Modeling of an alkaline electrolyzer and a proton exchange membrane fuel cell (PEMFC) is presented. Also, a parametric study is performed for both components in order to determine the effect of variable operating conditions on their performance. The aim of this study is to determine the optimum operating conditions when the electrolyzer and the PEMFC are coupled together as part of a residential solar powered stand-alone power system comprising photovoltaic (PV) arrays, an alkaline electrolyzer, storage tanks, a secondary battery, and a PEMFC. The optimum conditions are determined based on an economic study which is performed to determine the cost of electricity (COE) produced from this system so as to determine the lowest possible COE. All of the calculations are performed using a computer code developed by using MATLAB. The code is designed so that any user can easily change the data concerning the location of the system or the working parameters of any of the system's components to estimate the performance of a modified system. Cairo city in Egypt was used as the place at which the output of the system will be determined. It was found that the optimum operating temperature of the electrolyzer is 25^{∘}C. Also, the optimum coupling pressure of the electrolyzer and the PEMFC is 4 bars. The operating temperature of the PEMFC had a slight effect on its performance while an optimum current density of 400 mA/cm^{2} was detected. By operating the fuel cell at optimum conditions, its efficiency was found to be 64.66% with a need of 0.5168 Nm^{3} (Nm^{3} is a m^{3} measured at temperature of 0^{∘}C and pressure of 1 bar) of hydrogen to produce 1 kWh of electricity while its cogeneration efficiency was found to be 84.34%. The COE of the system was found to be 49 cents/kWh, at an overall efficiency of 9.87%, for an operational life of 20 years.

The use of nonrenewable fuel diminishes as time goes on. This is simply because such type of fuel will vanish at some point of time. Also, the increased use of biomass has had a negative effect on global warming and dramatically increased food prices by diverting forests and crops into biofuel production. Thus, the need of renewable sources of energy becomes a fact of life. Solar energy is the greatest available source of renewable energy.

Using solar energy appears to be a promising option. However, some serious concerns about its implementation include the cost of electricity obtained from solar source as well as the intermittent nature in solar power production. In order to overcome the latter concern, a system that can be used to utilize solar energy is proposed. Also, an investigation of the cost related to such system is included.

The proposed system, shown in Figure

Schematic of system.

The modeling of the system as a whole was presented by Khater et al. [

A brief description of the thermodynamics of the low-temperature hydrogen-oxygen electrochemical reactions used in the electrolyzer model is explained in this part. A maximum electrolyzer temperature of 100°C was assumed.

The following assumptions can be made about the water splitting reaction: (a) hydrogen and oxygen are ideal gases, (b) water is an incompressible fluid, and (c) the gas and liquid phases are separate. Based on these assumptions the change in enthalpy _{2}), oxygen (O_{2}), and water (H_{2}O) at standard temperature and pressure (25°C and 1 bar) [_{2} and O_{2}) and the reactants (H_{2}O). The same applies for the total change in entropy. The change in Gibbs energy is expressed by^{−1}. For an electrochemical process operating at constant pressure and temperature, the maximum possible useful work (i.e., the reversible work) is equal to the change in Gibbs energy ^{−1}.

The thermodynamic voltage for water splitting (^{−1}. The thermoneutral potential is expressed by

Using (

at standard conditions:

The curve which is used to model the electrolyzer is the

Table

In order to find the six parameters needed in the proposed empirical

Collect experimental or operational data for current

Organize the measured values for

Perform individual curve fits of the three coefficients

Repeat step (3) for few other temperatures (e.g.,

Perform intermediate curve fits on the temperature-dependent coefficients

Verify that the temperature-dependent coefficients in (

Perform an overall curve fit on the entire data set, using the values for the parameters

Actually, the working electric potential of an electrolysis cell (^{2}) [

The efficiency of water electrolysis is defined as the ratio of hydrogen energy content (the energy that can be recovered by reoxidation of the hydrogen and oxygen to water) to the electrical energy supplied to the electrolyzer [

The heat absorbed by the cooling water of the electrolyzer makes it possible to use this hot water for domestic purposes by the house residents. This heat is obtained from (^{−1}.

