Performance Analysis of Proton Exchange Membrane Fuel Cell During Transient Operations Using Artificial Intelligence

The shape of a fuel cell's polarization curve depends on its various operating parameters. A family of these curves can be used to analyze the stack's performance. The higher the parameter variation, the better the polarization curve's performance. This is because it increases the fuel cell's power and improves its electrochemical efficiency [11].

2.1 Impact of pressure on fuel cells

The increasing operating pressure of fuel cells causes the polarization curves to increase. On the other hand, the decrease in operating pressure causes the polarization curves to decrease. The chemical reaction that takes place in a fuel cell depends on the partial pressures of the two components, namely, hydrogen and oxygen. The effects of increasing operating pressure are most prominent when the fuel is used with a dilute oxidant or a reformate [12]. The higher the operating pressure, the more oxygen and hydrogen can be pushed into the electrolyte. This is also the case when the fuel is used at high currents. Although the increase in pressure helps in the electrochemical reaction, it can also introduce other problems. For instance, the flow field plates of fuel cells can suffer from the effects of flowing pressure [13].

When the fuel cell seals are subjected to additional stress, they have to work harder to absorb the additional air compression. This can cause system components to be redesigned. The increasing operating pressure helps in reducing returns. This effect is also beneficial for the overall system. Proton Exchange membrane fuel cells are commonly operated at pressures no higher than a few atmospheres. The use of a pure fuel, which is usually hydrogen or oxygen, can increase the stack polarization curves [14, 15].

2.2 Impact of temperature on fuel cells

The increasing operating temperature affects the fuel cell's polarization curve. On the other hand, the decreasing operating temperature affects the curve.

• The higher the operating temperature, the better the mass transfer between the fuel cells. As a result, the cell resistance decreases.
• The higher the operating temperature, the better the reaction rate. In addition, the accumulation of product water in the oxidant stream limits the operating temperature to below 212 degrees Fahrenheit.
• The higher the operating temperature, the more steam, and water boils which severely reduces the oxygen's partial pressure. This condition can cause the cell to perform poorly.

Some fuel cells can be operated at higher pressures to achieve higher temperatures. This can cause the water boiling point to increase. However, this effect is slight in the case of PEM fuel cells. The higher the operating temperature, the higher the cell's voltage. However, until the temperature reaches the boiling point, the voltage begins to decline. The optimal operating temperature for fuel cells is around 80 degrees Celsius. This temperature is balanced between the two effects [16]. As with high-pressure operations, elevated temperatures can affect various components of the system.

2.3 Impact of stoichiometry on fuel cells

The increase in the reactant gas stoichiometry of fuel cells leads to a decrease in the fuel cell's polarization curve. Insufficient stoichiometry can prevent the fuel cell stack from producing enough reactants. This issue can cause permanent damage to the system. Stoichiometry is a ratio that measures the amount of gas that's needed to complete a reaction. The correct stoichiometric ratio of gas is 1.01. This ensures that the correct number of reactants are produced [17].

• The higher stoichiometry of gas increases the likelihood that the various oxygen and hydrogen molecules will interact with the electrolyte.
• The higher the stoichiometric ratio, the more gas is needed to complete a reaction. A stoichiometric ratio greater than 2.01 provides twice as much gas as it's required.
• The higher the gas stream stoichiometric ratio, the higher the fuel cell voltage will eventually reach its terminal voltage.

For practical fuel cells, the stoichiometric ratios are typically 1.412 and 2.01. However, when operating at low power, higher ratios are required.

2.4 Impact of humidity on fuel cells

A properly humidified gas stream is required for the operation of a fuel cell. This process occurs when hydrogen ions exchange with water molecules. Without sufficient humidification, the water can cause the membrane to get damaged, which can lead to various problems such as cracks and holes. This can also cause a chemical short circuit. When the water gets too humid, it can cause flooding and condensation within the flow field plates, which can destroy the fuel cell. The relative humidity is a measure of the level of moisture in a given gas stream. It can be measured by the temperature and pressure of the gas. A gas that has a relatively high relative humidity level is considered to be saturated. This means that it has a lot of water absorbed by it. When the gas gets hotter, its relative humidity drops. However, if it cools, some of the water condenses, and the gas remains saturated. Ideally, fuel cells should be operated at a temperature that's close to saturated. This ensures that they have enough water to prevent flooding. The use of water for humidification helps limit the operating temperature of a fuel cell to around 0-100 degrees Celsius. Without a continuous flow of water through a demonizing filter, the water can cause corrosion currents and short circuits in the fuel cell stack [18, 19].

