Thermodynamic and Cost Analyses of a Residential HybridPV–Fuel Cell–Battery System for a Canadian House 16Mehdi Hosseini, Ibrahim Dincer, and Marc A. Rosen

Abstract

A residential photovoltaic (PV)-based hydrogen fuel cell system is analyzed using energy and exergy methods, and its

monthly performance is investigated. The PV system is accompanied by a water electrolyser for hydrogen production, a

lead acid battery pack, and a solid oxide fuel cell (SOFC) for reconverting the hydrogen produced to electricity during

periods of solar unavailability. The solar irradiance is based on a monthly average in Toronto in 2011. The energy and

exergy analysis results reported include the PV power output and the shares attributable to the battery and the SOFC in

meeting the electrical demand. The exergy destructions of the main components and the overall efficiencies are presented.

A cost analysis is performed to determine the electricity unit cost over the system lifetime.

Keywords

Photovoltaic � Hydrogen � Fuel cell � Energy � Exergy

Introduction

Solar photovoltaic (PV) systems are capable of converting 10–20 % of solar energy into electricity with zero greenhouse gas

emissions during their operation. These systems can be implemented in residential applications for electricity generation.

However, solar radiation is intermittent, and supplying the electricity of a house requires the use of some energy storage

options. While the PV system supplies the electricity demand of the house, the surplus electricity generated can be used in a

water electrolyser for hydrogen production. Hydrogen is stored in compressed hydrogen tanks, to be fed to a fuel cell later in

the night or during periods of solar unavailability. With this hybrid system, not only the power demand is supplied, but a

certain amount of the thermal demand is also met.

This type of hybrid PV–fuel cell–battery system is the focus of several studies [1–4]. The use of solar energy in a

renewable electricity generation system for a residential area in Italy is studied by Santarelli et al. [5], with solar energy

being one of three main renewable energy resources considered. The result revealed that wind energy is not capable of

meeting the demand, for that specific area. Since solar availability is more constant rather than micro-hydro energy

throughout the year, smaller hydrogen storage capacity is required. Uzunoglu et al. [6] investigate a renewable energy

power generation system which utilizes hydrogen and ultra-capacitors as energy storage options. The power generation

system provides the electricity demand of a house based on the solar irradiance data in Turkey. The main contribution is the

modeling and analysis of a renewable-based energy resource in a residential fuel cell hybrid system with short- and

long-term storage options. The parametric design and dynamic behavior of the hybrid system are examined.

M. Hosseini (*) � I. Dincer � M.A. Rosen

Faculty of Engineering and Applied Science, University of Ontario Institute of Technology,

2000 Simcoe St North, Oshawa, ON, Canada L1H 7K4

e-mail: mehdi.hosseini@uoit.ca

I. Dincer et al. (eds.), Progress in Exergy, Energy, and the Environment,DOI 10.1007/978-3-319-04681-5_16, # Springer International Publishing Switzerland 2014

181

The components of the PV–fuel cell–battery system have been modeled separately by researchers. Sukamongkol et al.

[7] study the performance of a PV system with simulation. Chenni et al. [8] and Nordin and Omar [9] validate the results of

detailed mathematical models with I–V characteristic and maximum power point of real PV modules. A direct coupling

of photovoltaic systems to water electrolysers for hydrogen production is the main focus of the study by Clarke et al. [10],

who found that the system cost and therefore hydrogen production cost decrease with their proposed configuration. This is

achieved while retaining minimum energy loss and maximum safety for the system. Solid oxide fuel cells (SOFC) are

increasingly being applied in stationary power generation, especially in combined heat and power (CHP) systems and in

remote areas. These systems have been studied comprehensively, in terms of experimentation, modeling, thermodynamic

analysis, and implementation [11–14].

The performance of the PV–fuel cell system depends on weather conditions; here, the system is analyzed for a Canadian

house with relevant solar data. The investigation of the hybrid PV–fuel cell system based on energy and exergy (quality of

energy) determines the rates of energy and exergy flows in each component. The results of the analyses are used for

calculating system outputs, efficiencies, and exergy destruction rates. The main contribution of the present research is the

analysis of the hybrid PV–fuel cell system on a monthly basis. The daily average solar irradiance during each month of

operation is taken as the input to the PV modules. The total daily average outputs of the system components are reported,

along with system efficiencies. The annual total exergy destructions of the system’s main components are presented, and the

electricity unit cost is calculated for the system lifetime.