_{1} | 8.05^{2} |

_{2} | −2.5^{2} °C^{−1} |

_{1} | 0.185 V |

_{1} | −1.002 A^{−1} m^{2} |

_{2} | 8.424 A^{−1} m^{2} °C |

_{3} | 247.3 A^{−1 }m^{2} °C^{2} |

Typical

The Faraday efficiency is defined as the ratio between the actual and theoretical maximum amount of hydrogen produced in the electrolyzer. An increase in temperature leads to a lower resistance, more parasitic currents losses, and lower Faraday efficiencies. An empirical expression that accurately depicts these phenomena for a given temperature is the Faraday’s efficiency

Hence, the total hydrogen production rate in an electrolyzer, which consists of several cells connected in series, can be expressed as
^{3}/h is calculated as

Faraday efficiency parameters (

80°C | |

_{1} | 250 mA^{2} cm^{−4} |

_{2} | 0.96 |

There is a need for an improvement in global energy efficiency of water electrolyzers and particularly in the reduction of the electric energy consumption of the electrolysis module, without decreasing the productivity.

Concerning the design of the electrolysis stack, new electrolysis cells’ configurations have been developed to reduce the internal electric resistance. The so-called zero-gap is the configuration adopted by most of the manufacturers. A number of investigations have been carried out aiming at achieving further performance improvements [

Nadal et al. [

Schiller et al. [

It has been reported that additional reductions of energy needs can be achieved by adding ionic activators into the electrolyte and changing cell geometries [_{2} production. This is simply due to the increase in electron emission. Also, increasing the cell size speeds the overall reaction with increasing the contact area. However, after a certain size, the resistance of the solution increases which causes decay in the hydrogen production rate and the speed of the reaction.

In other works, the process efficiency has been increased with improved membranes properties and materials [

An analytical simulation model of the PEMFC is presented in this part. Assuming in this model that the fuel is pure hydrogen at inlet to the anode and the oxidant is pure oxygen at inlet to the cathode. The fuel cell model implemented in this work, known as the Generalized Steady State Electrochemical Model (GSSEM), is zero dimensional, semiempirical, and static in nature, thus the parameters of the equations are determined experimentally to provide the time-independent polarization curves, power curves, and efficiencies at various operating conditions, and the model is applicable to an entire fuel cell. The voltage of the fuel cell is modeled as [

Mann et al. [

It is further noted that the expression in (

The reaction would produce a maximum amount of useful work if all the free energy is directed to transfer electrons from one electrode to the other. The value of maximum obtainable work from a fuel cell is given by [

Activation losses that are caused by the slowness of the reactions taking place on the surface of the electrodes (the activation of the anode and the cathode). A proportion of the voltage generated is lost in driving the chemical reaction that transfers the electrons to or from the electrodes. This voltage drop is highly nonlinear. For most values of overvoltage, one may use the following equation [^{2}); ^{2}); ^{2}).

Ohmic losses are due to the electrical resistance (electrons) of the electrodes and the resistance to the flow of ions (protons) in the electrolyte. To be consistent with the other equations for voltage loss, the equation should be expressed in terms of current density. The equation for the voltage drop then becomes [^{2}).

Concentration losses are the result of the pressure drop of the reactant gases. The overvoltage depends on the amount of current drawn from the cell, as well as the physical characteristics of the gas supply systems. In general, concentration or mass transport losses are given by [

The constant values used in this work are given in Table

Constants used to calculate potential losses for low-temperature PEMFC.

Constant | Units | Value |
---|---|---|

_{n} | (mA·cm^{−2}) | 3 |

(kΩ·cm^{2}) | 2.54 × 10^{−4} | |

_{o} | (mA·cm^{−2}) | 0.1 |

(volts) | 2.11 × 10^{−5} | |

(cm^{2}/mA) | 8 × 10^{−3} |

The main outputs of the fuel cell operation are power, water, and heat production. The power output of a fuel cell is the most important measure of its performance. Much of the current research in the area of fuel cells is focused on attempts to increase the power output while decreasing the manufacturing costs. The gross output of the fuel cell stack (in W) is given by:

A power conditioning unit is required to convert the DC current into alternating current (AC) current. The net power output in AC of the fuel cell stack is a more important consideration when assessing its performance and is given by

Similarly, in this model of the stand alone PEMFC, the cell electrical efficiency was calculated as the cell gross power output divided by the heating value of the hydrogen inlet to the cell

The amount of hydrogen and oxygen required to provide a certain current

Heat will be generated by the operation of the fuel cell since the enthalpy that is not converted to electrical energy will instead be converted to thermal energy. In order to operate the PEMFC at constant temperature, a cooling system must be added to absorb this heat and use it for cogeneration purposes [

Renewable energy needs to be more competitive with conventional methods of power generation, that is, to have a lower cost on the long run. Thus, a very important part of the proposed model is to provide an economic study for the whole system.