A schematic diagram of a typical jth node is shown in Figure 3. The inputs to such a node may come from system causal variables (or) outputs of other nodes depending on the layer that the node is located in these inputs form an input vector X=(x₁,…x_i…x_n). The sequence of weights leading to the node form a weight vector W_j = (w_ij…w_ij…w_nj). Where w_ij represents the connection weight from the ith node in the preceding layer to jth node.The output of node j, y_j is obtained by computing the value of function with respect to the inner product of vector X and w₁ minus b_j. Where b is the threshold value, also called the bias, associated with this node. In ANN, the bias b_j of the node must be exceeded before it can be activated. The following equation defines the operation.

$y_j=f\left(X . W_j-b_j\right)$       (1)

3.png

Figure 3. A Schematic diagram of node - j

The function f is called an activation function. Its functional form determines the response of a node to the total input signal it receives. The most commonly used form of f(.) in Eq. (1) is sigmoid function given as.

$\mathrm{f}(\mathrm{t})=1 / 1+\mathrm{e}^{-\mathrm{t}}$       (2)

The sigmoid function is a bounded, monotonic, non decreasing function that provides a graded, nonlinear response. This function enables a network to map any nonlinear process. The popularity of the sigmoid function is partially attributed to the simplicity of its derivative that will be used during training process. Some researchers also employ bipolar sigmoid and hyperbolic tangent as activation functions-both of which are transformed from the sigmoid function. A number of such nodes are organized to form a artificial neural network.

4.1 Network training

In order for an ANN to generate an output vector Y = (y₁, y₂,…..y_p) that is as close as possible to the target vector T = (t₁, t₂,……t_p), a training process, also called learning, is employed to find optimal weight matrices W and bias vectors V, that minimize a predetermined error function that usually has the form.

$\mathrm{E}=\sum \sum\left(\mathrm{Y}_{\mathrm{i}}-\mathrm{t}_{\mathrm{i}}\right)$         (3)

Here t_i is component of desired output T, Y_i is the corresponding ANN output, p is the number of the output nodes and P is the number of training patterns. Training is a process by which the connection weights of an ANN are adapted through a continuous process of stimulation by the environment in which the network is embedded. There are primarily two types of training supervised and unsupervised. A supervised training algorithm requires an external teacher to guide the training process. This typically implies that a large number of examples (or) patterns of inputs and outputs are required for training. The inputs are cause variables of a system and the outputs are the effect variables. This training procedure involves the iterative adjustment and optimization of connection weights and threshold values for each of nodes.

The primary goal of training is to minimize the error function by searching for a set of connection strengths and threshold values that cause the ANN to produce outputs that are equal (or) close to targets. After training has been accomplished, it is hoped that the ANN is then capable of generating reasonable results given new inputs. In contrast, an unsupervised training algorithm does not involve a teacher. During training, only an input data set is provided to the ANN that automatically adapts its connection weights to cluster those input patterns into classes with similar properties.

The algorithm for training the neural network is as follows:

1) Apply the input vector to the input units.

2) Calculate the net input values to the hidden layer units $\mathrm{Net}_{\mathrm{j}}^{\mathrm{h}}=\sum \mathrm{W}_{\mathrm{ji}}^{\mathrm{h}} \mathrm{x}_{\mathrm{i}}+\theta_{\mathrm{j}}^{\mathrm{h}} \quad$ for $\mathrm{I}=1,2, \ldots \ldots \ldots \ldots \ldots \ldots$n. Where $\mathrm{W}_{\mathrm{ji}}$ is connection weight and $\theta_{\mathrm{j}}^{\mathrm{h}}$ is bias value.

3) Calculate the outputs from the hidden layers: $\mathrm{I}_{\mathrm{j}}=\mathrm{f}_{\mathrm{j}}^{\mathrm{h}}\left(\right.$ net $\left._{\mathrm{j}}^{\mathrm{h}}\right)$

4) Move to the output layer. Calculate the net input values to each unit. $\mathrm{Net}_{\mathrm{k}}{ }^{\circ}=\Sigma \mathrm{W}_{\mathrm{kj}} \mathrm{I}_{\mathrm{i}}+\theta_{\mathrm{k}}{ }^{\circ}$

5) Calculate the outputs: $\mathrm{O}_{\mathrm{k}}=\mathrm{f}_{\mathrm{k}}^{\mathrm{o}}\left(\mathrm{net}_{\mathrm{k}}^{\mathrm{o}}\right)$