System Description

The configuration of the hybrid PV–fuel cell–battery system, shown in Fig. 16.1, is selected to meet the electricity

requirement of a Canadian house. Solar energy is converted to electricity by the PV modules. The electricity generated is

directed to a load controller, which makes the decision of energy distribution within the system components and the house.

The load controller directs a part of the electricity generated to meet the power demand. The electrolyser converts the surplus

electricity to hydrogen, which is stored in a pressurized hydrogen tank. During periods of solar unavailability, the fuel cell

and battery cover the load. The operation of the battery is limited to the conditions where the electric load exceeds the solid

oxide fuel cell (SOFC) nominal power.

The SOFC is fed with the hydrogen (the fuel, which is stored in the storage tank) and ambient air as the oxidant. Hydrogen

is preheated via heat transfer from an external source, while air preheating is performed utilizing the heat from the SOFC

Electrolyzer

HydrogenTank

H2

SOFC

HRSG

Steam

Cooling Air

Load C

ontroller

DC Current

DC Current

DC Current

DC/ACConverter

AC Current

AbsorptionChiller

Stack Gas

Water

Water

Air

Power Load

ThermalLoad

Battery Pack

Heat

Fig. 16.1 Schematic of the

residential PV–hydrogen–fuel

cell CHP system

182 M. Hosseini et al.

stack gases, which have adequate energy for recovery for heating or hot water production. This is accomplished using a heat

recovery steam generator (HRSG), which generates low pressure saturated steam. As shown in Fig. 16.1, the steam

generated in the HRSG can be used in an absorption chiller for cooling purposes, or it can be used for hot water production.

The operational algorithm is simplified and illustrated in Fig. 16.2. Once the PV output power and the load demand are

calculated, the control system decides on the operation of the system components. A lower demand than the PV output

results in the operation of the electrolyser or the charging of the battery pack. If the demand is higher than the electric power

of the photovoltaic system, the fuel cell and the battery will be in operation.

Energy and Exergy Analyses

The modeling and energy and exergy analyses of the hybrid PV–fuel cell–battery system are briefly presented in this section.

Photovoltaic System

A previous paper [4] reported energy and exergy analyses of a residential PV–fuel cell–battery for a Canadian detached

house. That analysis is used in this work. The current–voltage characteristics are calculated as a function of light current and

reverse saturation current. The cell temperature and series resistance affect the I–V characteristics, as well. The general

equation to obtain the I–V characteristics of the PV modules can be expressed as [8]

I ¼ G

Gref

� �IL, ref þ kt Tcell � Trefð Þð Þ � I0 exp

q V þ IRsð ÞγkTcell

� �� 1

� �ð16:1Þ

where G is solar insolation W/m2, Gref is the solar insolation at the design condition, IL,ref is calculated based on the

manufacturer data for short circuit and maximum point currents, and kt is the manufacturer supplied temperature coefficient

of short-circuit current (A/�C). The maximum power output of the PV modules is at a point where voltage and current have

their maximum values. The control system for the PV system is designed so that the system operates at the maximum power

point. The energy and exergy efficiencies of the PV cell at maximum power point are given by

ηPV,mp ¼Pmp

_Ensolar¼ Imp � Vmp

G� Acell

ð16:2Þ

ψPv,mp ¼Pmp

_Exsolar¼ Imp � Vmp

G� Acell � 1� 43

T0

Tsunþ 1

3T0

Tsun

� �4� � ð16:3Þ

Solar Irradiance

Calculate PV Electric PowerOutput

PPV

Electricity DemandPdemand

ΔP=PPV - Pdemand

Pelectrolyser = PVpower – Pcharge, Battery

ΔP ≥ 0

Yes

No

|ΔP| ≤ FCnominal

PSOFC = FCnominal

Pbattery = |ΔP|- PSOFC

No

PSOFC = FCnominal

Yes

Fig. 16.2 Solving algorithm for providing the detached house with electricity

16 Thermodynamic and Cost Analyses of a Residential Hybrid PV–Fuel Cell–Battery System for a Canadian House 183

Water Electrolyser

For surplus electricity from the PV system, Pin,el, the energy efficiency relation of the electrolyser is used to calculate the

produced hydrogen flow rate:

ηel ¼_mH2

LHVH2

Pin, elð16:4Þ

Solid Oxide Fuel Cell

The Butler–Volmer equation is used to relate the current and voltage output of the solid oxide fuel cell. Relevant voltage drops

due to ohmic, activation, and concentration losses are considered in the calculation of SOFC electric power output according

to Colpan et al. [12] and Motahar and Alemrajabi [13]. The energy and exergy efficiencies for the fuel cell system are

ηSOFC ¼_W net�SOFC

_mH2,SOFC LHVH2þ _QH2�preheat

ð16:5Þ

ψSOFC ¼_Wnet�SOFC

_mH2,SOFC exH2þ _ExH2�preheat

ð16:6Þ

The purpose of the hybrid system is to provide a detached house with zero-emission electricity. The system also provides

a part of the heating/cooling demand. This is performed through heat recovery from the fuel cell stack gases.

Heat Recovery Steam Generator

The HRSG is treated as a heat exchanger. Subcooled water enters the economizer section and receives heat from the gases

leaving the HRSG. After it heats up to the saturation temperature at the boiler pressure, water vapor is formed inside the

pipes. The saturated steam generated in the HRSG leaves the unit for hot water production or cooling purposes.

Hybrid PV–Fuel Cell–Battery System

The overall efficiencies of the hybrid system consider all the useful outputs and the inputs to the system. The electric power

demand of the house and the heat recovered from the fuel cell exhaust gases are considered as outputs. The inlets to the

overall hybrid PV–Fuel Cell–Battery system are solar irradiance and the heat required to preheat the fuel feed to the SOFC.

Both enenrgy and exergy efficiencies of the overall system are then defined as follows:

ηtotal ¼Pdemand þ _mH2

LHVþ _Qs,HRSG

_Ensolar þ _QH2�preheat

ð16:7Þ

ψtotal ¼Pdemand þ _mH2

exH2þ _Exs,HRSG

_Exsolar þ _ExH2�preheat

ð16:8Þ

Assumption and Data

The thermodynamic and cost analyses are based on the following assumptions and data:

• The average daily demand is used of a 140 m2 detached house (22.2 kWh/day).

• The solar irradiance is based on a monthly average in Toronto in 2011. The calculations are for each month, separately.

• The Proton Exchange Membrane (PEM) electrolyser is selected to operate at 30 bar and 65 % efficiency.

• The hydrogen generated by the electrolyser process is stored at 25 bar on a seasonal storage basis. The size of the storage

tank is determined based on the seasonal need for hydrogen.

184 M. Hosseini et al.

• The fuel cell is an atmospheric SOFC.

• The fuel cell nominal power is 1 kW (after accounting for 4 % internal consumption). The size of the fuel cell determines

the size of the PV array, the hydrogen storage tank, and the battery.

• The annual amount of the stored hydrogen must be positive; therefore, a PV panel with 86 modules is selected.

The nominal power output of each module is 210 W [at standard test conditions (STC)].

Figure 16.3 shows the daily electricity demand of the house. These sets of data are used in the previous work of the

authors [4] for comparison of the performance of the system in summer and winter of 2011. Here, the data, which are

adopted from the study for International Energy Agency [14], are used to perform the thermodynamic analysis and cost

evaluation of the system for each month of operation.

The University of Toronto publishes solar irradiance data in Toronto over the past 6 years. Here, the 2011 solar irradiance

presented in Fig. 16.4 is used [15]. Although the average monthly solar radiation on 24 h basis is used in the analyses,

Fig. 16.3 Hourly electric power

demand of the detached house

broken down by hour of the

day [14]

Fig. 16.4 Average daily solar

irradiance over each month

of 2011 (adapted from [15])

16 Thermodynamic and Cost Analyses of a Residential Hybrid PV–Fuel Cell–Battery System for a Canadian House 185

Fig. 16.5 is presented to illustrate the significant difference between the summer and winter solar availability.

The performance of the PV modules, and as a result the hybrid system components, are strongly dependent on the solar

irradiance, as discussed further in section “Results and Discussion”. The cost model considers only the purchase, installation

labor, and operation and maintenance of the system components. The details are provided in Table 16.1.

