Operating State Place

The operating state will contain the performance data from a FC model by Fly, et al [63]. It uses a model based upon Equation 1.8, using; Enernst, ηact,a, ηact,c, ηf c, ηohmic and ηconcentration.

Enernst is found for a PEMFC with liquid product, considering temperature and pressure dif-

ferences. The Tafel equation (Equation 1.9) is used for ηact,a, ηact,c and ηf c overpotentials.

ηconcentration values are determined from an empirical exponential relationship, and the re-

maining ηohmic value is determined from a membrane hydration model.

A PEMFC performance model was integrated into the Petri-Net degradation model, which increases the accuracy of the predictions made by the degradation model over using simple FC equations. A 1D dimensional FC model developed by Fly & Thring [64] is used to predict FC behaviour based upon key operational parameters. Sub-systems of the FC are modelled in separate blocks using Simulink including voltage, hydration, mass and energy balances, and are discusse din more detail below.

The key output from the 1D model is that of the voltage for the cell. This is what is modified by the degradation model to show a drop in performance.

Cell Voltage

The cell voltage is calculated using Equation 1.8 in section 1.6 using the OCV, and subtracting the losses due to activation, ohmic, mass transport and fuel crossover losses. OCV is found using Equation 1.5, whereas the activation and fuel crossover losses are found using the Tafel equation (Equation 1.9). The mass transport losses are determined by empirical exponential relationships, whereas ohmics losses come from the membrane hydration model block. The resulting voltage profile and potential loss mechanisms are shown in Figure 5.2.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0 0.2 0.4 0.6 0.8 1 1.2

Current density [A/cm2]

Voltage [V] V cell E n V act V fc V trans V ohm

Figure 5.2: Cell voltage polarisation curve [65].

Hydration

The hydration of the membrane, which is paramount to the performance of the cell/stack, is calculated from the empirical model of Springer, et al. [18]. This includes the effects of electro- osmotic drag and back diffusion across the membrane.

Mass Balance

The anode and cathode are modelled separately as lumped volumes, and the mass of each gas is calculated from the first order differential mass balances in equations 5.1 - 5.5.

Cathode

dmN2

dt = ˙mN2in− ˙mN2out (5.1)

dmO2

dt = ˙mO2in− ˙mO2out− ˙mO2reac (5.2)

dmH2O

Anode

dmH2

dt = ˙mH2in− ˙mH2out− ˙mH2reac (5.4)

dmH2O

dt = ˙mH2Oin− ˙mH2Oout+ ˙mH2Otrans (5.5)

Where m is the mass of the gas species,in shows the species in,out shows the species out, reac is the electrochemical reaction energy, andtransis the transport loss.

Energy Balance

The temperature of the FC is calculated using a single thermal capacitance model as shown in equations 5.6 & 5.7.

msCps

dTs

dt = ˙Qreac− ˙Qelec+ ˙Qin− ˙Qout− ˙Qloss (5.6) ˙ Q = ˙mH2Ov∆Hv+ n X j=1 ˙ mjCpj(T − T0) (5.7)

Where msis the mass of the stack, Cpsis the specific heat, ˙Qreac is the heat released during

the reaction, ˙Qelec is the electrical power generated by the cell/stack, ˙Qinand ˙Qout represent

the heat flows into and out of the cell/stack, ˙Qloss is a term to represent the small amount of

energy lost from the cell/stack surface due to natural convection, and Hv is the enthalpy of

water vapour.

1D model overview

Figure 5.3 shows how these separate blocks interlink to give the FC voltage based upon an input current. Cell voltage is determined in the ‘stack voltage’ block, hydration is determined in the ‘membrane hydration’ block, the anode and carthode mass balance equations are calculated in the ‘cathode model’ and ‘anode model’ blocks, and the energy balance is determined in the ‘thermal module’ block. The current is fed into the model and is the determining factor for the calculations. The cathode and anode blocks take the current, and determining variables from Equations 5.1 - 5.5. The membrane hydration block uses the product of the mass balance equa- tions to calculate the resistance of the MEA, and feeds back data into the anode and cathode mass balance blocks. The resistance values feed directly into the stack voltage calculation block, with its product being the stack power. The thermal block takes outputs from all of the other blocks for its calculations.