6) Calculate the error terms for the output units: $\delta_{\mathrm{k}}{ }^{\circ}$$=\left(\mathrm{y}_{\mathrm{k}}-\mathrm{o}_{\mathrm{k}}\right) \mathrm{f}_{\mathrm{k}}^{\mathrm{o}}\left(\mathrm{net}_{\mathrm{k}}^{\mathrm{o}}\right)$

7) Calculate the error terms for the hidden terms: $\delta_j{ }^{\mathrm{h}}=\mathrm{f}^{\mathrm{h}}{ }_{\mathrm{j}}\left(\right.$ net $\left.^{\mathrm{h}}\right) \sum \delta_{\mathrm{k}}{ }^{\mathrm{o}} \mathrm{w}_{\mathrm{kj}}^{\mathrm{o}}$

Notice that the error terms on the hidden units are calculated before the connection weights to input layer units have been updated.

8) Update weights on the input layer: $\mathrm{W}_{\mathrm{kj}}{ }^{\circ}(\mathrm{t}+1)=\mathrm{W}_{\mathrm{kj}}{ }^{\circ}(\mathrm{t})+\eta \delta_{\mathrm{k}}{ }^{\circ} \mathrm{i}_{\mathrm{j}}$

9）Update weights on the hidden layer: $\mathrm{W}_{\mathrm{ji}}^{\mathrm{h}_{\mathrm{i}}}=\mathrm{W}_{\mathrm{ji}}^{\mathrm{h}}(\mathrm{t})+\eta \delta_{\mathrm{j}}^{\mathrm{h}} \mathrm{x}_{\mathrm{i}}$

4.2 Back-propagation algorithm

Back-propagation is perhaps the most popular algorithm for training ANNs. It is essentially a gradient descent technique that minimizes the network error function- Eq. (3). Each input pattern of the training data set is passed through the network from the input layer to the output layer. The network output is compared to desired target output, and an error is computed based on Eq. (3). This error is propagated backward through the network to each node and correspondingly the connection weights are adjusted based on equation:

$\Delta W_{i j}(n)=-\varepsilon \frac{\partial E}{\partial W_{i j}}+\alpha \Delta W_{i j}(n-1)$      (4)

A similar equation is written for connection of bias values. In Eq. (4), and are called learning rate and momentum, respectively. The momentum factor can speed up training in very flat regions of the error surface and help prevent oscillations in the weights. A learning rate is used to increase the chance of avoiding the training processes being trapped in local minima instead of global minima. The back propagation algorithm involves two-steps. The first step is a forward pass, in which the effect of the input is passed forward through the network to reach the output layer. After the error is computed, a second step starts backward through the network. The errors at the output layer are propagated back towards the input layer with the weights being modified according to Eq. (4). Back- Propagation is a first order method based on steepest gradient descent, with the direction vector being set equal to the negative of the gradient vector. Consequently, the solution often follows a zigzag path while trying to reach a minimum error position, which may slow down the training process. It is also possible, which may slow down the training process. It is also possible for the training process to be trapped to be trapped in the local minimum despite the use of a learning rate. To design and control a Fuel Cell System (FCS) for the maximum power performance, a designer needs to acquire sufficient knowledge pertaining to the physical process, the internal structure of the process, as well as the dominant input/output variables of the system. In sequel, an accurate mathematical representation of the system may be developed with sufficient to accurately reflect the behavior of the physical process. During the last decade, several one-dimensional (1D) and multi- dimensional (MD) models have been developed to explain the electrochemical and thermodynamic phenomena inside the fuel cells. However, some of these models require specific knowledge of parameters were membrane thickness and resistance which are either unknown or known to the manufacturers. Therefore, the availability of the electrochemical equations or models may not be sufficient to accurately design the FCS for the optimum performances. In addition, these models as described above are commonly very complicated for large-scale FCSs. On the other hand, in most of control applications, the designer may be interested in relationship between inputs and outputs as well as the internal structure of the system. Such knowledge will provide the designers with the sufficient tool to control the inputs in order to reach the desired outputs were stack voltage and stack current for appropriate application. Such a prediction may be performed by using artificial neural networks. Investigate the reliability of the BP networks for the output prediction of an 18W FCS. The 18W fuel cell BP networks are described and the reliability of the constructed neural networks to predict the performance of the FCS is investigated. In addition, a comparison of the BP networks in term of error goal, training algorithms and network architectures have been investigated.

