By Christopher D. Rahn
Chapter 1 advent (pages 1–10):
Chapter 2 Electrochemistry (pages 11–22):
Chapter three Governing Equations (pages 23–48):
Chapter four Discretization equipment (pages 49–87):
Chapter five method reaction (pages 89–118):
Chapter 6 Battery process versions (pages 119–160):
Chapter 7 Estimation (pages 161–189):
Chapter eight Battery administration platforms (pages 191–229):
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Additional info for Battery Systems Engineering
One can also think of σ eff as the conductivity that one would measure across the electrode if the electrolyte were removed. The boundary conditions on the solid-phase electrode are related to the ﬂux of charge in and out of the electrode. 31) where I (t) (A) is the current and A (cm2 ) is the electrode plate area. At an electrically insulated boundary, no current ﬂows, so ∂φs = 0. 32) Positive current ﬂows from high potential to low potential. 4 shows the relationships between current and the gradient of solid-phase potential for current collectors on the left and right side of a porous electrode with the x-axis going from left to right.
In general, batteries have longer life for lower DOD cycles. Li-ion cells have the longest cycle life. At 100% DOD they typically last 3000 cycles at low discharge/charge rates and room temperature. At 20–40% DOD they can last up to 20 000 cycles. 2C charge/discharge and room temperature. For Pb–acid batteries, 200 cycles are typical at 100% DOD. Up to 1500 cycles can be attained at 25% DOD. The end of life is characterized by a drop in capacity to 50–80% of the initial capacity, depending on the chemistry and application.
21) x=0 =− x=δp ce (δp ) . 22) at the interface between the positive electrode and separator results from assuming a linear concentration distribution within the separator and zero concentration at the midpoint of the separator. 2. 23) where the concentration c(x, t) and potential φe (x, t) have zero ﬂux boundary conditions at the ends of the cell x = 0, L. Calculate the overall cell conservation of charge by calculating javg = 1 L L j(x, t) dx. 64) at T = Tref . 24) 4 Discretization Methods The governing PDEs derived in Chapter 3 constitute the building blocks of battery models.