The main economic parameter that is studied is the cost of electricity (COE), which is the cost of producing one kWh of electricity. This parameter is believed to be the major criterion that indicates whether the system can be economically competitive to other conventional systems or not. Other factors that will be studied in this part are the total annual cost (TAC) including the capital cost equivalent and the operating cost.

The main cost items that are included in this estimate are

photovoltaic panels,

electrolyzer,

hydrogen and oxygen storage tanks,

battery,

DC/AC converter (inverter),

PEMFC stack including: cell, piping, and insulation,

balance of plant (BOP),

operating and maintenance cost (C_{O&M}).

The following assumptions are extracted from various literatures and are used to estimate the purchase cost of different system components excluding the taxes [

prevailing interest rate (

average inflation rate (

stack replacement cost = 1/3 of stack initial cost (durability time = 40000 hr)

Installation cost = 15% Purchase cost,

operating and maintenance cost = 20% of annual fixed cost.

Also, the specifications as well as the cost of each of the system’s components are shown in Table

Component’s specification.

Component | Price (US$/Unit) | Replacement time (year) | Unit |
---|---|---|---|

PV | 2780 | 20 | 1 kW |

Electrolyzer | 800 | 20 | 1 kW |

Storage tank | 750 | 20 | 1 kg |

Inverter | 300 | 20 | 1 kW |

PEMFC stack | 3000 | 5 | 1 kW |

Battery | 250 | 5 | 1 kW |

The effective annual interest rate

The installation cost per kilowatt of system net electrical power can then be estimated as follows:

Two main key parameters affecting the performance of the electrolyzer are the current density and the operating temperature. Figure

Detailed measurements of the hydrogen production at various current densities for the PHOEBUS electrolyzer (26 kW, 7 bar) were only available for an operation temperature of 80°C. However, detailed experiments on the temperature sensitivity of the Faraday efficiency were performed on a very similar electrolyzer (10 kW, 5 bar) installed at the HYSOLAR test and research facility for solar hydrogen production in Stuttgart, Germany [

Faraday efficiency parameters for (

40 | 60 | 80 | |
---|---|---|---|

^{2}cm^{−4}) | 150 | 200 | 250 |

0.990 | 0.985 | 0.98 |

Figure

Faraday efficiency at 80°C of PHOEBUS electrolyzer.

Figure ^{2}.

Faraday efficiency of HYSOLAR electrolyzer at different temperatures.

A parametric study was carried out by varying the cell pressure versus the Nernst voltage at different values of cell temperature (333 K–363 K). The obtained results are shown below in Figure

Effect of cell pressure on Nernst voltage at different cell temperatures

Figure

Effect of current density on different types of potential losses.

Effect of current density on cell voltage at different cell pressures (

As shown in Figure

Figure

Effect of current density on cell voltage at different cell temperatures (

The above results are used to calculate the PEMFC electrical efficiency as a function of current density and cell operating pressure. Figure

Effect of current density on cell electrical efficiency (

It is seen from Figure ^{2}. As well, as explained earlier, it is seen that, at given current density, the electrical efficiency is higher for higher pressures.

As shown from the above results, the current density has a tremendous effect on the operating voltage and cell electrical efficiency (hence operating cost). Two important factors determine the range of acceptable operating current density: first, the obtained power density (kW/cm^{2}) and, second, the lifetime cost of operation.

Figure

Effect of current density on power density (

Figure ^{2}). However, operation at the higher power densities will mean operation at lower cell voltages or lower cell efficiency. Setting operation at the peak power density can cause instability in control because the system would have a tendency to vacillate between higher and lower current densities around the peak. It is usual practice to operate the cell to the left side of the power density peak and at a point that yields lower life cycle cost of PEMFC operation, to which we now turn.

Abdel-Raouf [^{2} yields lowest cost considering all the important parameters.