4.3 Artificial neural networks 18w 4-cell fuel cell model

4.3.1 FCS

The 18W FCS contains a fuel cell stack as well as all the auxiliary equipment such as Temperature monitor, voltage monitor, current monitor, Hydrogen leakage detector, Oxygen delivery and Hydrogen delivery necessary for fuel cell operation. The stack voltage and current of range from 4.5V/1A at idle to 2.5V/8A at full load. The hydrogen pressure is regulated by a regulator valve.

4.3.2 Load bank

The load bank has been developed which consists of 3.8VDC light 9bulbs system each 2w. The load bank can increase the stack current up to 7A. This load is a simple, inexpensive and more reliable.

4.3.3 Data collection and analysis

1. Data collection

The FCS was operated with the load bank up to maximum current of 7A and hydrogen pressure up to 1bar. The 60 data points have been taken to train the neural network algorithm. The data sets such as stack voltage (V), stack current (A), H2 pressure (bar) and all variables are constant.

2. Selection of process variables

To train the network successfully and efficiently, it is needed to select the appropriate variables like network inputs and outputs. To select the reliable variables, one need to understand the process, how each variable affects the system performance then identify which variables are dominant and which one can be discarded. If there are too many variables as network inputs, the network will be unnecessary complicated and the training may be difficult or take too long time to succeed. In contrast, if the fewest dominant variables can be selected, the network will be small and can provide the fastest training and instant recall. In the present system, there are several variables to be selected as inputs/outputs for the proposed neural networks. Hydrogen pressure is varied by using a regulated valve and current of the stack varied by using load bank. Discard the other input variables which have been forced to be constant by the system that are mass air flow and stack temperature (℃) as the dominant input variables. Stack voltage (V) is selected as the output variable due to their obvious relation to the fuel cell power generation.

3. Range of data

In general, neural network performs well in interpolation rather than extrapolation; therefore, in order to obtain a better prediction, the recall data should be in the range of training data. We randomly select the collected data to cover the range from minimum to maximum values as training data and the remaining as recall data. This approach will ensure that the recall data will always lie in the range of training data. The ranges of inputs/outputs data sets are as follows.

4. Ranges of inputs

Hydrogen pressure 0.2 to 1 bar and stack current (A) range from 1 to 8A.

5. Ranges of outputs   

Stack voltage range from 2.0 to 4.5V.

6. Size of training and recall data

When training data set is presented to the network, the weights and biases are updated on a pattern-by-pattern basis until the entire training data set is completed which is called one “epoch”. This training phase is repeated until the network performs well according to the error goal as provided by the designer. In sequel, the recall data is presented to ensure that the network has learned the general patterns, not just simply has memorized the data set. If the network still performs well, the training is completed. Training data set needs to be fairly large and contains variety of data in order to contain all the needed information. Therefore, in our investigation, from 60 data points collected, 40 data points is for training phase and 20 data points is for recall phase.

7. Preprocess data

Preprocess data to have two additional data sets; normalized data. In the subsequent sections, we will investigate which data set provides a better and faster prediction. The raw data can be normalized to have a range of [0, 1] by using base value selection.

4.4 Modeling

Inspired by the biological neural networks, an ANN is a massively parallel distributed processor made up of simple processing units, known as neurons. With ability to learn from input data with or without a teacher, modeling and Training will train using network. In this section, the BP networks to investigate how well it can predict the performance of the 18W FCS.

4.4.1 BP networks architecture

A BP network with one hidden layers is constructed. In hidden layer, the number of neurons is varied to investigate the network prediction performance. The input layer has two input variables which are hydrogen pressure and stack current. The output layer consists of one neuron for stack voltage. In this work considered two layer feed forward network, Two inputs and one output, one hidden layer, Sigmoid function,13 hidden nodes, input matrix size(2,60), output matrix size(1,60).

4.4.2 Implementation

The following three criteria’s are selected to investigate the prediction performances of the BP networks for 18W FCS:

1. Number of epochs(10000): indicates the training speed.
2. Root mean square error (E2): indicates average error of the prediction.
3. Learning Rate(0.1):indicates the speed.

4.5 Test cases and simulation results

Test cases results by varying the hydrogen pressure and load current of the stack are shown in Table 1 for both the practical and ANN model. Figure 4 shows the graphs of Voltage (V) versus the current density (A/sq. cm) for different hydrogen pressures. Using weight matrix of w1(13,2) and w2(1,13),20 testing patterns tested.

