is the power demand of the motor driving the hydraulic pump;  η_M denotes the working efficiency of the motor.

4. Simulation results and discussion

In this section, some simulations are described to show the power combination between PEM fuel cell and supercapacitor supply for a required power in a working cycle of the excavator. These simulations are implemented by using a co-simulation between AMESIM 15.2 and MATLAB 2017a with a sampling time of 10ms. The co-simulation structure which is shown in Fig. 5 includes two parts: one is the hydraulic part, and other is the power source part which includes PEM fuel cell, battery and supercapacitor. In the system dynamics group, an S-function block is used to import the excavator dynamics which is set up in the AMESIM 15.2 as presented in Fig. 6.

 

Fig. 5 Co-simulation structure

Fig. 6 Excavator AMESim hydraulic model

The movement simulation of excavator is carried out in a working cycle. First, the arm cylinder moves down to stretch the dipper and the bucket cylinder lifts the tipping to prepare for the digging process. Next, the boom cylinder moves down the arm to touch the objective. The bucket cylinder is extended to dig the ground. After that, the boom cylinder moves up to lift the load out of the original position. The swing system will rotate the system to the new place where the excavator can shed the load. After unloading, the swing rotates to return to the previous position. The arm cylinder moves up to return the dipper to the first position. The trajectory simulation of the excavator is shown in Fig. 7. In the working process, the excavator does a lot of motions which depend on the requirement of the operators. Hence, this paper only chooses an example motion of excavator in a working cycle. Based on this trajectory simulation, the required power is estimated by AMESim simulation and shown in Fig. 8. With this result, the parameters of PEMFC, supercapacitor and battery are designed to choose exactly the size of each component. The parameters of the PEM fuel cell used in the simulation are described in Table 1-3. The parameters of the real excavator applied to simulation model are presented in Table 4.

Fig. 7 Excavator trajectory of swing, boom, arm and bucket

 Table 1: Fuel cell system parameters

Table 2: Fuel cell model parameters

Table 3: Parameters for the reactant flow models

 Table 4: Parameters for the excavator model

According to Fig. 8, the performance of the total required power (P_total) varies depending on the tasks requested (for instance at the 5^th second, the arm starts moving that requires the system power to switch from a low power to a very high power in a very short time).

Fig. 8 Required power of the excavator

We suppose that the fuel cell (FC) can provide nominal of power at 65 kW. As can be seen in Fig. 9, the dash-dot line indicates the nominal power reference, and the rest one is for the maximum simulated power supplied by the FC. The energy losses between the reference and the simulated power in the FC due to the structure, temperature fluctuation, humidifier, and pressure during operation. In the first of 5 seconds, the power required from the excavator is less than the power supplied from the FC, then an excess power is used to charge the SC. As the necessary power exceeds the capacity of the FC at the 5^th second, the SC enters the system and boosts the excavator to finish its tasks. The performance of the supercapacitor (SC) is described in Fig. 10. The dash-dot line represents for the SC required power (extracted from the difference between the P_total and P_{FC_n}) and the solid line is for the power generated from the SC. Positive values indicate that the SC is in discharging mode and releasing power to the excavator, whereas negative value is charging mode and storing energy. The supercapacitor state of charge (SoC_SC) during performing is depicted in Fig. 11. Corresponding to the performance of the power supercapacitor (P_SC), the SoC_SC increases when receiving more energy from the fuel cell and decreases when releasing energy to the excavator. The total power of fuel cell and supercapacitor is shown in Fig. 12. As shown in this figure, the actual power can track the required value. This validates the effect of the proposed system.

Fig. 9 Fuel cell required power and simulated output power

Fig. 10 Supercapacitor required power

Fig. 11 Supercapacitor state of charge

Fig. 12 Total power of fuel cell and supercapacitor

5. Conclusion

This paper proposed a novel design of the PEM fuel cell excavator with supercapacitor/battery hybrid power source as a method to improve excavator efficiency and cut down to zero the greenhouse emission. The dynamic model of PEM fuel cell, supercapacitor and battery is presented and discussed. The hydraulic model of the excavator is also presented. Based on these models, a co-simulation of the whole system is implemented. The simulation results validate the performance of the proposed system. Future works will consider the control aspect of the system and energy management strategy for improving efficiency and reducing fuel consumption.