Results and Discussion

The load profile depends on the instantaneous demand, which requires precise measurement of electricity consumption.

However, the thermodynamic analyses can be performed based on average values to determine the initial sizes of the system

components, the pattern of energy flow in the electricity generation system, and the sources of losses. The results can also

help developing a control strategy and dynamic model for further investigations.

Fig. 16.5 Electric power output

of the PV–fuel cell system

component on a daily basis

as a monthly average

Table 16.1 Equipment purchase and operation and maintenance costs

System and component Nominal size Unit cost Cost

PV system [16]PV system 18.06 kW 5,156 $/kW US$ 93,113.66O&M [17] 47 $/kW/year US$/year 848.82

Fuel cell system [18]SOFC, balance of plant (BOP) 1 kW 2,296.73 $/kW US$ 2,296.73O&M 5 % of purchase US$/year 114.84Stored hydrogen 117.29 kg (3,909.28 kWh)Hydrogen storage tank 58.12 m3 at 25 bar, 300 K 4 $/kWh US$ 15,636.73O&M 3 % of purchase US$/year 469.10

ElectrolyserPEM electrolyser, BOP, installation 14.45 kW 586.5 $/kW US$ 8,474.93O&M 5 % of purchase US$/year 423.75Battery, BOP, installation 5 kWh 185 $/kWh US$ 937.50O&M 3 % of purchase US$/year 28.12

Total hybrid system capital cost US$ 120,459.55

Operation and maintenance US$/year 1,888.63

Total O&M cost over the system lifetime (25 years) US$ 47,115.75

Total estimated system cost over 25 years US$ 167,575.30

186 M. Hosseini et al.

In this study, the hourly solar irradiance and load demand are considered in the analyses. The data for solar irradiance are

derived from the average values over each month of the year 2011. However, the presented results only show the total daily

generation/consumption of each system component. The system is considered to perform the same throughout the month.

The electric power supply by each component of the hybrid PV–fuel cell–battery system (in kWh per day) is presented in

Fig. 16.5. The results are reported for each month, considering average values of solar irradiance in each month. Figure 16.5

presents the daily share of power supply of the PV modules, fuel cell, and batteries in each month. With the increase in solar

irradiance in the summer months (Fig. 16.4), the PV electric power output increases significantly. Therefore, most of the

electricity demand is directly met by the PV output, and the fuel cell has its minimum share in supplying the demand.

To quantify this significant difference, the power penetrations of the PV system and the fuel cell–battery are shown in

Fig. 16.6. Due to less solar irradiance in Fall-Winter months, the fuel cell–battery penetration in demand is as high as 80 %

in January and December. The supply share of the fuel cell–battery of the demand decreases with the rise in solar availability

in summer months.

The surplus electricity generated by the PV modules is directed to the electrolyser. The daily hydrogen production rate is

shown in Fig. 16.7, with July having the maximum production rate as 2.33 kg/day. The fuel cell hydrogen consumption is

related to its power output rate; therefore, more hydrogen is consumed by the SOFC during winter days. The difference

between the electrolyser hydrogen production rate and the SOFC fuel consumption rate is taken as the amount of the

hydrogen which needs to be stored in or provided by the hydrogen storage tank. The positive values for hydrogen storage in

Fig. 16.5 illustrate more production than what is consumed by the fuel cell. The negative values mean that the electrolyser

is not capable of producing enough hydrogen for the SOFC, and hydrogen is supplied by the storage tank. The hydrogen

storage tank must be large enough to cover the total consumption during the months with more consumption than

production.

The annual exergy destructions in the hybrid PV–fuel cell–battery system are given in Table 16.2, which shows that the

PVmodules are the main source of exergy destruction in the system. Improving the efficiency of the PV cells leads to a lower

exergy destruction. Exergy destruction in the fuel cell is caused by several phenomena, e.g., electrochemical reactions and

high temperature preheating of the air and hydrogen flows.

The efficiencies of the system components change when their operating conditions deviate from the nominal conditions.

The variations of the efficiencies of the PV and fuel cell systems are presented in Fig. 16.8. In summer days, the average

daily solar irradiance is closer to the standard test condition of the photovoltaic cells. However, the fuel cell appears to work

at its nominal power rate throughout the year. Higher values are obtained for exergy efficiency because solar exergy, the

input to the PV module, is less than solar energy. In the case of the fuel cell, the exergy of the required heat for hydrogen

preheating is less than its energy content, which results in higher efficiencies based on exergy rather than energy.

