BATTERIES AND FUEL CELLS pps

BATTERIES 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: Z el ¼ Electrical 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 Z ¼ DG 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 Z th ¼ Thermal 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 Z total ¼ Electrical energy supplied þ 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 as B85%. 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: Z el ¼ Z voltage  Z coulombic The voltage efficiency is the ratio between voltage during discharging to voltage during charging: Z voltage ¼ Average 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. Alter natively, the charge factor ( ¼ (coulombic 544 . 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 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. BATTERIES AND FUEL CELLS Contents Efficiency Lifetime Power Techno-Economic Assessments Efficiency H Wenzl,