4.5.1 Data set selection

To accuracy and time expenditure for the FCS are shown in Table 1. These data sets are provided to the BP network whose weight and bias values are updated using the BP algorithm with the error goal of 0.001.The fastest in training phase. The average error (E2) and maximum error (E∞) using these three data sets are not much different. The predictions of stack voltage for the FCS are shown. The results show the satisfactory predictions for the entire operating range except at the initial phase. It is observed that, at the starting phase of the FCS, the inputs are almost constant even though the outputs are changing due to transient response of the feedback system at the initial phase. Therefore, the NN prediction does not perform well at the initial phase.

4.5.2 Error goals

In the training phase, the network will adjust its weights and biases until the output error reaches the designated error goal. If the selected error goal is relatively too large, then the training will be completed in a relative short time. However, a large error is obtained in the recall phase. On the other hand, if the error goal is selected to be too small, it will take a very long time. The speed and accuracy of Error goals 0.1 and 0.01 are too large while the error of 0.0001 is too small. BP network is used to predict the performance of the 18w FCS. Stack voltage predictions done by using hydrogen pressure and load currents.

4.5.3 Code algorithm for test case-1

The following procedure explains about program code and functions. Here we have three important main MATLAB ANN functions. Apart from training parameter play major roles, approximately 4 training parameters considered.

The function “initff” it initializes the input inputs and it selects the activation functions. This function will gives initialized weight matrixes and biases matrixes. Another function is “trainbpx” this function trains the pattern by using architecture and it gives generalized weight matrixes and generalized biases.By using generalized matrices and testing input “simuff” function calculates the actual out puts of ANN model.The table.1 gives test results of the 18w 4cell Fuel cell stack.

Inputs: Pressure variation       load current variation

Outputs: Stack Voltage

Input data range=[.1 2;.5 10];

[w1,b1,w2,b2]=initff (input data range,13,’tansig’,1,’tansig’) validation=1000;

epochs =230000; learning rate=0.01; error goal=0.03; TP=[df me lr eg];

[W1,b1w2,b2,TE] = trainbpx (w1,b1, ‘tansig’, w2, b2, ‘tansig’, input data, target data, training parameters)

output=simuff (test data,w1,b1, ‘tansig’, w2,b2, ‘tansig’,)

Table 1. 18w 4Cell stack ANN model voltage

4.png

Figure 4. 18w 4-Cell stack voltage curves at various loads

4.5.4 Code algorithm for test case-2

In this test case 2, the patterns generated from simulation model. Here after training validated the ANN model with simulation model. In this case study not considered the practical results. The final test results shown in Table 2.

This model is validated with simulation model.

Inputs:

Hydrogen composition(97%,99.99%)

Oxidant composition(20%,30%)

Hydrogen flow rate(1lpm,3lpm)

Air flow rate(1lpm,10lpm)

System temperature(30℃,50℃)

Hydrogen supply pressure(.1bar,2bar)

Air supply pressure(.1bar,4bar)

Outputs:

Stack Voltage(.9volts,5volts)

Utilization of Hydrogen(95%,99%)

Utilization of Oxygen(10%,40%)

Stack Efficiency(40%,55%)

Stack Power(12watts,18watts)

P=[inputs(minimum rang, maximum rang)];

[w1,b1,w2,b2]=initff (input data range,13,’tansig’,1,’tansig’)

validation=1000;

epochs=230000;

learning rate=0.01;

error goal=0.03;

TP=[df me lr eg];

[W1,b1,w2,b2,TE]=trainbpx (w1, b1, ‘tansig’, w2, b2, ‘tansig’, input data, target data, training parameters)

output=simuff (test data,w1,b1, ‘tansig’, w2,b2, ‘tansig’,)

Table 2. Signal variations ANN 4cell stack model

The dynamic model is composed of all the subsystem level models that are independent of each other. The modifications and investigations of the dynamic model are performed to account for the various components of the model, such as the water content and temperature variations.

The parameters that are used to determine the effect of membrane humidity on fuel cell voltage are derived from the literature. An example of this effect is the polarization curve of the membrane water content. The results of the study are then compared with those obtained in the literature. The temperature variation in the system is then assumed to be constant. The concentration loss caused by the transient profile variations in the anode and cathode pressure can affect the performance of the stack. The polarization curve reflecting the variation in membrane water content is shown in Figure 12.

12.png

Figure 12. Polarization curves reflecting the variation in membrane water content

Different system models and their auxiliary components of the Transient model was represented in the Table 3.

Table 3. Transient model systems with auxiliary components