Fig. 16.6 PV and SOFC–battery

power penetration

16 Thermodynamic and Cost Analyses of a Residential Hybrid PV–Fuel Cell–Battery System for a Canadian House 187

Table 16.2 Total yearly exergy destruction in the major hybrid system components

Component PV Electrolyser SOFC HRSG

Exergy destruction, kWh/year 81,974.77 4,734.40 5,249.03 510.18

Fig. 16.8 Energy and exergy

efficiencies of the PV and SOFC

systems

Fig. 16.7 Monthly hydrogen

storage/consumption

188 M. Hosseini et al.

However, interesting results are obtained for the overall efficiencies of the hybrid PV–fuel cell–battery system.

According to Fig. 16.9, the efficiencies differ significantly with month. Higher values are reported for Fall-Winter months

in which the fuel cell–battery penetration is a maximum, and lower values are reported for Spring-Summer months in which

the PV modules provide a greater portion of the demand. The difference in the efficiencies of PV and fuel cell systems is the

cause of such results.

The unit cost of electricity is a function of the total estimated cost and the total electricity production over 25 years of

operation. The total annual electricity production is the sum of the daily production over 365 days of the year. Therefore, the

electricity unit cost (EUC) is 0.83 US$/kW. However, another analysis is made to estimate the cost of electricity in each year

of operation of the system. If the capital costs are assumed to be paid off in 10 years, considering the inflation rate (3 %), the

electricity unit cost will follow the trend shown in Fig. 16.10. A significant drop is observed for the 11th year of operation,

since the only costs of the system are associated with operation and maintenance costs.

Fig. 16.9 Energy and exergy

efficiencies of the hybrid PV–fuel

cell–battery system

Fig. 16.10 Annual electricity

unit cost during the hybrid system

lifetime

16 Thermodynamic and Cost Analyses of a Residential Hybrid PV–Fuel Cell–Battery System for a Canadian House 189

Conclusions

Several conclusions can be drawn from the thermodynamic and cost analyses reported here of a hybrid PV–fuel cell–battery

system as applied to a Canadian house. The nominal maximum power output of the PV modules is 18.06 kW, which is five

times higher than the demand maximum power. The photovoltaic system is sized to meet the demand either directly or

by storage of hydrogen generated in the electrolyser. Due to less solar irradiance in Fall-Winter months, the fuel cell–battery

penetration in supplying of the demand is as high as 80 % in January and December. The supply share of the fuel

cell–battery in meeting the demand decreases with the rise in solar availability in Summer months. The maximum H2

production rate is in July (2.3 kg/day), and the hydrogen consumption is maximum in January (0.99 kg/day).The efficiencies

differ significantly with the time of the year. Higher values are observed for fall-winter months in which the fuel cell–battery

penetration is a maximum, and lower values are observed for Spring-Summer months in which the PV module provides a

greater portion of the demand. The electricity unit cost is 0.83 $/kWh based on a 25-year economic evaluation period of the

hybrid PV–fuel cell–battery system.

Acknowledgment The authors acknowledge the support provided by the Natural Sciences and Engineering Research Council of Canada.

Nomenclature

ex Specific exergy, kJ/kg

En:

Energy flow rate, kW

Ex:

Exergy flow rate, kW

G Solar irradiance, W/m2

IL PV light current, A

I0 Reverse saturation current, A

I PV electric current, A

k Boltzmann constant

kt Manufacturer supplied temperature

coefficient of short-circuit current, A/�C

LHV Lower heating value, kJ/kg

_m Mass flow rate, kg/s

P Power, kW_Q Heat transfer rate, kW

Rs Series resistance of the PV cells, Ohm

T Temperature, K

V Voltage, V_W Work rate, kW

Greek Letters

γ PV cell shape factor

η Energy efficiency, %

ψ Exergy efficiency, %

Subscripts

0 Ambient condition

cell PV cells

H2 Hydrogen

in, el Input to the electrolyser

mp Maximum power

SOFC Solid oxide fuel cell

Acronyms

CHP Combined heat and power

PV Photovoltaic

SOFC Solid oxide fuel cell

STC Standard test condition

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