BATTERIES AND FUEL CELLSContents Efficiency Lifetime Power Techno-Economic Assessments Efficiency H Wenzl,Clausthal University of Technology, Clausthal-Zellerfeld, Germany & 2009 Elsevie
Trang 1BATTERIES AND FUEL CELLS
Contents
Efficiency
Lifetime
Power
Techno-Economic Assessments
Efficiency
H Wenzl,Clausthal University of Technology, Clausthal-Zellerfeld, Germany
& 2009 Elsevier B.V All rights reserved.
Definitions and Terms
The electrical efficiency Z of a galvanic cell or
super-capacitor is defined as the ratio of the electrical energy
that can be removed from it to the electrical energy
supplied Often the electrical efficiency of a galvanic cell
or supercapacitor is also called energy efficiency as heat
generation is never a useful by-product of the operation
of galvanic cells or supercapacitors:
Zel¼Electrical energy removed during discharge
Electrical energy required during charging 100%
This definition may readily be extended to fuel cells
provided that the ‘electrical energy supplied’ refers to the
enthalpy DH of the fuel It is possible to define the
the-oretical electrical efficiency of a fuel cell
thermo-dynamically This is given by the formula
Z¼DG
DH ¼ 12
T DS DH
where DH is the enthalpy, DG the Gibbs free energy, and
DS the entropy change of the reaction For secondary or
rechargeable electrochemical power sources, this
defin-ition is not useful as it does not take the energy losses
during charging into account Obviously, the theoretical
electrical efficiency cannot be obtained in real systems
and the reasons for this are given below
Heat is often a useful by-product of operation of fuel
cells, and therefore the term thermal efficiency is also
important In analogy to the electrical efficiency defined
above, the thermal efficiency is
Zth¼Thermal energy supplied
Energy content of fuel 100%
The thermal efficiency may differ significantly from the
electrical efficiency In fuel cells used for combined heat
and power (CHP) applications, the ratio of electrical and thermal efficiency is an important design parameter for CHP plants The total efficiency of a fuel cell or any other power generator for supplying heat and electricity
to loads is
Ztotal¼Electrical energy suppliedþ thermal energy supplied
Energy content of fuel
100%
The total efficiency of a fuel cell used for CHP appli-cations, sometimes also called fuel utilization or fuel ef-ficiency, can be as high asB85%
Also note that the concept ‘efficiency’ is not generally used for primary batteries
The electrical efficiency of batteries and super-capacitors is determined by the voltage efficiency and the coulombic efficiency:
Zel¼ Zvoltage Zcoulombic
The voltage efficiency is the ratio between voltage during discharging to voltage during charging:
Zvoltage¼Average voltage during discharging
Average voltage during charging 100%
As the voltage changes during discharging and charging, average values for the period under consideration are used and only constant current (CC) phases can be in-cluded The voltage efficiency is important for batteries with coulombic efficiency near 1, such as lithium bat-teries, because it determines their electrical efficiency The coulombic efficiency is used for batteries and supercapacitors and refers to the ratio between the amount of charge that can be removed during discharge,
to the amount of charge that has been supplied during charge Alternatively, the charge factor (¼ (coulombic
544