By Christopher D. Rahn
Chapter 1 creation (pages 1–10):
Chapter 2 Electrochemistry (pages 11–22):
Chapter three Governing Equations (pages 23–48):
Chapter four Discretization tools (pages 49–87):
Chapter five procedure reaction (pages 89–118):
Chapter 6 Battery approach versions (pages 119–160):
Chapter 7 Estimation (pages 161–189):
Chapter eight Battery administration structures (pages 191–229):
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Additional info for Battery Systems Engineering
2) where Y(s) and U(s) are the Laplace transforms of y(t) and u(t), respectively, and G(s) ∈ R P×M is the transfer function matrix. In this chapter we will study analytical and numerical methods for discretizing the governing equations of battery models. Analytical methods are typically restricted to linear problems with constant coefﬁcients or just a few coupled domains with constant coefﬁcients. In some special cases, solutions can be found for systems with spatially varying coefﬁcients or simple nonlinearities.
40) where c(x, t) is the concentration of lithium ions. 41) where c(x, t) is the concentration of hydroxide ions. Binary Electrolyte For a binary electrolyte, two ions of charge z + and z − with stoichiometries s+ and s− produce n electrons that ﬂow through the solid phase to the current collector. 2)) requires s+ z + + s− z − = −n. 42) For Pb–acid cells, we have different reactions in the positive and negative electrodes. 43) so s− = 1, z − = −1, s+ = −1, z + = 1, and n = 2. In the positive (PbO2 ) electrode, + − PbO2 + HSO− 4 + 3H + 2e PbSO4 + 2H2 O.
Irreversible heat (watts) from the electrochemical reaction qi , ohmic (Joule) heating qj , reversible entropic heat qr , and contact resistance qc drive the cell temperature. Volume-speciﬁc reaction heat generated in a ﬁnite control volume is equal to reaction current j(x, t) times overpotential η(x, t). The total reaction and Joule heat, qi + qj , is calculated by integrating the local volume-speciﬁc reaction heat across the one-dimensional cell domain and multiplying by plate area A or L qi + qj = A j (φs − φe − U ) dx.