The 1D model used is a highly complex model that is computationally intensive. As to reduce the computational time required to solve the model, certain aspects that were not required for the purposes of degradation were removed from the model. A significant area of improvement in the reduction of calculation time was achieved by removing the hybrid battery model. Automotive PEMFCs are always hybridised with conventional battery systems as to help with regenerative braking and load smoothing. However, for this work, precise control over the PEMFC current and voltage was required and therefore the battery system model was deemed redundant. Removal of this sub-system increased calculation time significantly.

A large section of the anode model was removed that calculated the mass flow of water in to the anode. This section was replaced with a more simple calculation of this value that doesn’t effect the outcome of the performance model. The more complex calculations were used by the creators of the 1D model to calculate heat transfer, and is not required for this work.

Additionally, simplifications were made to the RH calculations that gave a greater amount of control over the values if required. Simplifications were also made to the cathode model sub-blocks to reduce the computational time required while still retaining accuracy.

The 1D model runs in Simulink software which means that the calculations vary per real world second which could skew degradation results. Therefore the time-step was smoothed out to only offer values for the degradation model to handle at one second time-steps.

Figure 5.3: Modified simulink model of 1D FC model [65]

Model Parameters

The FC performance model is run based upon initialisation data that sets key variables as listed in Table 5.1. These data are the input data that are required before the running of the cell, and are representative of the type of FC being modelled, and are used in the equations that determine the FC performance during operation. The model can be run either in a steady state load or dynamic load mode, indicative of a drive cycle to match what would be required in an automotive environment.

The values presented in Table 5.1 are either representative of the test rig materials or common operational conditions used in the industry. ‘Test cell’ denotes that the value is inherent from the MEA used, ‘Standard’ denotes that it is common practise, ‘Test rig’ means that the value is set due to the rig itself, ‘FC model’ shows that the value is taken from the FC model by Fly & Thring [65], and ‘Calculated’ means that the value was derived from an equation for the specific MEA.

Table 5.1: Simulation parameters

Parameter Value Justification Fuel cell

Fuel cell rated power 67W Test cell

Number of cells 1 Test rig

Cell active area 200cm2 Test rig Cathode stoichiometry 2.5 Standard Anode stoichiometry 1.5 Standard Ambient humidity 55% Test rig Membrane thickness (z) 27.5µm Test cell Internal current density (in) 1.5 × 10−4A/cm2 FC model

Mass transport coefficient (atrans) 3 × 10−4 FC model

Mass transport coefficient (btrans) 3.0 FC Model

Exchange current density at STP (ioc,0) 3.2 × 10−8A/cm2 FC Model

Water entrainment constant (δ) 2.0 FC model Molar mass membrane (Mmem) 1.1 kg/mol FC Model

Dry density membrane (ρdry) 1.98g/cm3 FC Model

Cathode activation energy (Ec) 66kJ/mol Standard

Resistance Correction Factor 1.62 Calculated

The resistance correction factor is used to modify the membrane resistance to accurately represent the membrane and GDL used for comparison. The model uses the resistance value of 68.68mS/cm for the Nafion 117 membrane and no GDL resistance. The correction factor is based upon the Nafion XL membranes conductivity of 50mS/cm which is used in the experimentation, and the GDL resistance due to compression of an additional 0.018/cm2 [66] calculated based upon the resistivity of the GDL material and the clamping force applied to the end-plates of the test rig.

This modification of the 1D model is paramount to increasing the accuracy of this work. The output of the 1D model is heavily influenced by the thickness of the membrane, and thus, the resistance of said membrane. One of the main ways in which to increase the performance of a PEMFC is to reduce the thickness of the membrane, and therefore reduce the resistance value. However, a balance needs to be struck when thinning the membrane excessively, as too much thinning will weaken its structure and therefore become more susceptible to damage during use. It was therefore of paramount importance to make sure that the 1D model was modified in the aforementioned manor as to be certain that the output of the model was indicative of the exact materials being tested in the experimental rig.