Based on this analysis, a value for the current density of 600 mA/cm^{2} will be used in the analysis of PEMFC as a part of studying the performance of the proposed system in Cairo which is presented later on. This value is also consistent with the requirement of operation of the PEMFC to the left of the peak in the power density curve shown in Figure

The aim of this part is to determine the optimum operating conditions of the system to obtain a yearly best total energy output taking Cairo data variations all over the year in consideration.

Decreasing the operating temperature of the electrolyzer causes an increase in the reversible voltage. This in turn decreases the volume of hydrogen produced as well as the amount of heat generated inside the electrolyzer as shown in Figure

Effect of decreasing the operating temperature of the electrolyzer.

In order to determine the optimum operating temperature of the electrolyzer, it is important to locate the point at which the lowest possible COE exists. Figure

Effect of the operating temperature of the electrolyzer on the COE.

It is worth noting that any excess amount of hydrogen that exceeds that required by the demand load throughout the year can be utilized either by the PEMFC to an extra load or by burning it to obtain extra heat. The COE of both cases is shown in Figure

As mentioned before, the increase in the pressure of the electrolyzer causes a slight increase in the reversible voltage which in turn causes a decrease in the amount of hydrogen produced. Also, this increase in pressure and

Figure

Effect of the operating pressure of the electrolyzer/PEMFC on the COE.

As mentioned before, the cell temperature very slightly affects the resulting voltage and hence will be considered of minor effect, and the operating temperature of the PEMFC will be fixed at 80°C.

As concluded before, a range of current density of 400–800 mA/cm^{2} yields lowest cost considering all the important parameters. However, as the current density decreases, the cell voltage increases, as was shown in Figures ^{2} will be used which will cause a decrease in the number of PV modules installed to 45 instead of 52 at 800 mA/cm^{2}. The effect of decreasing the current density on the COE is shown in Figure

Effect of the operating current density of PEMFC on the COE.

For the PEMFC, at ^{2}, and in order to generate 1 kWh of electricity, it is found that

^{3} A,

^{3} at STP,

^{3} at STP,

It is clear in Figure

Effect of cost of PEMFC on COE.

Combining the expected future increase of PV efficiency up to 30% with the decrease of the cost of PEMFC will yield a COE of 0.212 $/kWh for the proposed system. This value will be small when compared to COE of

0.2798 $/kWh of a system comprising PV arrays and batteries in the future

0.3088 $/kWh by using a diesel generator recently (with expected increase of price of diesel in the future).

On the other hand, this COE is still 3 times higher than the current COE for a grid-connected house (0.0717 $/kWh). However, the on-grid COE is expected to increase in the future.

The aim of this work is to study and model a proposed stand-alone power system utilizing solar energy as its power source and comprising photovoltaic arrays, an alkaline electrolyzer, storage tanks, secondary battery banks, and a proton exchange membrane fuel cell as its main components.

The effect of each of the key parameters affecting the amount of solar radiation and the performance of the PV arrays, alkaline electrolyzer, and the PEMFC were studied. Also, an economic study was performed to determine the feasibility of the proposed system to be used on a residential scale. The modeling outcomes of this system were performed for Cairo city in Egypt using the developed program with the aid of MATLAB code.

The proposed model can predict the performance of a stand-alone power system. It can predict the output power of the system as a whole in any location as well as the effect of different parameters on its performance. Also, it can predict the output of each of the system components such as the output power of the PV arrays, the volume of hydrogen produced by the electrolyzer, and the electric as well as heat output of the PEMFC.

The variations of the output of this system were determined for Cairo city in Egypt at different periods throughout the year. It was clear that the PV power varies in the same manner as the radiation on the PV surface which reaches its peak at the solar noon. Also, the efficiency of the PV, tilted at 30°, is almost constant throughout the year with slight variations between the different months. Moreover, the proposed system produces an excess amount of hydrogen more than the amount required to satisfy the demand load during some months of the year. This excess hydrogen is used to satisfy the deficit in the other months so that the system can easily satisfy the estimated maximum demand load of the studied residential unit.

Furthermore, the proposed system has a COE of 49 cents/kWh, at an efficiency of 9.87%, which is high relative to the COE of using a PV and a battery only, using diesel generator, or a similar grid-connected house. However, as the market for fuel cells penetrate more and as the new higher efficiency PV systems become commercially available, this cost is expected to decrease to 21 cents/kWh in the near future which will make the proposed system a very competitive option, especially with its zero pollutants emissions to the environment.